I. Characteristics of a Gas
A) Gases assume the shape and
volume of a container.
B) Gases are the most compressible of
all the states of matter.
C) Gases will mix evenly and completely
when confined to the same container.
D) Gases have lower densities than
liquids or solids.
II. Historical Perspective
A) It was the first state studied in
detail.
B) It is the easiest state to understand
- for the purposes of general
chemistry, there is a simple
mathematical equation for the general
description of a gas which works well
in the real world, over a certain range
of temperatures and pressures.
C) The study of gases and its results
formed the primary experimental
evidence for our belief that matter is
made up of particles. MATTER IS
NOT CONTINUOUS.
III. Measurable Properties of a Gas
A) Mass - moles - symbol is n
B) Pressure - symbol is P
C) Volume - symbol is V
D) Temperature - must be in K symbol is T
Units of pressure and their
relationships are: 1 atm = 760 mm Hg
= 760 torr = 101.3 kPa = 14.7 psi =
29.92 inches of Hg
1) The volume of a gas is directly
proportional to the number of
molecules (moles) of gas at the same T
and P.
2) One mole of any gas occupies the
same volume for a given T and P and
contains the same number of particles
- atoms - molecules.
Boyle's Law: For a fixed
amount of gas and constant
temperature, PV =
constant.
Charles's Law: at constant
pressure the volume is
linearly proportional to
temperature. V/T =
constant
Gay-Lussac’s Law
 Old man Lussac studied the direct
relationship between temperature and
pressure of a gas.
• As the temperature increases the pressure a gas exerts on its container increases.
 During his experiments
volume of the system and
amount of gas were held
constant.
Dalton's Law = the sum of
the partial pressures of the
gases in a mixture = the total
pressure or P = PA + PB + PC
+ ...where Pi = the partial
pressure of component i.
Avagadro’s law for a
fixed pressure and
temperature, the volume of
a gas is directly
proportional to the number
of moles of that gas. V/n =
k = constant.
Avogadro's Law - EQUAL
VOLUMES OF DIFFERENT
GASES CONTAIN EQUAL
NUMBERS OF MOLECULES
WHEN MEASURED AT THE
SAME TERMPERATURE
AND PRESSURE.
Ideal gas law the functional
relationship between the
pressure, volume, temperature
and moles of a gas. PV = nRT;
all gases are ideal at low
pressure. V =nRT. Each of the
individual laws is contained in
this equation.
Ideal Gases
An “ideal” gas exhibits certain theoretical
properties. Specifically, an ideal gas …
• Obeys all of the gas laws under all conditions.
• Does not condense into a liquid when cooled.
• Shows perfectly straight lines when its V and T
& P and T relationships are plotted on a graph.
In reality, there are no gases that fit this
definition perfectly. We assume that gases
are ideal to simplify our calculations.
The Ideal Gas Law
PV = nRT
P = Pressure (in kPa)
V = Volume (in L)
T = Temperature (in K) n = moles
R = 8.31 kPa • L
K • mol
R is constant. If we are given three of P, V, n,
or T, we can solve for the unknown value.
From Boyle’s Law:
PiVi = PfVf or PV = constant
From combined gas law:
PiVi/Ti = PfVf/Tf or PV/T = constant
Developing the ideal gas law equation
PV/T = constant. What is the constant?
At STP: T= 273K, P= 101.3 kPa, V= 22.4 L/mol
Because V depends on mol,
PV = constant
we can change equation to: T • mol
Mol is represented by n,
PV = R
constant by R:
Tn
Rearranging, we get:
PV = nRT
At STP: (101.3 kPa)(22.4 L) = (1 mol)(R)(273K)
R = 8.31 kPa • L
K • mol
Note: always use kPa, L, K,
and mol in ideal gas law
questions (so units cancel)
Sample problems
How many moles of H2 is in a 3.1 L sample of
H2 measured at 300 kPa and 20°C?
PV = nRT P = 300 kPa, V = 3.1 L, T = 293 K
(300 kPa)(3.1 L) = n (8.31 kPa•L/K•mol)(293 K)
(300 kPa)(3.1 L)
= n = 0.38 mol
(8.31 kPa•L/K•mol)(293 K)
Ideal Gas Law Questions
1. How many moles of CO2(g) is in a 5.6 L sample
of CO2 measured at STP?
1. Moles of CO2 is in a 5.6 L at STP?
P=101.325 kPa, V=5.6 L, T=273 K PV = nRT
(101.3 kPa)(5.6 L) = n (8.31 kPa•L/K•mol)(273 K)
(101.325 kPa)(5.6 L)
(8.31 kPa•L/K•mol)(273 K)
= n = 0.25 mol
2. a) Calculate the volume of 4.50 mol
of SO2(g) measured at STP.
b) What volume would this occupy at
25°C and 150 kPa?
2. a) Volume of 4.50 mol of SO2 at STP.
P= 101.3 kPa, n= 4.50 mol, T= 273 K PV=nRT
(101.3 kPa)(V)=(4.5 mol)(8.31 kPa•L/K•mol)(273 K)
(4.50 mol)(8.31 kPa•L/K•mol)(273 K)
V=
= 100.8 L
(101.3 kPa)
2. b) Volume at 25°C and 150 kPa (two ways)?
Given: P = 150 kPa, n = 4.50 mol, T = 298 K
(4.50 mol)(8.31 kPa•L/K•mol)(298 K)
V=
= 74.3 L
(150 kPa)
3. How many grams of Cl2(g) can
be stored in a 10.0 L container
at 1000 kPa and 30°C?
3. How many grams of Cl2(g) can be stored in a
10.0 L container at 1000 kPa and 30°C?
PV = nRT P= 1000 kPa, V= 10.0 L, T= 303 K
(1000 kPa)(10.0 L)
= n = 3.97 mol
(8.31 kPa•L/K•mol)(303 K)
3.97 mol x 70.9
g/mol = 282 g
4. 98 mL of an unknown gas
weighs 0.087 g at STP.
Calculate the molar mass of the
gas. Can you determine the
identity of this unknown gas?
4. 98 mL of an unknown gas weighs 0.081 g at
STP. Calculate the molar mass.
PV = nRT P= 100 kPa, V= 0.098 L, T= 298 K
(100 kPa)(0.098 L)
= n = 0.00396 mol
(8.31 kPa•L/K•mol)(298 K)
g/mol = 0.081 g / 0.00396 mol = 20.47 g/mol
It’s probably neon
(neon has a molar mass of 20.18 g/mol)
Diffusion the process
whereby a gas spreads out
through another gas to
occupy the space with
uniform partial pressure.
Effusion the process in
which a gas flows through
a small hole in a container.