14.1 The Gas Laws
Objectives:
1. Describe the kinetic-molecular theory.
2. Use Boyle’s, Charles’ and Gay-Lussac’s Laws to predict changes in the
properties of a gas.
Kinetic Theory

Kinetic-Molecular Theory

The molecules of a gas display no attraction or repulsion.

Gases are separated by huge distances compared to their size.

Gases are composed of tiny particles in constant random motion.

The collisions between molecules are completely elastic.

Gases have the same average kinetic energy at a given temperature.

The Nature of Gases

Real gases do not conform to the postulates above, but behave
closely enough for us to make predictions about gas behavior.

The behavior of gases relate to four variables:

Pressure (P) – describes frequency of collisions of gas particles
with the wall of a container
○
Units = mmHg, Pa, kPa, atm, mbar, bar, etc.

Volume (V) – describes the space occupied by the movement of
the gas particles
○
Units = liters, m3, dm3

Moles (n) – describes the number of gas particles present in a
sample of gas in moles
○
Units = moles (of course)

Temperature (T) – describes the average kinetic energy of the
gas particles
○
Units must be Kelvin for calculations

Standard Temperature and Pressure (STP)

STP = 0oC (273K) and 1 atm (760mm Hg).

If the volumes of gases are known at STP, we can convert the
volumes to other temperatures or pressures.
Boyle’s Law

Robert Boyle – English Physicist (1627-1691)

The pressure and volume of a sample of gas at constant temperature
are inversely proportional.
PV = k
Where, k is constant for any sample of gas. Therefore, if you change pressure or
volume, you can use this expression to find the new volume or pressure.
P1V1 = P2V2
Charles’ Law

Jacques Charles – French Chemist (1746-1823)

The temperature and volume of a sample of gas at constant pressure
are directly proportional.
V = kT
Where, k is constant for any sample of gas. Therefore, if you change temperature
or volume, you can use this expression to find the new volume or temperature.
V1T2 = V2T1
2x Temperature
2 liters
1 liter
200 K
400 K
Gay-Lussac Law (P-T Relationship)

Joseph Gay-Lussac – French Chemist/Physicist (1778-1850)

The temperature and pressure of a sample of gas at constant volume
are directly proportional.
P = kT
Where, k is constant for any sample of gas. Therefore, if you change temperature
or pressure, you can use this expression to find the new pressure or temperature.
P1T2 = P2T1
The Gas Laws
Law
Constant Relationship Relationship
Formula
Boyle’s Law
T
P↑ V↓
P↓ V↑
P1/P2 = V2/V1
Charles’ Law
P
T↑ V↑
T↓ V↓
V1/T1 = V2/T2
Gay-Lussac Law
V
T↑ P↑
T↓ P↓
P1/T1 = P2/T2
T = Temperature, P = Pressure, V = Volume
14.2 The Combined Gas Law & Avogadro’s Principle
Objectives:
1. Use the Combined Gas law formula to predict changes in the properties of a
gas.
2. Describe how gas properties relate to the mole concept.
The Combined Gas Law

Boyle’s Law and Charles’ Law may be combined to help us find the
volume of gases at various temperatures and pressures.
new volume = old volume x
old pressure
new temperature
x
new pressure
old temperature
V2 = V1 x
P1
P2
x
T2
T1
Avogadro’s Principle

Amedeo Avogadro – Italian Chemist (1776-1856)

Equal volumes of different gases, at the same temperature and
pressure, contain the same number of molecules.
V=kn
Where, k is constant for any sample of gas. Therefore, if you change volume or
number of moles of gas, you can use this expression to find the new number of
moles or volume.
V1n2 = V2n1

Under the same conditions, the number of molecules in 1L of oxygen
is equal to the number of molecules of 1L of carbon dioxide or in 1L
of hydrogen.

This is useful because chemical reactions are governed by the
numbers of particles of a substance that interact, not the volume of
the substance that interacts.

All gases will have the same number of particles at standard
temperature and pressure (STP).

The volume of 1 mole of particles will be the same for all gases
(22.4 L).


22.4L of any gas at STP will contain 6.022 x 1023 molecules of
that gas.
22.4L is called the molar volume of a gas.
14.3 The Ideal Gas Law
Objectives:
1. Use the Ideal Gas Law Formula to determine properties of a gas.
2. Describe the conditions under which a gas deviates from ideal behavior.
3. Derive the value of R for a variety of pressure units.
The Ideal Gas Law Equation

The gas laws that describe the amount, temperature, volume, and pressure
of a gas can be combined into the following formula.
PV = nRT
Where
P
V
n
R
T
= Pressure
= Volume
= Number of moles
= The universal gas constant (0.0821 atmL/molK)
= Temperature

The Universal Gas Constant

If the Ideal Gas Law Equation is rearranged to solve for R at STP,
the value will be 0.0821 atmL/molK.

Note the units. This value is derived through the following
calculation.
PV
(1.00atm)(22.4L)
R=
=
= 0.0821atmL/molK
nT
(1.00mol)(273K)

The gas constant can be solved for a variety of units that describe a
gas at STP.

Deviations from Ideal Behavior

All real gases deviate from the properties of an ideal gas, but these
deviations are even greater at very high pressure and low
temperature.

Very High Pressure

Gases are pushed so close together that they begin to have a
noticeable volume compared to the container.

Very Low Temperature

When temperature is lowered, gas particles slow. Attractive
forces become more important and increase the effective
pressure operating on the particles. (Allows particles to
compress more.)
Applying the Ideal Gas Law

To find the number of moles of a substance present, the appropriate
conversion factor is:
mass (m)
number of moles (n) =
molar mass (M)

This may be substituted into the Ideal Gas Law Formula to get any
of the following:
PV =

mRT
mRT
or M =
M
PV
This may be further manipulated by remembering the formula for
density:
mass (m)
density (D) =
volume (V)
M=

mRT
MP
which may be
D=
PV rearranged to give us:
RT
All of these possible configurations of the Ideal Gas Law give us
many possible problem solving tools for dealing chemical
calculations (stoichiometry).
14.4 Gas Stoichiometry
Objectives:
1. Incorporate the concept of molar volume into stoichiometry calculations.
Calculations Involving Only Volume

Gaseous Reactions

In a homogenous gaseous reaction, the volumes of gasses reacted or
produced may be equated to the mole ratio since the particles all
have the same molar volume.

For example:
Find the volume of H2O produced from the reaction of 2L of H2 with
an excess of O2 according to the balanced reaction:
2H2 + O2 → 2H2O
2L H2
x
1 mol H2
2 mol H2O
22.4L H2O
x
x
= 2L H2O
22.4L H2
2 mol H2
1 mol H2O
2 moles of H2 produce 2 moles of H2O, so 2L of H2 produces 2L H2O