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Gases and the Kinetic Molecular Theory
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Speeds of gas molecules.
For a single molecule. Kinetic energy is:
KE = ½ mv2 m = mass; v = velocity
For a collection of gas molecules, the average kinetic energy is:
R = ideal gas constant = 8.314 J/Kmol
T = temperature in Kelvin
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How fast do gas molecules move?
Called the root mean square speed of the gas.
What is the rms speed of O2 molecules at room temperature?
in kg/mol
Equation gives speed in meters/second.
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Boltzmann Distributions
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Boltzmann Distributions and Molar Mass
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Boltzmann Distributions and Temperature
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Gas Diffusion
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Gas Effusion
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Graham’s Law of Gas Effusion: used for determining molar mass of a gas
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Example: A sample of ethane, C2H6, effuses through a small hole at a rate of 3.6 x 10-6 mol/hr. An unknown gas, under the sameconditions, effuses at a rate of 1.3 x 10-6 mol/hr. Calculate the molar mass of the unknown gas.
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Gas Laws: The Ideal Gas Law
PV = nRT
P = pressure in atmospheresV = volume in litersN = moles of gasT = temperature in KR = gas constant = 0.08257 Latm/Kmol
Two Uses:
1. You know three of the four variables and solve for the fourth.
2. You know the change in one variable and determine the change in another.
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The Ideal Gas Law: 1a: Determining one property, given the others
A sample of N2 gas has a volume of 250. mL,a pressure of 720 mm Hg, and is at 25 oC. What isthe mass of the gas?
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The Ideal Gas Law: 1b: Determining one property, given the others
A sample of 2.60 g Ar gas has a pressure of 720 mm Hg, and is at 25 oC. What is the volume of the gas?
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The Ideal Gas Law: 1c: Determining one property, given the others
What is the density of O2 gas at 20 oC, in grams per liter?
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The General Gas Law: Determining changes in a property when a different property changes.
General idea: cancel properties that don’t change.
PV = nRT always the samePV
RnT
1 1 2 2
1 1 2 2
PV PV
nT n T
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The General Gas Law: P and VA gas sample at 0.95 atm has a volume of 250 mL. What willthe pressure be if the volume is compressed to 100 mL? n and T are constant.
1 1 2 2
1 1 2 2
PV PV
nT n T
General Law:
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The General Gas Law: n and VA 0.35 mol gas sample has a volume of 250 mL. What willthe volume be if 0.20 mol more gas are added? P and T are constant.
1 1 2 2
1 1 2 2
PV PV
nT n T
General Law:
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The General Gas Law: T and VA gas sample has a volume of 250 mL at 100 oC. What willthe volume be if it is cooled to 10 oC? P and n are constant.
1 1 2 2
1 1 2 2
PV PV
nT n T
General Law:
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The General Gas Law: T and VA car tire has a pressure of 32 psi in winter, when T = -10 oC. What will the pressure be in summer if T increases to 33 oC,but 5% of the air in the tire has leaked out? Assume V is constant.
1 1 2 2
1 1 2 2
PV PV
nT n T