Atoms, Molecules And Moles2

Foundations to Chemistry - adapted from "Chemistry, Matter and the Universe"

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Questions 6. Which is more important in determining the chemical behavior of an atom, the number of neutrons or the number of protons? Why? 7. What holds two hydrogen atoms together in a molecule? Why do two helium atoms not form a stable molecule? 8. Why do two hydrogen atoms become more stable if they are brought together, but then become less stable again if they are brought too close? 9. How is the molecular weight of a molecule related to the atomic weights of the atoms from which it is made? 10. What is a mole of a chemical substance? How is the mole concept useful in chemistry? 11. How many molecules are present in one mole of water vapor? Of liquid water? Of ethyl alcohol? 12. What is the molecular explanation for the phenomenon of pressure?

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Questions

1. A common model-building kit has a scale of 2 cm to the angstrom unit. What magnification factor would this be over the actual atomic sizes? Roughly how big would atoms be in these models? If nuclei were shown, how big would they be on the same scale? 2. Which are heavier, neutrons or electrons? Which are more highly charged? What counterbalances the charge on the protons in a neutral atom? Where is the proton charge located in the atom, and where is the counterbalancing charge? 3. What is the difference between the nuclei of hydrogen and helium atoms? How does this affect the number of electrons in each atom? 4. What is the difference between the various kinds of hydrogen atoms? What are such variations in the same type of atom called? 5. If you know that an atom is a carbon atom, what can you tell about the number of electrons, neutrons, and protons? What new information do you have if you know that it is carbon-13?

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A Chemical World in Miniature: A Summary In practice, before this point is reached, van der Waals attractions and molecular volumes become too important to be ignored, and gases deviate from ideal behavior. The most striking deviation occurs when slowly moving molecules "stick" to one another, and a gas condenses into a liquid. At still lower temperatures, the liquid freezes into a crystalline solid. The boiling point of a liquid is a useful measure of the strength of van der Waals forces between molecules, because the smaller the molecules and the weaker these forces are, the lower the temperature can be before the gas molecules stick together and condense as a liquid. Of the two elements in our simple universe, molecules must be cooled to -253 , or 20K, before they condense. This is the boiling point of liquid hydrogen at a pressure of 1 atm. The single atoms of helium gas are smaller, with less surface area. They must be cooled to 4K before their attractive forces cause them to condense. Hydrogen and helium illustrate many chemical properties, but by themselves they are a dead end. They are not capable of the great variation seen in the chemistry of the heavier elements. If stellar syntheses had gone no farther than hydrogen fusion, the universe would have been stillborn. To continue, we must turn to the elements heavier than helium, and this is the subject of the next chapters.

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Foundations to Chemistry - adapted from "Chemistry, Matter and the Universe"

2. Atoms, Molecules and Moles

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A Chemical World in Miniature: A Summary In practice, before this point is reached, van der Waals attractions and molecular volumes become too important to be ignored, and gases deviate from ideal behavior. The most striking deviation occurs when slowly moving molecules "stick" to one another, and a gas condenses into a liquid. At still lower temperatures, the liquid freezes into a crystalline solid. The boiling point of a liquid is a useful measure of the strength of van der Waals forces between molecules, because the smaller the molecules and the weaker these forces are, the lower the temperature can be before the gas molecules stick together and condense as a liquid. Of the two elements in our simple universe, molecules must be cooled to -253 , or 20K, before they condense. This is the boiling point of liquid hydrogen at a pressure of 1 atm. The single atoms of helium gas are smaller, with less surface area. They must be cooled to 4K before their attractive forces cause them to condense. Hydrogen and helium illustrate many chemical properties, but by themselves they are a dead end. They are not capable of the great variation seen in the chemistry of the heavier elements. If stellar syntheses had gone no farther than hydrogen fusion, the universe would have been stillborn. To continue, we must turn to the elements heavier than helium, and this is the subject of the next chapters.

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Foundations to Chemistry - adapted from "Chemistry, Matter and the Universe"

2. Atoms, Molecules and Moles

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A Chemical World in Miniature: A Summary In practice, before this point is reached, van der Waals attractions and molecular volumes become too important to be ignored, and gases deviate from ideal behavior. The most striking deviation occurs when slowly moving molecules "stick" to one another, and a gas condenses into a liquid. At still lower temperatures, the liquid freezes into a crystalline solid. The boiling point of a liquid is a useful measure of the strength of van der Waals forces between molecules, because the smaller the molecules and the weaker these forces are, the lower the temperature can be before the gas molecules stick together and condense as a liquid. Of the two elements in our simple universe, molecules must be cooled to -253 , or 20K, before they condense. This is the boiling point of liquid hydrogen at a pressure of 1 atm. The single atoms of helium gas are smaller, with less surface area. They must be cooled to 4K before their attractive forces cause them to condense. Hydrogen and helium illustrate many chemical properties, but by themselves they are a dead end. They are not capable of the great variation seen in the chemistry of the heavier elements. If stellar syntheses had gone no farther than hydrogen fusion, the universe would have been stillborn. To continue, we must turn to the elements heavier than helium, and this is the subject of the next chapters.

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Foundations to Chemistry - adapted from "Chemistry, Matter and the Universe"

2. Atoms, Molecules and Moles

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A Chemical World in Miniature: A Summary In practice, before this point is reached, van der Waals attractions and molecular volumes become too important to be ignored, and gases deviate from ideal behavior. The most striking deviation occurs when slowly moving molecules "stick" to one another, and a gas condenses into a liquid. At still lower temperatures, the liquid freezes into a crystalline solid. The boiling point of a liquid is a useful measure of the strength of van der Waals forces between molecules, because the smaller the molecules and the weaker these forces are, the lower the temperature can be before the gas molecules stick together and condense as a liquid. Of the two elements in our simple universe, molecules must be cooled to -253 , or 20K, before they condense. This is the boiling point of liquid hydrogen at a pressure of 1 atm. The single atoms of helium gas are smaller, with less surface area. They must be cooled to 4K before their attractive forces cause them to condense. Hydrogen and helium illustrate many chemical properties, but by themselves they are a dead end. They are not capable of the great variation seen in the chemistry of the heavier elements. If stellar syntheses had gone no farther than hydrogen fusion, the universe would have been stillborn. To continue, we must turn to the elements heavier than helium, and this is the subject of the next chapters.

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A Chemical World in Miniature: A Summary All atoms and molecules have a very weak, short-range attraction for one another known as van der Waals attraction. They also have finite though tiny molecular volumes. At ordinary temperatures, where the molecules of a gas are moving rapidly, and at moderate pressures, where on the average they are far apart, both van der Waals attractions and molecular volumes can be neglected, and molecules can be treated as freely moving, nonattracting point particles. Under these conditions the behavior of all gases is described by the ideal gas law, PV = nRT, in which T is the absolute temperature, obtained by adding 273.15 to the centigrade temperature. The speed with which molecules move in a gas depends on its temperature; and in principle, if ideal gas behavior were followed all the way to absolute zero, all molecular motion would stop at that point and both pressure and volume would fall to zero.

Right: Johannes Diderik van der Waals (1837 - 1923)

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A Chemical World in Miniature: A Summary Electrons in atoms surround the nucleus in a series of shells, with similar energies within one shell and different energies from one shell to the next. The innermost shell can hold two electrons and the next, eight. A completely filled shell is a particularly stable arrangement for an atom. Helium atoms will not combine with one another, for each already has the two electrons necessary to fill its inner electron shell. Hydrogen atoms lack one electron of having a completely filled shell, and two H atoms can share a pair of electrons to form an molecule. In this way each of the atoms in the molecule has two electrons in its immediate vicinity, and thereby attains a fullshell structure. The bond in the H-H molecule can be thought of as the prototype of the electron-pair or covalent bond in larger molecules. An amount of any compound in grams, numerically equal to its atomic or molecular weight in amu, is one mole of that substance. The mole concept allows one to measure equal numbers of atoms or molecules of various material, even without a knowledge of how many molecules there are. The actual number of molecules in one mole, Avogadro's number, has been measured as N = 6.022 X 10 . From the way in which the mole is defined, this value is also the conversion factor between amu and grams as units of mass: 1 g = 6.022 X 10 amu. One mole of molecules weighs 2.016 grams, and one mole of He atoms, 4.003 g.

