Gas & Its Law

Gas & Its Law

Gas  Gases are composed of particles that are moving around very fast in their container(s).

 These particles moves in straight lines until

they collides with either the container wall or another particle, then they bounce off.

 there is a lot of empty space separated the particles

Properties of Gas •

• • •

•

Gases have a small mass but can take a large volume. (Low Density) Gases can be squeezed together.(Compressibility) Gases fill their containers. (Expansion) Gases diffuse. (Diffusion & Effusion) Gases flow easily and without resistance throughout their container. (Fluidity)

Gases have mass.

Gases are squeezable If you squeeze any gas, its volume can be reduced considerably Gases have a low density which allows for a lot of empty space between gas molecules.

Gases fill their containers Gases expand until they take up as much room as they possibly can. Gases spread out to fill containers until the concentration of gases is uniform throughout the entire space. This is why that nowhere around you is there an absence of air.

Gases diffuse Gases can move through each other rapidly. The movement of one substance through another is called diffusion. Because of all of the empty space between gas molecules, another gas molecule can pass between them until each gas is spread out over the entire container, the gases mix uniformly.

Gases flow past other gases If a close container of hot food is opened, you would soon be able to smell it in the back. The popcorn smell easily diffuses throughout the other gas molecules in the room.

Diffusion & Effusion When gas molecules randomly move about a room  diffusion. When gas molecules pass through a tiny opening into a vacuum  effusion. Some gases diffuse more rapidly then other gases based on their size and their energy. The heavier and colder the gas the slower it moves.

Physical Characteristics of Gases Physical Characteristics

Typical Units

Volume, V

liters (L)

Pressure, P Temperature, T

atmosphere (1 atm = 1.015x105 N/m2) Kelvin (K)

Number of atoms or molecules, n

mole (1 mol = 6.022x1023 atoms or molecules)

Gas Pressure  Just as a ball exerts a force when it

bounces against a wall, a gaseous atom or molecule exerts a force when it collides with a surface.

 The result of many of these molecular collisions is pressure.

 Pressure is the force exerted per unit

area by gas molecules as they strike the surfaces around them.

Gas Pressure Gas pressure is a result of the constant

movement of the gas molecules and their collisions with the surfaces around them.

The pressure of a gas depends on several factors:   

Number of gas particles in a given volume (concentration) Volume of the container Average speed of the gas particles

Gas Pressure 

As volume increases, concentration of gas molecules decreases (number of molecules does not change, but since the volume increases, the concentration goes down). 



This in turn results in fewer molecular collisions, which results in lower pressure.

The fewer the gas particles, the lower the force per unit area and the lower the pressure. 

A low density of gas particles results in low pressure. A high density of gas particles results in high pressure.

Volume The volume of a gas depends on The pressure of the gas 2. The temperature of the gas 3. The number of moles of the gas 1.

The volume of a gas is expressed in mL and L

Temperature Temperature

of the gas is related to the KE of the molecule The velocity of gas particles increases as the temp. increases When working problems, temperature is expressed in Kelvin not Celcius

Amount of Gas  Gases

are usually measured in grams

 Gas

law calculations require that the quantity of a gas is expressed in moles

 Moles

of a gas represents the number of particles of a gas that are present When working gas law problems, convert mass (in grams) to moles

The Simple Gas Laws 

  

There are four basic properties of a gas: pressure (P), volume (V), temperature (T), and amount in moles (n).  These properties are interrelated—when one changes, it affects the others.  The simple gas laws describe the relationships between pairs of these properties. Boyle’s Law Charles’s Law Avogadro’s Law

Boyle’s Law Pressure of a gas is inversely proportional to its volume. 

Constant T and amount of gas



T & the amount of gas (n) are held constant

As P increases, V decreases by the same factor.

P × V = constant P1 × V1 = P2 × V2

Molecular Interpretation of Boyle’s Law

As the volume of a gas sample is decreased, gas molecules collide with surrounding surfaces more frequently, resulting in greater pressure.

