CH 5 REVIEW – GAS LAWS
The gas laws show up on all portions of the AP test. It is critical that you have a good understanding of the Ideal Gas and all the other
gas laws that can derived from it (Charles’ Law – Avogadro’s Law – Boyle’s Law). The previously mentioned laws will show up
many times in the multiple choice section of the test (and you do not have the formula sheet for the MC section!) The Ideal Gas Law
shows up in problem solving (stoichiometry and Kp/Kc). You should also be familiar with the Kinetic Molecular Theory which
describes an Ideal gas. You also need to have an understanding of the van-der-Waal’s equation for a Real gas.
STANDARD PRESSURE
The following are all examples of standard pressure. 1 atm, 760 torr, 760 mm Hg, 101.3 KPa (kilopascals)
Know how to determine the pressure of an enclosed gas with a device called a manometer. Page 189 in your textbook.
IDEAL GAS LAW
PV = nRT
You should be able to use the Ideal Gas Law to determine every other gas law simply by knowing what is being held constant –
moving the constants to one side – and leaving the variables on the other.
EXAMPLE.
If temperature is being held constant then PV = k. This means that pressure and volume are inversely related to one another. If one
increases the other decreases. This is Boyle’s Law and the working equation for problem solving is P 1V1 = P2V2.
If the gas is in a rigid container, that is saying that volume is being held constant. The result is that an increase in Kelvin temperature
will result in a direct increase in pressure. This is sometimes referred to as Gay-Lussac’s Law – P/T = k. The working equation for
problem solving is P1/T1 = P2/T2.
If the gas is under constant pressure in a nonrigid container, then an increase in temperature will result in a direct increase in the
volume of the gas. This is Charle’s Law – V/T = k. The working equation is V1/T1 = V2/T2
If pressure and temperature are being held constant, then as the number of moles increase the volume of the gas increases. This
Avogadro’s Law – V/n = k. The working equation would be V1/n1 = V2/n2. This law is significant in that it states conditions under
which coefficients in a balanced equation can be used with volume – LITERS. The critical part is that it MUST be specified that the
gases are all at constant temperature and pressure (this is NOT STP!!!!!!!!!!!!!!)
Example Problems:
1. How many liters of ammonia can be produced from 10.0 L of N 2 gas reacting with 20.0 L of H2 gas?
N2 + 3H2  2NH3
2. A gas at 30.0 oC and 1.00 atm occupies a volume of 0.842 L. What volume will the gas occupy at 60.0 oC and 1.00 atm?
GAS STOICHIOMETRY AND STP
STP refers to a specific condition of 0oC for temperature (273K) and 1 atm. What is significant with this is that the volume of 1 mole
of ANY gas at STP is 22.4 L. Expect to find basic stoichiometry problems that will ask you to determine the volume of a gas at STP
given a certain amount of reactant(s). Also expect to find stoichiometry problems that
The Ideal gas law can be expressed in many forms that will include density and molar mass. Expect to find this on the multiple choice
portion of the test.
MM = dRT
P
3. An unknown gas has a density of 3.78 g/L at a pressure of 1.50 atm and 280.K. Calculate the molar mass of this gas.
Is this gas methane, ethane, propane, or butane?
4. HCl (g) can be prepared by the reaction of NaCl (s) with sulfuric acid. What mass of NaCl is required to prepare enough HCl
to fill a 340. mL cylinder to a pressure of 151 atm at 20.0 oC?
DALTON’S LAW OF PARTIAL PRESSURE
This is a very basic – but yet very important law. It simply says that the total pressure of a series of gases in a container is equal to the
sum of the individual partial pressures of the gases in the container.
Dalton’s Law of partial pressures is used most frequently when a gas is being produced by water displacement. There is the pressure
of the “wet gas” which is the pressure of the gas and pressure due to the water vapor. The pressure of the dry gas has the water vapor
pressure removed. The water vapor pressure is given in problems and depends on temperature. The higher the temperature the greater
the water vapor pressure will be.
MOLE FRACTION
Mole fraction is a unit of concentration that you frequently use with gases. Very simply it is the ratio of moles of a given gas
component in a mixture to the total number of moles in the mixture.