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A Chemical World in Miniature: A Summary We began these first two chapters with the statement that ours was a universe mainly of hydrogen and helium, which at the same time are the simplest and the oldest two elements. These two elements illustrate in miniature most of the chemical principles that we will encounter with the heavier elements. The other elements, like hydrogen and helium, are built from positively charged nuclei containing protons and neutrons, surrounded by enough negatively charged electrons to neutralize the positive charge of the protons. The number of protons, or the atomic number, determines the chemical behavior of an atom because it determines the number of electrons that surround a neutral atom; and the gain, loss, and sharing of electrons is responsible for an atom's chemical properties. The number of neutrons usually is equal to or slightly greater than the number of protons. Neutrons have little effect on chemical properties of an atom, except for those that are influenced by mass. Atoms with the same atomic number but different numbers of neutrons are called isotopes. The total number of neutrons and protons in the nucleus is the mass number of the atom, and the actual mass in amu is the atomic weight relative to that of carbon-12 as exactly 12 amu. Observed atomic weights usually are averages of the weights of several naturally occurring isotopes.

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The Ideal Gas Law The ideal gas law describes the behavior of a fictional gas. Real gases act at room temperature as if they would shrink to nothing at absolute zero, when in fact they condense first. Before reaching absolute zero, all real gases liquefy or solidify, behavior for which the ideal gas law cannot account. No gas obeys the conditions PV = nRT perfectly, but all gases come close at room temperatures and low pressures. This is the reason that we can apply the gas law to any gas, including an atmospheric mixture of and , without worrying about the composition of the mixture. One molecule is the same as any other in an ideal gas.

This is close to being true at room temperature and 1 atm pressure. At lower temperatures and slower speeds, the attractive forces between molecules no longer can be ignored. At higher pressures, at which molecules are closer together, the volume occupied by the molecules themselves becomes an appreciable part of the volume filled by the gas. The ideal gas law begins to fail badly. Nevertheless, under ordinary conditions the expression PV=nRT is a surprisingly good description of real gas behavior.

The ideal gas law assumes that attractions between molecules are negligible when compared with their energies of motion, and that the actual volumes of gas molecules are negligible in comparison with the total volume occupied by the gas.

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The Ideal Gas Law

At the beginning of the section on gas laws, we said that all gases have the same volume per mole at constant pressure and temperature. We now can calculate what this molar volume is. Scientists refer to 1 atm pressure and 0 (273.15K) as "standard temperature and pressure," or STP. At STP, the volume per mole of a gas is

A 22.4-liter sphere has a diameter of 35 cm, and this was the calculation that produced the figure quoted previously in this chapter. One mole of any gas at STP fills a flask fourteen inches in diameter (right).

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The Ideal Gas Law Example. An eight-foot diameter weather balloon is filled with 7600 liters of gas at 1 atm. pressure and 25 . As the balloon rises to an altitude where the pressure is only 0.70 atm, the temperature drops to -20 . What then is the volume of the balloon? Solution. Let sea-level conditions be denoted by subscript 1, and high altitude conditions, by 2. The number of moles of gas does not change, so we can use the ideal gas law in the form

or

The decrease in pressure to 0.70 atm causes an increase in volume by a factor of 1.00/0.70, but the simultaneous drop in temperature causes a shrinkage by a factor of 253/298. The balloon does not expand as much as it would have if the temperature had remained constant.

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The Ideal Gas Law Example. An eight-foot diameter weather balloon is filled with 7600 liters of at 1atm pressure and 25 . How many moles of hydrogen gas are present? Solution. P = 1 atm, V = 7600 liters, T = 25

The average molecular weight of the air mixture then is 80 % x 28.013 g =28.81 g

+ 20 % x 32.000 g

= 298K. The weight of air displaced is 311 moles x 28.81 g

As an interesting sidelight, we can calculate the lifting power of the balloon. gas weigh 311 moles X 2.016 g Solution. The 311 moles of = 627 g. The lifting power of the balloon is the difference between this and the weight of the air that the balloon displaces. The same volume of air also would contain 311 moles (Avogadro's principle), and air can be considered a mixture of 80% nitrogen gas and 20% oxygen gas.

= 8960 g

The buoyancy of the balloon is the difference in weight of air and hydrogen: 8960 g - 627 g = 8333 g The balloon therefore can lift slightly more than 8 kilograms, or 18 pounds, of payload. We now can take into account the simultaneous change of pressure and temperature, and correct the flaw in the weather balloon example first used to illustrate Boyle's law.

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The Ideal Gas Law

Boyle's law describes the relationship between pressure and volume when temperature is fixed; Charles' law relates volume and temperature when the pressure is constant. We can combine these two laws into the ideal gas law-ideal because it is obeyed strictly by no real gases, but is followed more and more closely as the pressure decreases and temperature increases. For n moles of an ideal gas PV = nRT The gas constant, R, is a fixed quantity, independent of pressure,

volume, temperature, or amount of gas. If pressure is measured in atmospheres, volume in liters, and temperature in degrees Kelvin, then R has the numerical value R = 0.0821 liter deg The ideal gas law is much more powerful than either Boyle's or Charles' laws alone. We now can calculate how many moles of hydrogen gas there were in the weather-balloon example, assuming a temperature of 25 .

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The Ideal Gas Law

Boyle's law describes the relationship between pressure and volume when temperature is fixed; Charles' law relates volume and temperature when the pressure is constant. We can combine these two laws into the ideal gas law-ideal because it is obeyed strictly by no real gases, but is followed more and more closely as the pressure decreases and temperature increases. For n moles of an ideal gas PV = nRT The gas constant, R, is a fixed quantity, independent of pressure,

volume, temperature, or amount of gas. If pressure is measured in atmospheres, volume in liters, and temperature in degrees Kelvin, then R has the numerical value R = 0.0821 liter deg The ideal gas law is much more powerful than either Boyle's or Charles' laws alone. We now can calculate how many moles of hydrogen gas there were in the weather-balloon example, assuming a temperature of 25 .

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Gas Molecules And Absolute Zero Example. A hot-air balloon heated by a propane burner has a volume of 500,000 liters when the air inside is heated to 75 . What will the volume be after the air has cooled to 25 , if the pressure remains constant? Solution. The first step is to convert temperature from centigrade to absolute: T = 75 T = 25

+ 273 + 273

= 348K = 298K

Then we can use Charles' law:

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Gas Molecules And Absolute Zero The work of Charles tells us that the volume of a gas at constant pressure is directly proportional to its absolute temperature, T (not to its centigrade temperature): V = k' T Here k' is a constant that relates V and T, and is the slope of the lines in the plots at the top of page 36. We also can write Charles' law as

If two sets of experimental conditions at the same pressure are being compared, 1 and 2, then Charles' law can be written as

It is important to remember that this equality holds only at constant pressure.

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Gas Molecules And Absolute Zero Charles' data suggest that, if a gas continued to behave at lower temperatures in the way that it does at room temperature, its volume would shrink to nothing at -273 . This is the point at which, in principle, all molecules would come to rest and gases would cease to exert pressure or occupy volume. This theoretically possible but experimentally unattainable temperature is known as absolute zero. We can define an absolute temperature scale (also known as the Kelvin scale after the British thermodynamicist Lord Kelvin), in which the temperature (T) in degrees absolute or Kelvin (K) is related to the temperature in degrees centigrade (t) by the expression T(K) = t (

) + 273.15

Top Right: Jacques Charles (1746 - 1823) Bottom Right: Lord Kelvin (1824 - 1907)

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Gas Molecules and Absolute Zero

Boyle's experiments all were carried out at constant temperature. A century later, Jacques Charles, in France, studied what happens to the volume of a gas when the temperature is changed and the external pressure is kept constant. This is the problem of heating or cooling a balloon full of air, with a fixed outside pressure exerted by the surroundings. In every gas he studied, Charles observed a steady increase in volume with an increase in temperature.

Translating his data into modern units, he found that for every degree Celsius, or centigrade, rise in temperature, the gas volume increased by 1/273 of its volume at 0 . This is easier to understand from the graph of volume versus temperature shown above. Within the observed range of temperatures, the plot is a straight line. If we extend this straight line back to zero volume, it crosses the temperature axis at -273.15 . (For simplicity in the discussion that follows, we often shall use -273 .)

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Gas Molecules and Absolute Zero

Boyle's experiments all were carried out at constant temperature. A century later, Jacques Charles, in France, studied what happens to the volume of a gas when the temperature is changed and the external pressure is kept constant. This is the problem of heating or cooling a balloon full of air, with a fixed outside pressure exerted by the surroundings. In every gas he studied, Charles observed a steady increase in volume with an increase in temperature.

Translating his data into modern units, he found that for every degree Celsius, or centigrade, rise in temperature, the gas volume increased by 1/273 of its volume at 0 . This is easier to understand from the graph of volume versus temperature shown above. Within the observed range of temperatures, the plot is a straight line. If we extend this straight line back to zero volume, it crosses the temperature axis at -273.15 . (For simplicity in the discussion that follows, we often shall use -273 .)

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Gas Molecules and Absolute Zero

Boyle's experiments all were carried out at constant temperature. A century later, Jacques Charles, in France, studied what happens to the volume of a gas when the temperature is changed and the external pressure is kept constant. This is the problem of heating or cooling a balloon full of air, with a fixed outside pressure exerted by the surroundings. In every gas he studied, Charles observed a steady increase in volume with an increase in temperature.

