Chemistry - Dr. May Notes
Predicting Gas Behavior
Defining the Ideal Gas Law
We can combine all three gas laws (Charles’, Boyle’s, and Avogadro’s) to get the
Ideal Gas Law:
PV = nRT
R is the Universal Gas Constant and understanding how it is calculated will give
an example of what the other variables are. R is calculated at STP (Standard
Temperature and Pressure).
Under those conditions, P = 1 atm, T = 273 Kelvins (0oC), V = 22.4 liters, and n =
1 mole.
R ‗ PV ‗ 1.00 atm x 22.4 liters ‗ 0.0821 liter atm
nT
1.00 mole x 273 K
mole K
or if we want to use SI units, we will define it as:
(1 liter = 1 dm3 and 1 atm = 101.325 kPa)
R = 8.315 dm3 kPa
K mole
This whole exercise is to give you an idea of the Ideal Gas Law. R will be defined
as we need it. The R we use depends on what the units of the other variables are.
Applying the Ideal Gas Law
The most familiar form of the Gas Law is the combined Laws of Charles and
Boyle, assuming a constant number of moles (n) and, of course, the gas constant (R).
P1V1 ‗ nR ‗ P2V2
T1
T2
P1V1 ‗ P2V2
T1
T2
1
Gas Stoichiometry - STP and Molar Volume
There are several ways to calculate the volume of gas formed during a chemical
reaction. My preference is to calculate everything in STP then convert to the given
conditions using the Combined Gas Law above where P1, V1, and T1 are STP conditions
and P2, V2, and T2 are the given conditions.
We have already learned how to do everything at STP, just convert with the
Combined Gas Law!
Determining Volume Ratios
Coefficient Ratios (Constant temperature and pressure)
Balanced Equation
3H2
+
N2 
2NH3
Molecular Ratio
3
1
2
Mole Ratio
3
1
2
Volume Ratio
3
1
2
Explaining Gas Behavior - Deviations from Ideal Behavior
PV = nRT does not apply to every possible combination of temperature, pressure,
and volume. The Ideal Gas Law is intended for the ideal gas, which does not exist.
Kinetic Molecular Theory
Kinetic Molecular Theory
1. The molecules of an ideal gas are dimensionless points.
2. The molecules of an ideal gas are in constant, random, straight-line motion.
3. The average kinetic energy of the ideal gas molecules is proportional to the
absolute temperature of the molecules.
4. When molecules collide with each other, the collisions are elastic.
5. The molecules of an ideal gas do not exert any attractive or repulsive forces on
each other.
2
Graham’s Law and Diffusion
Diffusion is the ability of a gas to move from one place to another.
Graham’s Law can be mathematically represented:
vA/vB = √mB/mA
vA is the velocity of the molecules of substance A and mA is the molar mass of
the substance. The lighter gas has a greater velocity than the heavier gas. Hydrogen
would disperse faster than nitrogen, for example.
One way to use Graham’s Law is to determine the molar mass of an unknown gas.
An example may be: An unknown gas diffuses 4 times as fast as oxygen. What is the
molar mass of the gas? Using Graham’s Law, 1/ 4 = √molar mass of unknown/32.0
g/mole. Molar Mass of Unknown = 32.0 x 0.0625 = 2 g/mole. The unknown is, of
course, hydrogen.
Summary
The Ideal Gas Law is used to determine the properties of a volume of gas under
static conditions.
PV = nRT
We can express the equation as a function of each of the variables by solving for
them algebraically. These equations can then be used to solve for any of the four
variables when the other three are known and expressed in the proper units.
P ‗ nRT
V
V ‗ nRT
P
T ‗ PV
nR
n
‗ PV
RT
It is very important that the numbers used in calculations in the Ideal Gas Law
have the proper units.





R is the universal gas constant and is always 0.0821 when P is in atmospheres and
is always 8.3 when P is in kilopascals.
V is always in liters
P is in atmospheres or kilopascals ( 1 atm = 760 mm Hg or 1 atm = 101.32 kPa)
and must be matched up with the proper universal gas constant. (With
atmospheres use R = 0.0821 and with kilopascals use R = 8.3)
n is always in moles
T is always in Kelvins (To get Kelvins add 273 to oC)
3