Gaseous State

GASES

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Kinetic-Molecular Theory 

Theory of moving molecules

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1. Gases consists of large numbers of molecules that are in continuous, random motion (molecule: smallest particle of any gas)

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2.The volume of all the molecules of the gas is negligible compared to the total volume in which the gas is contained 2

Kinetic-Molecular Theory 

3. Attractive and repulsive forces between gas molecules are negligible

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4. Collisions are perfectly elastic.

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5. The average kinetic energy of the molecules is proportional to the absolute temperature.

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Properties of Gases •

Gases are described in terms of four properties: pressure (P), volume (V), temperature (T), and amount (n).

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Gas Pressure Gas pressure: • Caused by collisions of the molecules with the walls of the container. • MAGNITUDE: determined by how often and how forcefully the molecules strike the walls of the container

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Gas Pressure Gas pressure: • Is described as a force acting on a specific area Pressure (P) = Force Area • Has units of atm, mm Hg, torr, and pascals • 1 atmosphere (1 atm) is 760 mm Hg • 1 mm Hg = 1 torr 1.00 atm = 760 mm Hg = 760 torr

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Units of Pressure Gas pressure, • Is described as a force acting on a specific area

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Learning Check A. What is 475 mm Hg expressed in atm? 1) 475 atm 2) 0.625 atm 3) 3.61 x 105 atm B. The pressure in a tire is 2.00 atm. What is this pressure in mm Hg? 1) 2.00 mm Hg 2) 1520 mm Hg 3) 22 300 mm Hg

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Solution A. What is 475 mm Hg expressed in atm? 2) 0.625 atm 475 mm Hg x 1 atm = 0.625 atm 760 mm Hg B. The pressure of a tire is measured as 2.00 atm. What is this pressure in mm Hg? 2) 1520 mm Hg 2.00 atm x 760 mm Hg = 1520 mm Hg 1 atm

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Atmospheric Pressure The atmospheric pressure: • Is the pressure exerted by a column of air from the top of the atmosphere to the surface of Earth • Is about 1 atmosphere or a little less at sea level

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Altitude and Atmospheric Pressure Atmospheric pressure: • Depends on the altitude and the weather • Is lower at high altitudes where the density of air is less • Is higher on a rainy day than on a sunny day

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Barometer A barometer: • Measures the pressure exerted by the gases in the atmosphere • Indicates atmospheric pressure as the height in mm of the mercury column

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END 13

Learning Check A. The downward pressure of the Hg in a barometer is _____ than (as) the pressure of the atmosphere. 1) greater

2) less

3) the same

B. A water barometer is 13.6 times taller than a Hg barometer (DHg = 13.6 g/mL) because: 1) H2O is less dense 2) H2O is heavier 3) air is more dense than H2O

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Solution A.The downward pressure of the Hg in a barometer is 3) the same (as) the pressure of the atmosphere. B. A water barometer is 13.6 times taller than a Hg barometer (DHg = 13.6 g/mL) because: 1) H2O is less dense

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GAS LAWS

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Gas Laws 

Ideal gas  Exhibits simple linear relationships among volume, pressure, temperature, and amount (moles). 

NO ideal gas exists

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N2, O2, H2, and the noble gases show nearly ideal behavior at ordinary temperatures and pressures.

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GAS LAWS 1. Ideal Gas Equation 2. Boyle’s Law 3. Charles’ Law 4. Combined Gas Law 5. Avogadro’s Law 6. Dalton’s Law of Partial Pressures 7. Graham’s Law of Diffusion

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Ideal Gas Equation 

Ideal Gas Equation

PV = nRT P = pressure V = volume n = amount in moles R = universal gas constant (0.08206 L-atm / mol-K) T = temperature (in K)

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Ideal Gas Equation 

Problem Calcium carbonate, CaCO3, decomposes upon heating to give CaO(s) and CO2(g). A sample of CaCO3 is decomposed, and the carbon dioxide is collected in a 250-mL flask. After the decomposition is complete, the gas has a pressure of 1.3 atm at a temperature of 310C. How many moles of CO2 gas were generated? Answer: n = 0.013 mol CO2 20

Ideal Gas Equation 

Combination of the 3 gas laws: Boyle’s, Charles’, and Avogadro’s Law

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Boyle’s Law 

Boyle’s Law (V-P)  relationship between volume and pressure  at constant T, the V occupied by a gas is inversely related to its P.

k Vα P

[T and n fixed]

P1V1= P2V2

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Boyle’s Law 

Problem A sample of argon gas occupies 105 mL at 0.871 atm. If the temperature remains constant, what is the volume in L at 26.3 kPa?

Answer: 0.352 L

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Charles’ Law 

Charles’ Law (V-T)  relationship between volume and temperature  at constant P, V occupied by a fixed amount of gas is directly proportional to its T.

V α kT

[P and n fixed] V1T2 = V2T1

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Charles’ Law 

Problem If the volume of a certain gas changes from 200 K to 400 K, what will be the volume occupied by 1 mol of gas?

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Relationships based on Boyles’ and Charles’ Laws 

Pressure – Temperature Relationship  At constant V, P exerted by a fixed amount of gas is directly proportional to T (in K).

P α kT

[V and n fixed]

P1T2 = P2T1

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Relationships based on Boyles’ and Charles’ Laws 

Problem A steel tank used for fuel delivery is fitted with a safety valve that opens if the internal pressure exceeds 1.00 x 103 torr. It is filled with methane at 230C and 0.991 atm and placed in boiling water at exactly 1000C. Will the safety valve open?

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Relationships based on Boyle’s and Charles’ Laws 

Combined Gas Law  Combination of Boyle’s and Charles’ laws  Relationship between P, V, and T – applied when two of the three variables are changed and you must find the effect on the third

T Vαk P

[n is fixed] P1V1T2 = P2V2T1

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Avogadro’s Law 

Avogadro’s Law  Relationship between volume and amount  at fixed T and P, V occupied by a gas is directly proportional to n.

V α kn

[P and T fixed]

At fixed T and P, equal volumes of any ideal gas contains equal number of particles (or moles).

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Gas Laws 

Dalton’s Law of Partial Pressures Ptotal = P1 + P2 + P3 + ...

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Graham’s Law of Diffusion

Rate1 = Rate2

M2 M1 30