Translating his data into modern units, he found that for every degree Celsius, or centigrade, rise in temperature, the gas volume increased by 1/273 of its volume at 0 . This is easier to understand from the graph of volume versus temperature shown above. Within the observed range of temperatures, the plot is a straight line. If we extend this straight line back to zero volume, it crosses the temperature axis at -273.15 . (For simplicity in the discussion that follows, we often shall use -273 .)

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Gas Molecules and Absolute Zero

Boyle's experiments all were carried out at constant temperature. A century later, Jacques Charles, in France, studied what happens to the volume of a gas when the temperature is changed and the external pressure is kept constant. This is the problem of heating or cooling a balloon full of air, with a fixed outside pressure exerted by the surroundings. In every gas he studied, Charles observed a steady increase in volume with an increase in temperature.

Translating his data into modern units, he found that for every degree Celsius, or centigrade, rise in temperature, the gas volume increased by 1/273 of its volume at 0 . This is easier to understand from the graph of volume versus temperature shown above. Within the observed range of temperatures, the plot is a straight line. If we extend this straight line back to zero volume, it crosses the temperature axis at -273.15 . (For simplicity in the discussion that follows, we often shall use -273 .)

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Measuring Moles; The Gas Laws The molecular explanation of Boyle's law is simple. The pressure exerted by a gas on the walls of its container arises because the gas molecules strike the walls and rebound (right). How great the pressure is depends on how fast the molecules are moving, and how often they rebound from the container walls. The speed of the molecules depends on the temperature and does not affect Boyle's law, which applies only at a constant temperature. But if we squeeze the gas into half its initial volume, then each cubic centimeter of gas has twice as many molecules (below right). Impacts with the walls occur twice as often, so the pressure is twice as great. Boyle's law is simply a reflection of how often the gas molecules bounce off the walls of the container.

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Measuring Moles; The Gas Laws

Solution 2. Use Boyle's law in the form P V = P V , where conditions (1) are at sea level and (2) are at the higher altitude: (1atm) (7600 liters) = (0.70 atm) V

A drop in pressure to 0.70 atm has permitted the gas in the balloon to expand.

Right: Sir Robert Boyle (1627 - 1691)

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Measuring Moles; The Gas Laws

Example. An eight-foot diameter weather balloon is filled with 7600 liters of hydrogen gas at sea level where the pressure is 1 atm. By the time the balloon has ascended to an altitude at which the pressure is 0.70 atm, what is the volume of the balloon? Solution 1. Use Boyle's law in the form PV = k and evaluate k. At sea level, P = 1 atm, and V = 7600 liters; thus k = PV = (1 atm) (7600 liters) = 7600 liter atm. This constant is equally valid for any other P and V, as long as the temperature is unchanged. (This is a flaw in our example. The temperature actually would change with altitude.) We can then write (0.70 atm) V = 7600 liter atm

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Measuring Moles; The Gas Laws

Example. An eight-foot diameter weather balloon is filled with 7600 liters of hydrogen gas at sea level where the pressure is 1 atm. By the time the balloon has ascended to an altitude at which the pressure is 0.70 atm, what is the volume of the balloon? Solution 1. Use Boyle's law in the form PV = k and evaluate k. At sea level, P = 1 atm, and V = 7600 liters; thus k = PV = (1 atm) (7600 liters) = 7600 liter atm. This constant is equally valid for any other P and V, as long as the temperature is unchanged. (This is a flaw in our example. The temperature actually would change with altitude.) We can then write (0.70 atm) V = 7600 liter atm

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Measuring Moles; The Gas Laws Pressure is usually measured in atmospheres or millimeters of mercury; 1 atm = 760 mm of Hg. As you can see on the previous page, throughout the experiment the volume is inversely proportional to pressure; or to express matters another way, the product of pressure and volume is unchanged. This can be written as PV = k - Boyle's law in which k is a constant that can be evaluated for a particular temperature from one particular set of pressurevolume conditions. In the table at the top of the page, this constant k is equal to 20 liter atmospheres. If we want to compare two sets of experimental conditions at constant temperature, designated by subscripts 1 and 2, then Boyle's law can be written P V =P V Either form of Boyle's law can be used in an actual problem.

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Measuring Moles; The Gas Laws Pressure is usually measured in atmospheres or millimeters of mercury; 1 atm = 760 mm of Hg. As you can see on the previous page, throughout the experiment the volume is inversely proportional to pressure; or to express matters another way, the product of pressure and volume is unchanged. This can be written as PV = k - Boyle's law in which k is a constant that can be evaluated for a particular temperature from one particular set of pressurevolume conditions. In the table at the top of the page, this constant k is equal to 20 liter atmospheres. If we want to compare two sets of experimental conditions at constant temperature, designated by subscripts 1 and 2, then Boyle's law can be written P V =P V Either form of Boyle's law can be used in an actual problem.

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Measuring Moles; The Gas Laws Pressure is usually measured in atmospheres or millimeters of mercury; 1 atm = 760 mm of Hg. As you can see on the previous page, throughout the experiment the volume is inversely proportional to pressure; or to express matters another way, the product of pressure and volume is unchanged. This can be written as PV = k - Boyle's law in which k is a constant that can be evaluated for a particular temperature from one particular set of pressurevolume conditions. In the table at the top of the page, this constant k is equal to 20 liter atmospheres. If we want to compare two sets of experimental conditions at constant temperature, designated by subscripts 1 and 2, then Boyle's law can be written P V =P V Either form of Boyle's law can be used in an actual problem.

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Measuring Moles; The Gas Laws Pressure is usually measured in atmospheres or millimeters of mercury; 1 atm = 760 mm of Hg. As you can see on the previous page, throughout the experiment the volume is inversely proportional to pressure; or to express matters another way, the product of pressure and volume is unchanged. This can be written as PV = k - Boyle's law in which k is a constant that can be evaluated for a particular temperature from one particular set of pressurevolume conditions. In the table at the top of the page, this constant k is equal to 20 liter atmospheres. If we want to compare two sets of experimental conditions at constant temperature, designated by subscripts 1 and 2, then Boyle's law can be written P V =P V Either form of Boyle's law can be used in an actual problem.

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Measuring Moles; The Gas Laws Pressure is usually measured in atmospheres or millimeters of mercury; 1 atm = 760 mm of Hg. As you can see on the previous page, throughout the experiment the volume is inversely proportional to pressure; or to express matters another way, the product of pressure and volume is unchanged. This can be written as PV = k - Boyle's law in which k is a constant that can be evaluated for a particular temperature from one particular set of pressurevolume conditions. In the table at the top of the page, this constant k is equal to 20 liter atmospheres. If we want to compare two sets of experimental conditions at constant temperature, designated by subscripts 1 and 2, then Boyle's law can be written P V =P V Either form of Boyle's law can be used in an actual problem.

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Measuring Moles; The Gas Laws

In 1660, Robert Boyle published a book entitled "New Experiments Physico-Mechanical, Touching [concerning] the Spring of the Air." In it he gave the evidence for what is known today as Boyle's law. Air does have "spring." If you compress it, it pushes back. Poke an airfilled plastic balloon chair with your fingertip, and you will easily make a large dent, which vanishes when you take your finger away. Yet if you sit down on the chair, the air inside pushes back with enough force to hold up your weight. If you compress an enclosed body of gas until it is half its

original volume, and keep the temperature constant, the pressure will be doubled. If you continue to squeeze until the volume is a quarter of the starting volume, the pressure will be four times as great. Conversely, if you release the constraints on a gas and allow it to expand to twice its initial volume, the pressure of the gas will be halved, if the temperature is kept constant. This behavior is illustrated in the table and PV plot above, which describe a hypothetical experiment beginning with 20 liters of a gas at 1 atmosphere pressure.

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Measuring Moles; The Gas Laws

We can do even better than this. Given the pressure and temperature, we can calculate the volume that a mole of gas should occupy, and can find out how the volume changes as a gas is expanded or compressed, and heated or cooled. The relationship between pressure (P), volume (V), temperature (T), and number of moles (n), is given by the ideal gas law, PV = nRT in which R is a constant. But to understand what this gas law means and how to use it, we must back up a step or two.

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Measuring Moles; The Gas Laws

We can do even better than this. Given the pressure and temperature, we can calculate the volume that a mole of gas should occupy, and can find out how the volume changes as a gas is expanded or compressed, and heated or cooled. The relationship between pressure (P), volume (V), temperature (T), and number of moles (n), is given by the ideal gas law, PV = nRT in which R is a constant. But to understand what this gas law means and how to use it, we must back up a step or two.