Xa = na /ntot
ntot = na + nb + nc
If you know the total pressure in the container, you can find the pressure exerted by each gas by using
Pa = XaPtot
5. A gaseous mixture of O2, H2, and N2 has a total pressure of 1.50 atm and contains 8.20 g of each gas. Find the partial pressure
of O2 gas in the mixture.
KINETIC MOLECULAR THEORY
The Kinetic Molecular Theory describes the behavior and properties of an ideal gas in the following manner.
1.
2.
3.
4.
The volume of the individual particles of a gas can be assumed to be neglible.
The particles of a gas are in constant motion. When they strike the walls of their container they exert a pressure on the walls
of the container.
The particles of a gas are assumed to exert no forces on each other – neither attractive forces nor repulsive forces.
The average kinetic energy of a collection of gas particles is directly proportional to the Kelvin (absolute) temperature of the
gas.
Root Mean Square Velocity
6. Calculate the root mean square velocity of oxygen molecules at 300 K.
It is important to realize that in the Kinetic Molecular Theory, statement 1 and 3 have no meaning in terms of a REAL GAS. A real
gas has particles that do volume. Real gas particles DO exert forces on each other – therefore affecting pressure.
7. Which gas deviates the least from ideal behavior – H2 or SO2?
All real gases behave most like an ideal gas under conditions of HIGH TEMPERATURE and LOW PRESSURE.
The REAL GAS law (van der Waal’s equation) adds corrections for volume (constant “b”) and pressure
(constant “a”)so that the IDEAL gas law becomes REAL under the following equation.
Remember, the observed pressure (what is real) will always be less than the Ideal pressure. You can never attain an ideal.
EFFUSION / DIFFUSION
Diffusion is the term used to describe the mixing of gases. Open a bottle of perfume and it DIFFUSES throughout the room.
Effusion is the term used to describe the rate at which a gas escapes through a tiny hole in its container to an evacuated container.
In problem solving it is important to remember Graham’s Law for both EFFUSION and DIFFUSION.
8. Which gas would effuse faster, argon or oxygen? How many times faster?
HOMEWORK: GAS LAW REVIEW
1. (AP FR Essay Question)
Represented above are five identical balloons, each filled to the same volume at 25°C and 1.0 atmosphere pressure with the pure gas
indicated.
(a) Which balloon contains the greatest mass of gas? Explain.
(b) Compare the average kinetic energies of the gas molecules in the balloons. Explain.
(c) Which balloon contains the gas that would be expected to deviate most from the behavior of an ideal gas? Explain.
(d) Twelve hours after being filled, all the balloons have decreased in size. Predict which balloon will be the smallest. Explain your
reasoning.
2. A gaseous mixture containing 7.0 moles of nitrogen, 2.5 moles of oxygen, and 0.50 mole of helium exerts a total pressure of 0.90
atmosphere. What is the partial pressure of the nitrogen?
(a) 0.13 atm
(b) 0.27 atm
(c) 0.63 atm
(d) 0.90 atm
(e) 6.3 atm
3. Hydrogen gas is collected over water at 24 °C. The total pressure of the sample is 755 millimeters of mercury. At 24 °C, the vapor
pressure of water is 22 millimeters of mercury. What is the partial pressure of the hydrogen gas?
(a) 22 mm Hg
(b) 733 mm Hg
(c) 755 mm Hg
(d) 760 mm Hg
(e) 777 mm Hg
4. A 2.00-liter sample of nitrogen gas at 27 °C and 600. millimeters of mercury is heated until it occupies a volume of 5.00 liters. If
the pressure remains unchanged, the final temperature of the gas is
(a) 68 °C
(b) 120 °C
(c) 477 °C
(d) 677 °C
(e) 950. °C
5. 2 K + 2 H2O ---> 2 K+ + 2 OH¯ + H2
When 0.400 mole of potassium reacts with excess water at standard temperature and pressure as shown in the equation above, the
volume of hydrogen gas produced is
(a) 1.12 L
(b) 2.24 L
(c) 3.36 L
(d) 4.48 L
(e) 6.72 L
6. A 2 L container will hold about 4 g of which of the following gases at 0 oC and 1 atm?
(a) SO2
(b) N2
(c) CO2
(d) C4H8
(e) NH3