Chemistry 100
Gases and Gas Laws
The Definition of a Gas


Gas - a substance that is
characterised by widely separated
molecules in rapid motion.
Mixtures of gases are uniform. Gases
will expand to fill containers.
Examples of Gaseous
Substances


Common gases O2 and N2, the major
components of "air"
Other gases F2, Cl2, H2  gaseous
diatomic molecules


H2 and He are the ‘lighter than air’ gases
N2O (laughing gas)
Three States of Matter
Solids
Liquids
Gases
Gases (cont’d)


Most molecular compounds are solids
or liquids at room temperature, but
they can be converted to a gas
relatively easily
Important exception  ionic solids
(e.g., NaCl) can't be easily coverted to
gases
Gases and Vapours

What is the difference between a gas
and a vapour?


Gases  normally in the gaseous state
at 25°C and 1 atm pressure
A vapour is the gaseous form of any
substance that is normally in the liquid or
solid state at normal temperatures and
pressures
The Definition of Pressure

The pressure of a gas is best defined
as the forces exerted by gas on the
walls of the container


Define
P = force/area
The SI unit of pressure is the Pascal
1 Pa = N/m2 = (kg m/s2)/m2
The Measurement of Pressure



How do we measure gas pressure?
Barometer - invented by Torricelli
Gas pressure conversion factors


1 atm = 760 mm Hg = 760 Torr
1 atm = 101.325 kpa = 1.01325 bar
The Barometer
The Gas Laws

Four variables were sufficient to fully
describe the state of a gas




Pressure (P)
Volume (V)
Temperature (T)
The amount of the gas in moles (n)
Boyle's Law


The gas volume/pressure relationship
The volume occupied by the gas is
inversely proportional to the pressure




V  1/P
Temperature and the amount of the gas
are fixed
V = k1/ P or PV = k1
k1 is a proportionality constant
Boyle's Law
Charles and Gay-Lussac's
Law

Defines the gas volume/temperature
relationship


V  T (constant pressure and amount of
gas)
Note T represents the temperature on
Lord Kelvin's temperature Scale
V = k2 T
k2  proportionality constant
Charles and Gay-Lussac's
Law
An Aside

The Kelvin temperature scale 



Lord Kelvin recognised the significance of
the intercept in the volume/temperature
relationship
All temperature (°C) vs. volume plots
extrapolated to 0 volume at -273.15°C
Kelvin - absolute 0
all thermal motion ceases
The Kelvin Temperature Scale

Relating Kelvin scale and the Celcius
scale





T (K) = [ tc (°C) + 273.15°C] K/°C
Freezing point of water: tc = 0 °C; T = 273.15
K
Boiling point of water: tc = 100 °C; T = 373.15
K
Room temperature: tc = 25 °C; T = 298 K
NOTE tc = C; T (K) = K NO DEGREE SIGN
Amonton’s Law


The pressure/temperature relationship
For a given quantity of gas at a fixed
volume, P  T
P = k3 T
P1 = k3T1
P2 = k3T2
 P1 / T1 = P2 / T2 Amonton's law
Amonton’s Law
V1
V2
V3
P/
atm
t = -273.15C
V4
t / C
Avogadro’s Law

The volume of a gas at constant T and
P is directly proportional to the number
of moles of gas
V = k4 n => n = number of moles of gas
Avogadro’s Law
The Ideal Gas Equation of
State

We have four relationships
V  1/P; Boyle’s law
V  T; Charles’ and Gay-Lussac's law
V  n; Avogadro’s law
P  T; Amonton’s law
Ideal Gas Equation of State

We combine these relationships into a
single fundamental equation of state
 the ideal gas equation
PV = nRT
R is the universal gas constant
R = 0.082057 L atm / (K mol)
= 8.314 J / (K mol)
The Definition of an Ideal Gas

An ideal gas is a gas that obeys totally
the ideal gas law over its entire P-V-T
range


Ideal gases - molecules have negligible
intermolecular attractive forces
Occupy a negligible volume compared to
the container volume
Standard Temperature and
Pressure

Define: STP (Standard Temperature
and Pressure)



Temperature  0.00 °C = 273.15 K
Pressure  1.000 atm
The volume occupied by 1.000 mole of
an ideal gas at STP is 22.41 L!
Gas Density Calculations


A simple expression for calculating the
molar mass of an unknown gas.
Molar mass and gas density
M = (dRT) / P
d = the gas density
Partial Pressures

Let's consider two ideal gases (gas 1
and gas 2) in a container of volume V.
2
1 2
1 2
1
2
2 1 2
1 1 2
1
Dalton's Law of Partial
Pressure

In a gaseous mixture,



each gas exerts the same pressure as if
it was alone and occupied the same
volume.
the partial pressure of each gas, Pi, is
related to the total pressure by Pi = Xi PT
Xi is the mole fraction of gas i.
Partial Pressures (cont’d)