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Measuring Moles; The Gas Laws If two molecules of hydrogen gas are to react with one molecule of oxygen gas, + then we obtain the correct ratio of reactants by starting with two volumes of hydrogen and one of oxygen (right). Since the reaction produces two molecules of water, we can predict that if the product obtained is water vapor, there will be two volumes of vapor. The reaction by which ammonia, , is prepared from nitrogen and hydrogen gases is + Avogadro's principle tells us that if we want to carry out this reaction without waste, we should begin with three times as much hydrogen as nitrogen by volume at the same pressure and temperature. The product, ammonia, will have twice the volume of the starting , or half the volume of the entire starting gas mixture. For gases, equal volumes at the same temperature and pressure contain equal numbers of moles.

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Measuring Moles; The Gas Laws There is an easier way of measuring moles when one is dealing with gases. To a very good first approximation, the molecules of any gas are independently moving particles, having mass but negligible volume, and with negligible interactions except at the instant of collision. To the extent that this is so, all gas molecules are alike except for mass. At the same pressure and temperature, equal volumes of any gases will contain equal numbers of moles and of molecules. This is known as Avogadro's principle, after the man who first proposed it in 1811. It means that we do not have to weigh gases that are to enter into a reaction, we only have to bring them to a common temperature and pressure and measure volumes.

Right: Apparatus and scientists associated with the chemistry in the following pages; Robert Boyle and Jacques Charles.

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Molecules, Molecular Weight, and Moles

This number can be measured experimentally by several independent methods, using gases, liquids, and crystals, and has been found to have the value N = 602, 209, 430, 000, 000, 000, 000, 000 N = 6.022 x 10 molecules As an illustration of how many molecules there are in one mole, if each molecule were represented by an ordinary glass marble, and these marbles were packed as closely together as possible, one mole of marbles would cover the entire United States with a layer seventy miles deep! All these molecules are contained in only 2.016 grams of hydrogen gas (a balloon 35 cm in diameter), 18.015 grams of water (half of a one ounce shot glass), or a cube of rock salt 3 cm on a side.

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Molecules, Molecular Weight, and Moles

This number can be measured experimentally by several independent methods, using gases, liquids, and crystals, and has been found to have the value N = 602, 209, 430, 000, 000, 000, 000, 000 N = 6.022 x 10 molecules As an illustration of how many molecules there are in one mole, if each molecule were represented by an ordinary glass marble, and these marbles were packed as closely together as possible, one mole of marbles would cover the entire United States with a layer seventy miles deep! All these molecules are contained in only 2.016 grams of hydrogen gas (a balloon 35 cm in diameter), 18.015 grams of water (half of a one ounce shot glass), or a cube of rock salt 3 cm on a side.

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Molecules, Molecular Weight, and Moles

This number can be measured experimentally by several independent methods, using gases, liquids, and crystals, and has been found to have the value N = 602, 209, 430, 000, 000, 000, 000, 000 N = 6.022 x 10 molecules As an illustration of how many molecules there are in one mole, if each molecule were represented by an ordinary glass marble, and these marbles were packed as closely together as possible, one mole of marbles would cover the entire United States with a layer seventy miles deep! All these molecules are contained in only 2.016 grams of hydrogen gas (a balloon 35 cm in diameter), 18.015 grams of water (half of a one ounce shot glass), or a cube of rock salt 3 cm on a side.

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Molecules, Molecular Weight, and Moles

This number can be measured experimentally by several independent methods, using gases, liquids, and crystals, and has been found to have the value N = 602, 209, 430, 000, 000, 000, 000, 000 N = 6.022 x 10 molecules As an illustration of how many molecules there are in one mole, if each molecule were represented by an ordinary glass marble, and these marbles were packed as closely together as possible, one mole of marbles would cover the entire United States with a layer seventy miles deep! All these molecules are contained in only 2.016 grams of hydrogen gas (a balloon 35 cm in diameter), 18.015 grams of water (half of a one ounce shot glass), or a cube of rock salt 3 cm on a side.

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Molecules, Molecular Weight, and Moles

The mole represents a scale-up from atomic mass units to grams. Instead of counting molecules, an impossible task, we can count moles. How many molecules are there in one mole of a substance? We really do not need to know this to use moles in solving chemical problems, any more than the hardware store clerk needed to know how many bolts there were in a pound. But there are situations when this knowledge is useful.

The number of molecules of a substance per Avogadro's number and given the symbol N. (By the way in which a mole was defined as a substance in grams, equal in numerical value weight in amu, Avogadro's number also is the num gram.)

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Molecules, Molecular Weight, and Moles

The mole represents a scale-up from atomic mass units to grams. Instead of counting molecules, an impossible task, we can count moles. How many molecules are there in one mole of a substance? We really do not need to know this to use moles in solving chemical problems, any more than the hardware store clerk needed to know how many bolts there were in a pound. But there are situations when this knowledge is useful.

The number of molecules of a substance per Avogadro's number and given the symbol N. (By the way in which a mole was defined as a substance in grams, equal in numerical value weight in amu, Avogadro's number also is the num gram.)

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Molecules, Molecular Weight, and Moles Most chemical measurements are made in grams. An amount of any substance in grams that is numerically equal to its atomic or molecular weight in amu has been defined as one mole of that substance. By this definition, one mole of hydrogen is 2.016 grams, one mole of methane is 16.043 grams, and one mole of water is 18.015 grams. We can convert any gram quantity of a chemical substance to moles by dividing by its molecular weight. Once we have done this, we know that equal numbers of moles of all kinds of substances must have equal numbers of molecules. The same number of molecules is present in a mole of hydrogen, water, methane, or any other substance. This is very useful, because then we can measure the right amounts of starting material for chemical reactions, and can tell from the results how many molecules of product were formed per molecule of reactants.

Solution. The number of moles of carbon is (100g carbon / 12.011 g

) = 8.33 moles of c

Four times as many hydrogen atoms are needed a to make methane, , so four times as man required also: (4 moles H / 1 mole C) x 8.33 moles C = 33.3 mole Since the atomic weight of hydrogen is 1.008, this 33.3 moles hydrogen x 1.008 g

= 33.6g of

This is the same answer as we obtained previous we used moles instead of merely the ratio of atom

Example. How many moles of carbon are present in the 100 g of the preceding example? How many moles of hydrogen atoms would be needed to combine with these? How many grams of hydrogen would be needed?

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Molecules, Molecular Weight, and Moles Example. A hardware store clerk is told to weigh one pound of machine bolts for a customer, and also to weigh approximately enough hexagonal nuts to go with them. He finds that a hex nut weighs 0.40 as much as a machine bolt of the type requested. How many nuts should he include with the order? Answer. He should include 0.40 X 1 pound = 0.40 pound of hex nuts Such a procedure would be good enough for most real situations, and a lot easier and faster than sitting down and counting individual pieces. This is exactly what the chemist does with molecules. , as he can from Example. A chemist wants to make as much methane, 100 g of carbon. How much hydrogen will be required? Solution. The atomic weight of hydrogen is 1.008 amu, and that of carbon is 12.011 amu. Four hydrogen atoms are required for each carbon atom, so 4x1.008 amu = 4.032 amu of hydrogen will be needed for each 12.011 amu of carbon. The relative weights of hydrogen and carbon will be 4.032 units of hydrogen to 12.011 units of carbon, whatever the weighing units chosen. The problem was expressed in grams. Thus 100g carbon x (4.032g hydrogen / 12.011g carbon) = 33.6g hydrogen will be required. Like the hardware store clerk, the chemist can weigh 100g of carbon and 33.6g of hydrogen and assume that he has the right relative number of atoms without counting them.

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Molecules, Molecular Weight, and Moles Example. A hardware store clerk is told to weigh one pound of machine bolts for a customer, and also to weigh approximately enough hexagonal nuts to go with them. He finds that a hex nut weighs 0.40 as much as a machine bolt of the type requested. How many nuts should he include with the order? Answer. He should include 0.40 X 1 pound = 0.40 pound of hex nuts Such a procedure would be good enough for most real situations, and a lot easier and faster than sitting down and counting individual pieces. This is exactly what the chemist does with molecules. , as he can from Example. A chemist wants to make as much methane, 100 g of carbon. How much hydrogen will be required? Solution. The atomic weight of hydrogen is 1.008 amu, and that of carbon is 12.011 amu. Four hydrogen atoms are required for each carbon atom, so 4x1.008 amu = 4.032 amu of hydrogen will be needed for each 12.011 amu of carbon. The relative weights of hydrogen and carbon will be 4.032 units of hydrogen to 12.011 units of carbon, whatever the weighing units chosen. The problem was expressed in grams. Thus 100g carbon x (4.032g hydrogen / 12.011g carbon) = 33.6g hydrogen will be required. Like the hardware store clerk, the chemist can weigh 100g of carbon and 33.6g of hydrogen and assume that he has the right relative number of atoms without counting them.

