AP CHEMISTRY: GASES
KINETIC-MOLECULAR THEORY
Kinetic molecular theory is based on the idea that particles of matter are always in motion.
Ideal gas- a hypothetical gas that perfectly fits all the assumptions of the kinetic-molecular theory.
5 Assumptions of the Kinetic-Molecular Theory
1. Gases consist of large numbers of tiny particles that are far apart relative to their size
2. Collisions between gas particles and between particles and container walls are elastic collisions.
3. Gas particles are in continuous, rapid, random motion. They therefore possess kinetic energy.
4. There are no forces of attraction between gas particles.
5. The temperature of a gas depends on the average kinetic energy of the gas.
Real gas- does not behave completely according to the assumptions of the k-m theory.
Conditions in which real gases behave most ideally:
Low pressure, high temperature, non polar molecules
GAS LAWS
PRESSURE CONVERSIONS
1atm = 760 mmHg
=760 torr
= 103.5 kPa
=1.023 x 10 5 Pa
=14.7 psi
TEMP CONVERSIONS
C = K - 273
K= C + 273
FOUR QUANTITIES NEEDED TO ACCURATELY MEASURE A GAS
1. Volume
2. Pressure
3. Amount (moles)
4. Temperature (in Kelvin)
GAS LAWS
1. Boyle’s law
 Pressure and volume are inversely proportional (at constant temperature and amount (moles) )
 Graph of pressure vs volume is a curve

P1V1=P2V2
P1= original pressure (atm, mmHg, torr, …..)
V1= original volume ( L, mL, cm3……)
V2= final volume
P2= final pressure
2. Charle’s law
 Temperature and volume are directly proportional (at constant pressure and moles)
 Graph of temp vs volume is a straight line

V1 / T1 = V2/ T2




V1= original volume (L, mL, cm3…)
T1= original temp (must be in Kelvin)
V2= final volume
T2 = final temp (KELVIN)
3. Gay-Lussac’s law
 Pressure and temperature are directly proportional ( at constant volume and moles)
 Graph of pressure vs temp is a straight line

P1 / T1 = P2 / T2

TEMPS MUST BE IN KELVIN
4. Avogadro’s law
 Volume and moles are directly related (at constant temp and pressure)

V1 / n1 = V2 / n2
5. Combined gas law
P1 V1 / T1 = P2 V2 / T2 OR
P1V1T2 = P2V2T1
TEMPS MUST BE IN KELVIN
Example 1
To what pressure would you have to compress 48.0 L of oxygen gas at 99.3 kPa in order to reduce its volume to 1.2
atm?
Example 2
A mylar balloon is filled with helium gas to a pressure of 107 kPa when the temperature is 22° C. If the
temperature changes to 45 °C, what will be the pressure of the helium in the balloon?
Example 3
A student collects 450. mL of HCl (g) hydrogen chloride gas at a pressure of 100. kPa and a temperature of 17° C.
What is the volume of HCl at 0° C and 101.3 kPa?
6. Ideal gas law-
PV = nRT
P= pressure in atm
V = volume in L
n = amount in moles
T = temp in Kelvin
R = ideal gas constant = 0.08206 L atm / mol K
MP = dRT
M= molar mass in g/mol
P = pressure in atm
d = density in g/L
T = temp in K
R = 0.08206 L atm/ mol K
Example 4
A student collects 425 mL of oxygen at a temperature of 24 °C and a pressure of 0.899 atm. How many moles of
oxygen did the student collect?
Example 5
Aluminum chloride sublimes at high temperatures. What density will the vapor have at 225 °C and 0.939 atm
pressure?
Dalton’s law of partial pressures
The total pressure of a mixture of gases is equal to the sum of the partial pressures of each gas in the mixture.
Ptot = P1 + P2 + P3…..
PA = χA(Ptot)
Gases collected over water:
Ptot= Pgas + PH2O or Pgas= Ptot-PH2O
Example 6:
Some hydrogen gas is collected over water at 10 °C and 105.5 kPa pressure. The total volume of the sample was
1.93 L. Calculate the volume of the hydrogen at STP.
Example 7:
A tank contains a mixture of 3.0 mol of N2, 2.0 mol of O2, and 1.0 mol of CO2 at 25 °C and a total pressure of 10.0
atm. Calculate the partial pressure (in torr) of each gas in the mixture.
Example 8:
What pressure exists in a 25.0 L tank that contains 50.1 g of O2 and 26.3 g of N2 at 27 °C?
GAS STOICHIOMETRY
Gas stoichiometry at STP
Molar volume of a gas = 22.4 L / mol
Example 9:
Consider the following reaction:
P4 (s) + 6H2 (g)  4PH3 (g)
What volume of hydrogen gas at STP is needed to react exactly with 2.51 g of phosphorus?
Example 10:
Consider the following unbalanced equation for the decomposition of nitrogen triiodide.
NI3 (s)  N2 (g) + I2 (s)
What volume of nitrogen gas is produced at 27 °C and 755 mm Hg if 1.24 g of nitrogen triiodide
decomposes?
KINETIC ENERGY AND VELOCITY
Average kinetic energy depends only on temperature
KE av= 3/2 RT
Average velocity depends on temperature and the mass
Urms= (3RT/m)1/2
Example 11:
Consider separate 1.0 L gaseous samples of H2, Xe, Cl2, and O2, all at STP.
a. Rank the gases in order of increasing average kinetic energy.
b. Rank the gases in order of increasing average velocity.
c. How can separate 1.0 L samples of O2 and H2 each have the same average velocity?
EFFUSION AND DIFFUSION
Diffusion EffusionGraham’s Law:
rate A = √MMB
rate B
√MMA
Example