The pressure exerted by the gases is
the sum of the partial pressures of the
individual gases
Let P1 and P2 be the partial pressures of
gas 1 and 2, respectively.
PT = P1 + P2 = nT (RT/V),
PT = n1 (RT/V) + n2 (RT / V)
The Mole Fraction


The mole fraction is defined as follows
For a two component mixture
n1 = moles of substance 1
n2 = moles of substance 2
nT = n 1 + n 2
X1 = n1 / nT; X2 = n2 / nT
Gas Collection Over Water
Gas Collection Over Water


Many gas measurements are carried
out over water.
Water vapour is collected with the gas.
PT = Pgas + PH2O
Kinetic Molecular Theory of
Gases


Macroscopic (i.e., large quantity)
behaviour of gases.
The kinetic molecular theory of gases
attempts to explain the behaviour of
gases on a molecular level.
Kinetic Theory of Gases




Gases consist of molecules widely separated
in space. Volume of molecules is negligible
compared to total gas volume.
Gas molecules are in constant, rapid, straightline motion. Collisions are elastic.
Average kinetic energy (K.E.) of molecules
depends on absolute temperature (T) only.
Attractive forces between molecules are
negligible.
Kinetic Theory of Gases
Gas Laws Explanations


Gas pressure results
from collisions of gas
molecules with the
container walls.
Pressure depends on


the number of
collisions per unit time
how hard gas
molecules strike the
container wall!
Avogadro’s Law

Let's increase the amount of gas in the
container (T, P constant)
More collisions of gas with container wall.
V  n at constant P, T.
Boyle's Law

Let's decrease the volume of the
container (constant n and T).
More collisions of the gas molecules with
the container wall and P increases. (V  1/P)
Charles’ and Gay-Lussac’s
Law

Let container volume increase (P, n
are held constant).
High Temp.
Low Temp.
The molecules
must move faster
T must increase.
Molecular Speeds
K.E. = 1/2 M U2
M = the molar mass of the gas
U2 =the mean square speed of the gas

This speed is an average speed (some
will always be fast, some slow).
The Mean Square Speed


Kinetic Molecular Theory of Gases
allows us to relate macroscopic
measurements to molecular quantities
P, V are related to the molar mass and
mean square seed, U2
P V = 1/3 n M U2 = n R T
The Root Mean Square Speed
1/3 MU2 = RT
U2 = 3RT / M
(U2)1/2 = urms = (3RT/M)1/2
urms = the root mean square speed
The Root Mean Square Speed
The Mean Free Path


Gas molecules encounter collisions
with other gas molecules and with the
walls of the container
Define the mean free path as the
average distance between successive
molecular collisions
The Mean Free Path
The Mean Free Path

As the pressure of the gas increases,
the mean free path decreases, i.e., the
higher the pressure, the greater the
number of collisions encountered by a
gas molecule.
Diffusion


Diffusion - gradual mixing of gas
molecules caused by kinetic
properties.
Graham's Law  Under constant T, P,
the diffusion rates for gaseous
substances are inversely proportional
to the square roots of their molar
masses.
Graham’s Law
r1/r2 = (M2 / M1)1/2


r1 and r2 are the diffusion rates of gases 1
and 2.
M1 and M2 are the molar masses of gas 1
and gas 2, respectively.
Effusion

Effusion - the process by which a gas
under pressure goes (escapes) from
one compartment of a container to
another by passing through a small
opening.
Effusion
The Effusion Equation

Graham’s Law - estimate the ratio of
the effusion times for two different
gases.
t1/t2 = (M1 / M2)1/2


t1 and t2 are the effusion times of gases 1
and 2.
M1 and M2 are the molar masses of gas 1
and gas 2, respectively.
Deviations from Ideal Gas
Behaviour


The ideal gas equation is not an
adequate description of the P,V, and
T behaviour of most real gases.
Most real gases depart from ideal
behaviour at deviation from


low temperature
high pressure
Deviations from Ideal Gas Behaviour
at Low Temperatures
Deviations from Ideal Gas
Behaviour at High Pressures
Deviations from Ideal
Behaviour

Look at assumptions for ideal gas

Real gas molecules do attract one
another.
(i.e., Pid = Pobs + constant).

Real gas molecules do not occupy an
infinitely small volume (they are not point
masses).
(Vid = Vobs - const.)
The Van der Waal’s Equation
Vid = Vobs - nb where b is a constant for
specific different gases.
Pid = Pobs + a (n / V)2 where a is also
different for different gases.
Ideal gas Law Pid Vid = nRT
The Van der Waal's Equation
(cont’d)


(Pobs + a (n / V)2) x (Vobs - nb) = nRT
Van der Waals’s equation of state for
real gases.
Two constants (a, b) that are
experimentally determined for each
separate gas

Table 10.3 in text.