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Molecules, Molecular Weight, and Moles Example. A hardware store clerk is told to weigh one pound of machine bolts for a customer, and also to weigh approximately enough hexagonal nuts to go with them. He finds that a hex nut weighs 0.40 as much as a machine bolt of the type requested. How many nuts should he include with the order? Answer. He should include 0.40 X 1 pound = 0.40 pound of hex nuts Such a procedure would be good enough for most real situations, and a lot easier and faster than sitting down and counting individual pieces. This is exactly what the chemist does with molecules. , as he can from Example. A chemist wants to make as much methane, 100 g of carbon. How much hydrogen will be required? Solution. The atomic weight of hydrogen is 1.008 amu, and that of carbon is 12.011 amu. Four hydrogen atoms are required for each carbon atom, so 4x1.008 amu = 4.032 amu of hydrogen will be needed for each 12.011 amu of carbon. The relative weights of hydrogen and carbon will be 4.032 units of hydrogen to 12.011 units of carbon, whatever the weighing units chosen. The problem was expressed in grams. Thus 100g carbon x (4.032g hydrogen / 12.011g carbon) = 33.6g hydrogen will be required. Like the hardware store clerk, the chemist can weigh 100g of carbon and 33.6g of hydrogen and assume that he has the right relative number of atoms without counting them.

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Molecules, Molecular Weight, and Moles Chemists talk about reactions between molecules, yet except for certain extraordinary experimental conditions, no one can see a molecule. There is no easy way to count out equal numbers of various kinds of molecules in preparation for a chemical reaction. There is a simple way, however, to weigh different amounts of various molecules and to be sure that the resulting amounts each contain the same number of molecules. Since the molecular weights of hydrogen gas, methane, and water are 2.016 amu, 16.043 amu, and 18.015 amu, respectively, we can be sure that 2.016 tons of hydrogen gas, 16.043 tons of methane, and 18.015 tons of water each contain the same number of molecules, although we may have no idea what that number is. By the same principle, if we know that walnuts weigh twice as much as peanuts, we can be sure that two pounds of walnuts and one pound of peanuts contain the same number of nuts, without counting them or knowing exactly how many there are. If our only goal is to pair off walnuts with peanuts, or to pair off molecules in chemical reactions, then this limited information is good enough.

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Molecules, Molecular Weight, and Moles

The average atomic weight of the naturally occurring mixture of , is 12.011 amu, so the molecular weight of methane gas, , is

The molecular weight of water,

and

, is

Large biological molecules can have molecular weights of several millions.

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Molecules, Molecular Weight, and Moles

A molecule is a collection of atoms held together by covalent bonds. In our simple universe of hydrogen and helium, the only possible molecule is ; but the one-in-a-thousand heavier atoms are the basis for a vast array of more complex molecules. The champion of molecule-forming atoms is carbon, for reasons that will become clear as we learn more about atomic structure. The chemistry of carbon compounds is so varied that it is given a special name, organic chemistry.

The term "organic" is a reminder that carbon compounds are the basis for the most complex chemical phenomenon of all, life. The molecular weight of any molecule is the sum of the atomic weights of all its atoms. Since the atomic weight of a hydrogen atom is 1.008 amu (relative to carbon-12 as exactly 12 amu), the molecular weight of the H2 molecule is twice this value, or 2.016 amu.

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Molecules, Molecular Weight, and Moles

A molecule is a collection of atoms held together by covalent bonds. In our simple universe of hydrogen and helium, the only possible molecule is ; but the one-in-a-thousand heavier atoms are the basis for a vast array of more complex molecules. The champion of molecule-forming atoms is carbon, for reasons that will become clear as we learn more about atomic structure. The chemistry of carbon compounds is so varied that it is given a special name, organic chemistry.

The term "organic" is a reminder that carbon compounds are the basis for the most complex chemical phenomenon of all, life. The molecular weight of any molecule is the sum of the atomic weights of all its atoms. Since the atomic weight of a hydrogen atom is 1.008 amu (relative to carbon-12 as exactly 12 amu), the molecular weight of the H2 molecule is twice this value, or 2.016 amu.

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Molecules, Molecular Weight, and Moles

A molecule is a collection of atoms held together by covalent bonds. In our simple universe of hydrogen and helium, the only possible molecule is ; but the one-in-a-thousand heavier atoms are the basis for a vast array of more complex molecules. The champion of molecule-forming atoms is carbon, for reasons that will become clear as we learn more about atomic structure. The chemistry of carbon compounds is so varied that it is given a special name, organic chemistry.

The term "organic" is a reminder that carbon compounds are the basis for the most complex chemical phenomenon of all, life. The molecular weight of any molecule is the sum of the atomic weights of all its atoms. Since the atomic weight of a hydrogen atom is 1.008 amu (relative to carbon-12 as exactly 12 amu), the molecular weight of the H2 molecule is twice this value, or 2.016 amu.

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Molecules, Molecular Weight, and Moles

A molecule is a collection of atoms held together by covalent bonds. In our simple universe of hydrogen and helium, the only possible molecule is ; but the one-in-a-thousand heavier atoms are the basis for a vast array of more complex molecules. The champion of molecule-forming atoms is carbon, for reasons that will become clear as we learn more about atomic structure. The chemistry of carbon compounds is so varied that it is given a special name, organic chemistry.

The term "organic" is a reminder that carbon compounds are the basis for the most complex chemical phenomenon of all, life. The molecular weight of any molecule is the sum of the atomic weights of all its atoms. Since the atomic weight of a hydrogen atom is 1.008 amu (relative to carbon-12 as exactly 12 amu), the molecular weight of the H2 molecule is twice this value, or 2.016 amu.

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Electron Shells The innermost shell in any atom can hold a maximum of only two electrons, and the second shell can hold eight. We will defer the reasons for this to Chapter 8, but can use the conclusions now. Each hydrogen atom lacks one electron of having a closed inner shell, so when the two atoms combine to form an molecule, each atom gains an electron and satisfies its deficiency. Helium atoms do not combine because they already have their shells filled with two electrons. If two helium atoms were forced together, they would have four electrons in the vicinity of the nuclei (right). Two would be located between the nuclei and would hold the atoms together as in . The other two would be forced to the outside of the molecule, away from the first two. Not only would these contribute no screening and bonding, they would attract the nuclei and pull them away from one another. With two electrons pulling together and two pulling apart, there would be no net bonding, and the two He atoms would separate. The two electrons that would tend to hold the molecule together are called bonding electrons, and the two that would tend to pull the nuclei apart and rupture the molecule are antibonding electrons.

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Electron Shells We still have not answered the question as to why hydrogen atoms form molecules but helium atoms do not. From what has been said so far, you might expect that helium atoms would share two electron pairs to make two bonds per molecule, or perhaps to make long -He-He-He-He- chains or rings of atoms. Why doesn't this happen? To answer this question we must introduce another idea from quantum mechanics, that of electron shells. Electrons in atoms behave as though they were grouped into levels or shells, with all electrons in one shell having approximately the same energies, but with large energy differences between shells. Each shell can hold only a certain maximum number of electrons. If one shell is filled, then an additional electron will be forced to go into a higher-energy, less-stable shell, and this electron will be lost easily during chemical reactions. Conversely, if an atom lacks only one or two electrons to complete a shell, the atom will have a strong attraction for electrons, and can take them away from the type of atom mentioned previously. A completely filled electron shell, with no vacancies and no extra electrons outside it, is a particularly stable situation for an atom. Not only can atoms gain and lose electrons, they can share them in covalent bonds. When they do, all the shared electrons contribute toward filling vacancies in the outer electron shell of each atom.

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Bonds Between Atoms Energy continues to decrease as the atoms come closer and the screening of nuclear charges by electrons increases. If the process is carried too far, however, the electrons are "squeezed out" from between the nuclei, which have come so close together that the repulsion between their positive charges becomes quite strong. The molecule is made less stable.

G. N. Lewis symbolized an electron-pair bond by electrons. It is more common today to represen single line connecting the bonded atoms, b remember that each such bond consists of a pair o

At some intermediate point, screening by electrons and repulsion of nuclei will balance: The H-H molecule will have the lowest energy and will be most stable. If the nuclei are pushed any closer, nuclear repulsion pushes them back again; if they are pulled apart, electron-pair screening is lost. This lowest-energy separation, , is the bond length of the H-H bond, and the energy required to pull the molecule apart into isolated atoms again, , is the bond dissociation energy or bond energy. The atoms in a molecule oscillate about this minimumenergy position; thus is the average bond length. In the H-H or , molecule this distance is 0.74 .

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Bonds Between Atoms

The energy of two hydrogen atoms can be represented in a diagram such as that above. The horizontal axis indicates the distance between atoms in angstrom units, and the vertical axis indicates the energy, with lower energy and greater stability represented downward. The zero point of energy has been chosen to be that of two infinitely separated, noninteracting atoms. Two hydrogen atoms infinitely far apart obviously do not interact, and thus have no bond between them.