Charles’s Law: Volume and Temperature 

The volume of a fixed amount of gas at a constant pressure increases linearly with increasing temperature in kelvins: 

The volume of a gas increases with increasing temperature.

 Kelvin T = Celsius T + 273  V = constant × T (if T measured in Kelvin)

Charles’s Law

If the lines are extrapolated back to a volume of “0,” they all show the same temperature, −273.15 °C = 0 K, called absolute zero

The extrapolated lines cannot be measured experimentally because all gases condense into liquids before –273.15 °C is reached.

Charles’s Law – A Molecular View When T increase: -increase speed of molecules -increase force with which they hit the walls If V can change: Force stretches out its container until it ends up with the same P it had before, just a larger V

If we move a balloon from an ice water bath to a boiling water bath, its volume expands as the gas particles within the balloon move faster (due to the increased temperature) and collectively occupy more space.

Charles’s Law – A Molecular View 



When the temperature of a gas sample increases, the gas particles move faster. 

Collisions with the walls are more frequent.



The force exerted with each collision is greater.

The only way for the pressure (the force per unit area) to remain constant is for the gas to occupy a larger volume so that collisions become less frequent and occur over a larger area.

Gay-Lussac 

discovered the relationship between gas pressure and temperature of a gas The pressure of a sample of gas, at a constant volume, is directly proportional to its temperature (K)



As long as V and n are constant



as the temperature increases, the speed of the gas molecules increases

PT

Temperature and Pressure By KM theory, as the temperature increases, the speed of the gas molecules increases  Increase in the number of collisions the molecules have with the container wall  Thus, an increase in P 

P1 P2 P k T  T 1 2 T

Vapor pressure and Boiling Point 

  

If a glass of water is left out in a room it will eventually evaporate Liquids are constantly evaporating Molecules at the surface of the liquid will break away from the liquid and enter into the gas phase But in a closed container the molecules cannot escape to the atmosphere

Vapor pressure and Boiling Point 

At a certain point molecules will continue to evaporate and at the same rate molecules will return to the liquid



At equilibrium the rates of vaporization and condensation are equal

Liquid to Gas = Gas to Liquid 

Vapor Pressure of a liquid is the pressure exerted by its vapor at equilibrium



The vapor pressure of a liquid will increase with increase in temperature



The normal boiling point of a liquid is the temperature at which its vapor pressure equals the atmospheric pressure



An increase in altitude will lower the atmospheric pressure so liquids will boil at a lower temperature

The Combined Gas Law  An

expression which combines Boyle’s, Charles’s, and Gay-Lussac’s Law P1V1 P2V2  T1 T2

 Applies

to all gases and mixtures of gases  If five of the six variables are known, the sixth can be calculated

Avogadro’s Law  Volume directly proportional to the number of gas

molecules  V = constant × n  Constant P and T  More gas molecules = larger volume  More molecules push on each other and the walls, stretching the container and making it larger until the pressure is the saem as before  Count number of gas molecules by moles.  Equal volumes of gases contain equal numbers of molecules.

Avogadro’s Law When the amount of gas in a sample increases at constant temperature and pressure, its volume increases in direct proportion because the greater number of gas particles fill more space. The volume of a gas sample increases linearly with the number of moles of gas in the sample.

STP and Molar Volume 

Gas volumes can only be compared at the same T and P



The universally accepted conditions are T = 0 °C and P = 1.00 atm Standard Temperature and Pressure = STP Standard Temperature = 0 °C (273 K) and Standard Pressure = 1.00 atm (760 mmHg)



The volume of one mole of gas at STP is 22.4 L,



Known as the standard molar volume

1 mol gas 22.4 L  22.4 L 1 mol gas

Density of a Gas at STP At the same T and P, one mole of any gas will occupy the same volume

 

At STP, the density of a gas depends on its molar mass The higher the molar mass, the greater the density 

CO2 has a higher molar mass than N2 and O2, so it is more dense than air



CO2 released from a fire extinguisher will cover the fire and prevent O2 from reaching the combustible material



Helium is less dense than air so a balloon filled with helium rises in the air

Ideal Gas Law 

Describes the relationship among 4 variables: P, T, V, n (moles)



IDEAL GAS: 

V of the molecules is insignificant when compared to the V of container



All collision are elastic



No force of attraction exist between the molecules

Ideal Gas Law 

R is called the gas constant.



