Gases and the Kinetic Molecular Theory

1
Gases and the Kinetic Molecular Theory
2
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/K?mol T
temperature in Kelvin
3
How fast do gas molecules move? Called the root
mean square speed of the gas.
in kg/mol
Equation gives speed in meters/second.
What is the rms speed of O2 molecules at room
temperature?
4
Boltzmann Distributions
5
Boltzmann Distributions and Molar Mass
6
Boltzmann Distributions and Temperature
7
Gas Diffusion
8
Gas Effusion
9
Grahams Law of Gas Effusion used for
determining molar mass of a gas
10
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
same conditions, effuses at a rate of 1.3 x 10-6
mol/hr. Calculate the molar mass of the unknown
gas.
11
Gas Laws The Ideal Gas Law
PV nRT P pressure in atmospheres V volume
in liters N moles of gas T temperature in K R
gas constant 0.08257 L?atm/K?mol
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.
12
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
is the mass of the gas?
13
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?
14
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?
15
The General Gas Law Determining changes in a
property when a different property changes.
General idea cancel properties that dont change.
16
The General Gas Law P and V
A gas sample at 0.95 atm has a volume of 250 mL.
What will the pressure be if the volume is
compressed to 100 mL? n and T are constant.
General Law
17
The General Gas Law n and V
A 0.35 mol gas sample has a volume of 250 mL.
What will the volume be if 0.20 mol more gas are
added? P and T are constant.
General Law
18
The General Gas Law T and V
A gas sample has a volume of 250 mL at 100 oC.
What will the volume be if it is cooled to 10 oC?
P and n are constant.
General Law
19
The General Gas Law T and V
A 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.