As the atoms come closer together, little hap interatomic distance decreases to a few angst electron of one atom begins to be "seen" by the other. Each electron is attracted by the othe electrons become concentrated between the nuc begins to form. The energy of the two atoms de attraction of each nucleus for the other ele significant.

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Bonds Between Atoms

The energy of two hydrogen atoms can be represented in a diagram such as that above. The horizontal axis indicates the distance between atoms in angstrom units, and the vertical axis indicates the energy, with lower energy and greater stability represented downward. The zero point of energy has been chosen to be that of two infinitely separated, noninteracting atoms. Two hydrogen atoms infinitely far apart obviously do not interact, and thus have no bond between them.

As the atoms come closer together, little hap interatomic distance decreases to a few angst electron of one atom begins to be "seen" by the other. Each electron is attracted by the othe electrons become concentrated between the nuc begins to form. The energy of the two atoms de attraction of each nucleus for the other ele significant.

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Bonds Between Atoms

The energy of two hydrogen atoms can be represented in a diagram such as that above. The horizontal axis indicates the distance between atoms in angstrom units, and the vertical axis indicates the energy, with lower energy and greater stability represented downward. The zero point of energy has been chosen to be that of two infinitely separated, noninteracting atoms. Two hydrogen atoms infinitely far apart obviously do not interact, and thus have no bond between them.

As the atoms come closer together, little hap interatomic distance decreases to a few angst electron of one atom begins to be "seen" by the other. Each electron is attracted by the othe electrons become concentrated between the nuc begins to form. The energy of the two atoms de attraction of each nucleus for the other ele significant.

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2. Atoms, Molecules and Moles

Page 1 of 1

-- Jump to --

Bonds Between Atoms

The energy of two hydrogen atoms can be represented in a diagram such as that above. The horizontal axis indicates the distance between atoms in angstrom units, and the vertical axis indicates the energy, with lower energy and greater stability represented downward. The zero point of energy has been chosen to be that of two infinitely separated, noninteracting atoms. Two hydrogen atoms infinitely far apart obviously do not interact, and thus have no bond between them.

As the atoms come closer together, little hap interatomic distance decreases to a few angst electron of one atom begins to be "seen" by the other. Each electron is attracted by the othe electrons become concentrated between the nuc begins to form. The energy of the two atoms de attraction of each nucleus for the other ele significant.

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2. Atoms, Molecules and Moles

Page 1 of 1

-- Jump to --

Bonds Between Atoms

The energy of two hydrogen atoms can be represented in a diagram such as that above. The horizontal axis indicates the distance between atoms in angstrom units, and the vertical axis indicates the energy, with lower energy and greater stability represented downward. The zero point of energy has been chosen to be that of two infinitely separated, noninteracting atoms. Two hydrogen atoms infinitely far apart obviously do not interact, and thus have no bond between them.

As the atoms come closer together, little hap interatomic distance decreases to a few angst electron of one atom begins to be "seen" by the other. Each electron is attracted by the othe electrons become concentrated between the nuc begins to form. The energy of the two atoms de attraction of each nucleus for the other ele significant.

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2. Atoms, Molecules and Moles

Page 1 of 1

-- Jump to --

Bonds Between Atoms

The energy of two hydrogen atoms can be represented in a diagram such as that above. The horizontal axis indicates the distance between atoms in angstrom units, and the vertical axis indicates the energy, with lower energy and greater stability represented downward. The zero point of energy has been chosen to be that of two infinitely separated, noninteracting atoms. Two hydrogen atoms infinitely far apart obviously do not interact, and thus have no bond between them.

As the atoms come closer together, little hap interatomic distance decreases to a few angst electron of one atom begins to be "seen" by the other. Each electron is attracted by the othe electrons become concentrated between the nuc begins to form. The energy of the two atoms de attraction of each nucleus for the other ele significant.

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2. Atoms, Molecules and Moles

Page 1 of 1

-- Jump to --

Bonds Between Atoms

The energy of two hydrogen atoms can be represented in a diagram such as that above. The horizontal axis indicates the distance between atoms in angstrom units, and the vertical axis indicates the energy, with lower energy and greater stability represented downward. The zero point of energy has been chosen to be that of two infinitely separated, noninteracting atoms. Two hydrogen atoms infinitely far apart obviously do not interact, and thus have no bond between them.

As the atoms come closer together, little hap interatomic distance decreases to a few angst electron of one atom begins to be "seen" by the other. Each electron is attracted by the othe electrons become concentrated between the nuc begins to form. The energy of the two atoms de attraction of each nucleus for the other ele significant.

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Bonds Between Atoms A simple explanation of a chemical bond was given by G. N. Lewis in 1914: A bond is formed between two atoms when a pair of electrons is shared between them. This is the electron-pair, or covalent bond, which is the subject of Chapter 4. Two hydrogen atoms, each with a single electron, can share their electrons and form a covalent bond, as shown at center left. If you were to perform a quantum-mechanical calculation to see how the electrons in an H-H bond were distributed, you would find that most of the time they are between the two H nuclei. One positive nucleus is attracted to the two electrons, which simultaneously attract the other nucleus. At the same time, the two electrons shield or screen the nuclei from one another and decrease the repulsion between their positive charges. The negatively charged electrons are the "glue" that holds the positive nuclei together.

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Page 1 of 1

-- Jump to --

Bonds Between Atoms A simple explanation of a chemical bond was given by G. N. Lewis in 1914: A bond is formed between two atoms when a pair of electrons is shared between them. This is the electron-pair, or covalent bond, which is the subject of Chapter 4. Two hydrogen atoms, each with a single electron, can share their electrons and form a covalent bond, as shown at center left. If you were to perform a quantum-mechanical calculation to see how the electrons in an H-H bond were distributed, you would find that most of the time they are between the two H nuclei. One positive nucleus is attracted to the two electrons, which simultaneously attract the other nucleus. At the same time, the two electrons shield or screen the nuclei from one another and decrease the repulsion between their positive charges. The negatively charged electrons are the "glue" that holds the positive nuclei together.

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2. Atoms, Molecules and Moles

Page 1 of 1

-- Jump to --

Bonds Between Atoms A simple explanation of a chemical bond was given by G. N. Lewis in 1914: A bond is formed between two atoms when a pair of electrons is shared between them. This is the electron-pair, or covalent bond, which is the subject of Chapter 4. Two hydrogen atoms, each with a single electron, can share their electrons and form a covalent bond, as shown at center left. If you were to perform a quantum-mechanical calculation to see how the electrons in an H-H bond were distributed, you would find that most of the time they are between the two H nuclei. One positive nucleus is attracted to the two electrons, which simultaneously attract the other nucleus. At the same time, the two electrons shield or screen the nuclei from one another and decrease the repulsion between their positive charges. The negatively charged electrons are the "glue" that holds the positive nuclei together.

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2. Atoms, Molecules and Moles

Page 1 of 1

-- Jump to --

Bonds Between Atoms A simple explanation of a chemical bond was given by G. N. Lewis in 1914: A bond is formed between two atoms when a pair of electrons is shared between them. This is the electron-pair, or covalent bond, which is the subject of Chapter 4. Two hydrogen atoms, each with a single electron, can share their electrons and form a covalent bond, as shown at center left. If you were to perform a quantum-mechanical calculation to see how the electrons in an H-H bond were distributed, you would find that most of the time they are between the two H nuclei. One positive nucleus is attracted to the two electrons, which simultaneously attract the other nucleus. At the same time, the two electrons shield or screen the nuclei from one another and decrease the repulsion between their positive charges. The negatively charged electrons are the "glue" that holds the positive nuclei together.

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2. Atoms, Molecules and Moles

Page 1 of 1

-- Jump to --

Bonds Between Atoms A simple explanation of a chemical bond was given by G. N. Lewis in 1914: A bond is formed between two atoms when a pair of electrons is shared between them. This is the electron-pair, or covalent bond, which is the subject of Chapter 4. Two hydrogen atoms, each with a single electron, can share their electrons and form a covalent bond, as shown at center left. If you were to perform a quantum-mechanical calculation to see how the electrons in an H-H bond were distributed, you would find that most of the time they are between the two H nuclei. One positive nucleus is attracted to the two electrons, which simultaneously attract the other nucleus. At the same time, the two electrons shield or screen the nuclei from one another and decrease the repulsion between their positive charges. The negatively charged electrons are the "glue" that holds the positive nuclei together.