The value of R depends on the units of P and V. 



We will use

and convert P to atm and V to liters.

The ideal gas law allows us to find one of the variables if we know the other three.

R = gas constant

Using the Ideal Gas Law Grams A

Grams B

Moles A

Moles B

pV=nRT PA or VA

PB or VB

Using the Combined Gas Law 

Allows to calculate a change in one of the three variables (P, V, T) caused by a change in both of the other two variables: 1) 2) 3) 4)

Determine the initial values Determine the final values Set two equations equal to one another, one for initial values, one for final values Solve for the unknown variable

P1V1 P2 V2  T1 T2

P1V1T2  T1 P2 V2

Example 1 A

balloon is filled with 1300 mol of H2. If the temperature of the gas is 23 °C and the pressure is 750 mm Hg, what is the volume of the balloon? 1300 mol H2 23 °C 750 mm Hg V=?

Ideal Gas Law Example 1 p  750 torr

1 atm 760 torr

 0.987 atm

n = 1300 mol T = 23 + 273 = 296 K L•atm R = 0.082 mol•K

V=?



nRT V p

L•atm )(296 K) (1300 mol)(0.082 mol•K V (0.987 atm) V  31, 969.2 L

Example 2-Determining the Molar Mass of a Gas A

0.105 g sample of gaseous compound has a pressure of 561 mm Hg in a volume of 125 mL at 23.0 °C. What is its molar mass?

Example 2

p  561torr

1atm 760torr

 0.738 atm

T  23  273  296 K V  125 mL  0.125 L g  0.105 g

Example 2 pV n RT

(0.778 atm)(0.125 L) n L•atm (0.082 mol•K )(296 K) 3

n  4.004x10 mol



g 0.105 g  MW   3 mol 4.004x10 mol MW  26.26 g/mol

Example 3  Gaseous

ammonia is synthesized by the following reaction.

N2 (g)  3 H2 (g)  2 NH3 (g)

 Suppose

you take 355 L of H2 gas at 25.0 °C and 542 mm Hg and combine it with excess N2 gas. What quantity of NH3 gas, in moles, is produced? If this amount of NH3 gas is stored in a 125 L tank at 25 °C, what is the pressure of the gas?

Example 3 H

Excess N2

2

355 L 25.0 °C

Part 1: Mol = ? Part 2: Pressure = ?

542 mm Hg

NH3

125 L 25.0 °C

Ideal Gas Law Example 3 1) Find the moles of hydrogen using ideal gas law

N2 (g)  3 H2 (g)  2 NH3 (g) 1 atm  0.713 atm p  542 torr 760 torr

V  355 L T  25  273  298 K n? (0.713 atm)(355 L) n L•atm (0.0802 mol•K (298 K)

pV n RT

n  10.59 mol H2

Example 3 2) Determine the moles of ammonia produced using the mole-mole factor in the balanced equation

N2 (g)  3 H2 (g)  2 NH3 (g)

3 moles H2 = 2 moles NH3

2 mol NH 3 3 mol H 2

and

3 mol H 2 2 mol NH 3

Now, combine steps 1 and 2 to calculate moles

10.59 mol H 2 2 mol NH 3  7.06 mol NH 3 3 mol H 2

Example 3 3) Calculate the pressure of the ammonia gas

N2 (g)  3 H2 (g)  2 NH3 (g) T  25  273  298 K n  7.06 mol V  125 L p?

nRT p V

(7.06 mol)(0.082)(298 K) p p  1.38 atm (125 L)