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Bonds Between Atoms Atoms combine into molecules because by doing so they achieve a state of lower energy. Making molecules from atoms is a "downhill" process, and tearing molecules apart again into atoms always requires energy to go back up the energy hill. We usually can think of molecules as being held together by bonds between pairs of atoms within them. A key question in chemistry is: Which atoms will combine with one another, in what way, and why? At the beginning of this century chemical bonding was still a mystery. One of the triumphs of quantum mechanics, a shatteringly unorthodox theory developed between 1900 and 1926, was the successful explanation not only of atomic structure, but of bonding between atoms in molecules. We can take some of the pictorial conclusions from quantum mechanics and use them to predict the behavior of atoms in molecules, without becoming involved in the mathematics. This is done in Chapters 79.

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Bonds Between Atoms Atoms combine into molecules because by doing so they achieve a state of lower energy. Making molecules from atoms is a "downhill" process, and tearing molecules apart again into atoms always requires energy to go back up the energy hill. We usually can think of molecules as being held together by bonds between pairs of atoms within them. A key question in chemistry is: Which atoms will combine with one another, in what way, and why? At the beginning of this century chemical bonding was still a mystery. One of the triumphs of quantum mechanics, a shatteringly unorthodox theory developed between 1900 and 1926, was the successful explanation not only of atomic structure, but of bonding between atoms in molecules. We can take some of the pictorial conclusions from quantum mechanics and use them to predict the behavior of atoms in molecules, without becoming involved in the mathematics. This is done in Chapters 79.

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Page 1 of 1

-- Jump to --

Bonds Between Atoms Atoms combine into molecules because by doing so they achieve a state of lower energy. Making molecules from atoms is a "downhill" process, and tearing molecules apart again into atoms always requires energy to go back up the energy hill. We usually can think of molecules as being held together by bonds between pairs of atoms within them. A key question in chemistry is: Which atoms will combine with one another, in what way, and why? At the beginning of this century chemical bonding was still a mystery. One of the triumphs of quantum mechanics, a shatteringly unorthodox theory developed between 1900 and 1926, was the successful explanation not only of atomic structure, but of bonding between atoms in molecules. We can take some of the pictorial conclusions from quantum mechanics and use them to predict the behavior of atoms in molecules, without becoming involved in the mathematics. This is done in Chapters 79.

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Page 1 of 1

-- Jump to --

Bonds Between Atoms Atoms combine into molecules because by doing so they achieve a state of lower energy. Making molecules from atoms is a "downhill" process, and tearing molecules apart again into atoms always requires energy to go back up the energy hill. We usually can think of molecules as being held together by bonds between pairs of atoms within them. A key question in chemistry is: Which atoms will combine with one another, in what way, and why? At the beginning of this century chemical bonding was still a mystery. One of the triumphs of quantum mechanics, a shatteringly unorthodox theory developed between 1900 and 1926, was the successful explanation not only of atomic structure, but of bonding between atoms in molecules. We can take some of the pictorial conclusions from quantum mechanics and use them to predict the behavior of atoms in molecules, without becoming involved in the mathematics. This is done in Chapters 79.

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Bonds Between Atoms

At ordinary temperatures and pressures, both hydrogen and helium are gases (upper left). Individual particles move freely, are far apart on the average, and are independent of one another except when they collide. Their energy of motion is sufficiently greater than the van der Waals attractions that when they do collide, they rebound rather than stick together. Hydrogen and helium gases both are made up of essentially free particles.

There is one important difference, however, il movie at the top. In helium gas the particles ar atoms, but the particles in hydrogen gas are tw together in an hydrogen molecule. Why the diffe

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Bonds Between Atoms

At ordinary temperatures and pressures, both hydrogen and helium are gases (upper left). Individual particles move freely, are far apart on the average, and are independent of one another except when they collide. Their energy of motion is sufficiently greater than the van der Waals attractions that when they do collide, they rebound rather than stick together. Hydrogen and helium gases both are made up of essentially free particles.

There is one important difference, however, il movie at the top. In helium gas the particles ar atoms, but the particles in hydrogen gas are tw together in an hydrogen molecule. Why the diffe

Page 14 of 48

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2. Atoms, Molecules and Moles

Page 1 of 1

-- Jump to --

Bonds Between Atoms

At ordinary temperatures and pressures, both hydrogen and helium are gases (upper left). Individual particles move freely, are far apart on the average, and are independent of one another except when they collide. Their energy of motion is sufficiently greater than the van der Waals attractions that when they do collide, they rebound rather than stick together. Hydrogen and helium gases both are made up of essentially free particles.

There is one important difference, however, il movie at the top. In helium gas the particles ar atoms, but the particles in hydrogen gas are tw together in an hydrogen molecule. Why the diffe

Page 14 of 48

http://www.chem.ox.ac.uk/vrchemistry/AMM/HTML/page14.htm

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2. Atoms, Molecules and Moles

Page 1 of 1

-- Jump to --

Bonds Between Atoms

At ordinary temperatures and pressures, both hydrogen and helium are gases (upper left). Individual particles move freely, are far apart on the average, and are independent of one another except when they collide. Their energy of motion is sufficiently greater than the van der Waals attractions that when they do collide, they rebound rather than stick together. Hydrogen and helium gases both are made up of essentially free particles.

There is one important difference, however, il movie at the top. In helium gas the particles ar atoms, but the particles in hydrogen gas are tw together in an hydrogen molecule. Why the diffe

Page 14 of 48

http://www.chem.ox.ac.uk/vrchemistry/AMM/HTML/page14.htm

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2. Atoms, Molecules and Moles

Page 1 of 1

-- Jump to --

Bonds Between Atoms

At ordinary temperatures and pressures, both hydrogen and helium are gases (upper left). Individual particles move freely, are far apart on the average, and are independent of one another except when they collide. Their energy of motion is sufficiently greater than the van der Waals attractions that when they do collide, they rebound rather than stick together. Hydrogen and helium gases both are made up of essentially free particles.

There is one important difference, however, il movie at the top. In helium gas the particles ar atoms, but the particles in hydrogen gas are tw together in an hydrogen molecule. Why the diffe

Page 14 of 48

http://www.chem.ox.ac.uk/vrchemistry/AMM/HTML/page14.htm

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2. Atoms, Molecules and Moles

Page 1 of 1

-- Jump to --

Bonds Between Atoms

At ordinary temperatures and pressures, both hydrogen and helium are gases (upper left). Individual particles move freely, are far apart on the average, and are independent of one another except when they collide. Their energy of motion is sufficiently greater than the van der Waals attractions that when they do collide, they rebound rather than stick together. Hydrogen and helium gases both are made up of essentially free particles.

There is one important difference, however, il movie at the top. In helium gas the particles ar atoms, but the particles in hydrogen gas are tw together in an hydrogen molecule. Why the diffe

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2. Atoms, Molecules and Moles

Page 1 of 1

-- Jump to --

Bonds Between Atoms

At ordinary temperatures and pressures, both hydrogen and helium are gases (upper left). Individual particles move freely, are far apart on the average, and are independent of one another except when they collide. Their energy of motion is sufficiently greater than the van der Waals attractions that when they do collide, they rebound rather than stick together. Hydrogen and helium gases both are made up of essentially free particles.

There is one important difference, however, il movie at the top. In helium gas the particles ar atoms, but the particles in hydrogen gas are tw together in an hydrogen molecule. Why the diffe

Page 14 of 48

http://www.chem.ox.ac.uk/vrchemistry/AMM/HTML/page14.htm

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2. Atoms, Molecules and Moles

Page 1 of 1

-- Jump to --

Bonds Between Atoms

At ordinary temperatures and pressures, both hydrogen and helium are gases (upper left). Individual particles move freely, are far apart on the average, and are independent of one another except when they collide. Their energy of motion is sufficiently greater than the van der Waals attractions that when they do collide, they rebound rather than stick together. Hydrogen and helium gases both are made up of essentially free particles.

There is one important difference, however, il movie at the top. In helium gas the particles ar atoms, but the particles in hydrogen gas are tw together in an hydrogen molecule. Why the diffe

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Isotopes and Observed Atomic Weights

The atomic weight of an element in nature is the weighted average, in terms of natural abundance, of the atomic weights of its naturally occurring isotopes. Boron is a good example since it has appreciable amounts of two stable isotopes. Because isotopes of the same element have such similar chemical properties, the ratio of isotopes ordinarily is unchanged during chemical reactions. If individual isotopes are wanted, they must be separated by some technique, such as diffusion or mass spectrometry, that is sensitive to small mass differences. To the chemist, all isotopes of an element react in much the same way. What is important to chemical behavior is not the number of neutrons in an atom, but the number of protons because this determines the number of electrons, and electrons give rise to all of the important chemical properties of the elements.

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Isotopes and Observed Atomic Weights Most of the naturally occurring elements are mixtures of several isotopes. Of the carbon found on this planet, 98.9% is carbon-12, or , which has six protons and six neutrons. (The atomic mass scale is defined so that an atom of carbon- 12 weighs exactly 12 amu.) 1.1% is carbon-13, with one additional neutron. Both of these isotopes are stable, but carbon-14 is radioactive, and is present in minute amounts only because it is being produced constantly by cosmic-ray bombardment of nitrogen in the upper atmosphere. Carbon-14 is the basis of radiocarbon dating. As long as a tree or other organism is alive, it constantly takes in more carbon from its surroundings, and the ratio of to equals that in the atmosphere as a whole. Radioactive decay and replenishment from the atmosphere are in balance. When the tree dies, this intake stops and what little carbon-14 it has begins to disappear. By measuring the ratio of to in a wood or other carbon containing relic from an archaeological site, scientists can calculate how long in the past the specimen ceased to be alive and thus ceased to exchange with its surroundings.

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Isotopes of Helium

When one of the two neutrons in the tritium nucleus breaks down into a proton and an electron, then a oneproton, two-neutron nucleus of hydrogen is converted into a two-proton, one-neutron nucleus of helium: + This reaction is illustrated above.

One element is changed into another, and the elec from the nucleus as beta radiation. We shall no with radioactive decay and unstable isotopes, but at least that atomic nuclei are stable when their ra to protons lie within a certain range, namely, 1:1 excess of neutrons. With too many neutrons or to a nucleus becomes unstable and decays spont more stable isotope of an element with an atomic that of the original element.

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Isotopes of Helium

When one of the two neutrons in the tritium nucleus breaks down into a proton and an electron, then a oneproton, two-neutron nucleus of hydrogen is converted into a two-proton, one-neutron nucleus of helium: + This reaction is illustrated above.

One element is changed into another, and the elec from the nucleus as beta radiation. We shall no with radioactive decay and unstable isotopes, but at least that atomic nuclei are stable when their ra to protons lie within a certain range, namely, 1:1 excess of neutrons. With too many neutrons or to a nucleus becomes unstable and decays spont more stable isotope of an element with an atomic that of the original element.

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Isotopes of Helium

The reaction on the previous page was written using the notation introduced previously, with the subscript now representing the charge on a particle (rather than the number of protons in the nucleus), and the superscript giving the mass number, or approximate mass in amu.

A proton, which has a +1 charge and unit mass nu ; a neutron, which has no charge and unit mas electron, which has a - 1 charge and no negligib rough-counting scale, is . When a nuclear react one is written and balanced properly, the total cha and the total mass number (superscripts) on the the total charge and mass on the right.

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Isotopes of Helium

Helium also has isotopes. The difference between superscript and subscript gives the number of neutrons in the nucleus, and this can be 1, 2, 3, or 4. An atom has m nuclear n particles, n protons, and m - n neutrons. Instead of special names, the isotopes of helium and heavier elements are distinguished by giving their name and mass number, for example, helium-3 for . All but a minute fraction of helium atoms found on Earth are helium-4. Only one atom per million is helium-3, and helium-5 and -6 do not exist naturally.

Some isotopes of an element are stable and show break down; others decompose spontaneously a radioactive. Light hydrogen and deuterium are sta radioactive. The or T nucleus apparently has an neutrons to protons. In time it decays spontaneo converting one of the neutrons into a proton and a +

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Isotopes of Hydrogen If protons and neutrons each weighed exactly 1 amu, and there was no change in mass when the nucleus was formed, then the mass number of an isotope would equal the sum of the masses of the protons and neutrons in amu, or its atomic weight. This is not strictly true. Not only are protons and neutrons slightly heavier than 1 amu, there is a small loss in mass when they combine to form a nucleus. This missing mass is converted to energy during the nucleus-forming process and is lost by the atom. The nucleus cannot be taken apart again unless the lost energy is resupplied to make up the full mass, that is, the mass of the initial protons and neutrons. This missing energy represents the binding energy of the nucleus, or the energy that holds the nucleus together. Nevertheless, for approximate calculations we can think of the atomic weight of an isotope as being approximately equal to the sum of its protons and neutrons, or to its mass number.

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Isotopes of Hydrogen For heavier elements, the addition of one or two neutrons has a less important effect on properties; thus isotopes are not given special names. Only for hydrogen, in which additional neutrons double or triple the atomic mass, have special names and symbols been developed:

= H = light hydrogen or "ordinary" hydrogen, with one proton and no neutrons in the nucleus. = D =deuterium (from "deutero-" or two), with one proton and one neutron in the nucleus. = T =tritium (from "tri-" or three), with one proton and two neutrons in the nucleus Ordinary water has the chemical formula . Heavy water, , has become familiar because of its use as a moderator or neutron absorber in certain types of nuclear reactors. About 150 hydrogen atoms per million on our planet are D atoms. Tritium is radioactive and must be produced artificially.

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Isotopes of Hydrogen So far we have said nothing about neutrons. The most common type of hydrogen has none in its nucleus (right). Other kinds of hydrogen atoms have either one or two neutrons, in addition to the proton that defines their chemical character. Atoms such as these three, with the same atomic number but with different numbers of neutrons in their nuclei, are called isotopes of the same chemical element. The sum of the number of protons and neutrons is the mass number, and is written as a superscript before the symbol of the element: , , . The three isotopes of hydrogen have quite different masses: approximately 1, 2, and 3 amu. But because the number of protons is the same, they have the same number of electrons around the nucleus. To an approaching atom, all hydrogen atoms look much the same, and exhibit virtually the same chemical behavior. The differences are important only in properties such as rates of reaction or rates of diffusion of molecules, for which the mass of an atom and its speed are important.

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Electrons, Nuclei, and Atomic Number The way in which electrons are arranged around a nucleus and the effect that this has on chemical behavior are the subject of the next chapter. At the moment, notice only the trend from metals, to nonmetals, to an inert gas, and the beginning of a repetition of properties with the inert gas neon and the soft metal sodium. Chemical properties are periodic functions of the atomic number - in a listing of elements by increasing atomic number, similar properties are encountered again and again at regular intervals. This is one of the most important generalizations in chemistry.

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2. Atoms, Molecules and Moles

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Electrons, Nuclei, and Atomic Number The two simplest kinds of atoms are hydrogen (H),and helium (He), diagramed on Page 1. Hydrogen has one proton in its nucleus and one electron around it. Helium has two protons and hence must have two electrons, since the number of positive and negative charges in a neutral atom must be the same. Because electrons surround an atom, and the nucleus is small and deeply buried, the outer part of the electron cloud is all that another atom "sees." It is the electron cloud that gives each atom its chemical character. Reactions leading to the making of chemical bonds involve the gain, loss, or sharing of electrons between atoms, as we shall see in subsequent chapters. Since the number of electrons in a neutral atom must equal the number of protons in its nucleus, the number of protons indirectly decides the chemical behavior of the atom. All atoms with the same number of protons are defined as the same chemical element, and the number of protons is its atomic number. The atomic number sometimes is written as a subscript in front of the symbol of the element, such as H and He. This is convenient but unnecessary, since, for example, every atom with atomic number 2 by definition is called helium and given the symbol He.

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2. Atoms, Molecules and Moles

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Electrons, Nuclei, and Atomic Number

An atomic nucleus is built from two major kinds of particles: protons and neutrons. A proton carries one unit of positive charge, which balances the negative charge on an electron. The neutron is uncharged. The standard unit for measuring masses of atoms is the atomic mass unit (amu) defined such that the most common kind of carbon atom weighs exactly 12 amu.

On this scale, a proton has a mass of 1.00728 am lighter than a neutron, which has a mass of 1.0086 and neutrons usually are thought of as having amu) unless exact calculations are called for. O electron weighs only 0.00055 amu. The cha relationships between these three fundamenta summarized in the table to the left.

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2. Atoms, Molecules and Moles

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Electrons, Nuclei, and Atomic Number An atom is made up of a very small but heavy central nucleus with a positive charge, surrounded by a negatively charged cloud of electrons. Because atoms are so small, the familiar units of feet or centimeters are useless in measuring them. A more common unit of length is the angstrom, symbolized . There are 100,000,000 or 10 in one centimeter, or to express matters the other way around, 1 = 1/10 cm = 10

cm = 0.00000001 cm

Most atoms are of the order of 1.0 to 2.4 in diameter, which is why angstroms are so convenient. The nucleus of an atom is much smaller yet, typically with a diameter of 10 cm or 10 . If an atom were as large as a football stadium, the nucleus would be the size of a small ladybug crawling across the 50-yard line. In spite of this size difference, virtually an of the mass of an atom is concentrated in its nucleus. One electron, which has a negative charge, weighs only 1/1836 as much as the lightest of all nuclei, that of the hydrogen atom (proton).

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2. Atoms, Molecules and Moles

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Introduction

Hydrogen and helium occupy a special place in the chemical world because they are the elements from which all other elements were made. They have another aspect that makes them useful to us now:

They are the simplest of all atoms. All of the ide atomic structure that can be illustrated with hydro will carry directly over to the study of the heavier a

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