AP Chemistry
Ms. Grobsky

We have already considered 4 laws that describe the behavior of
gases
• Boyle’s law
𝑘
𝑃
(at constant T and n)
𝑉=
• Charles’ law
𝑉 = 𝑘𝑇
(at constant P and n)
• Amonton’s law
𝑃 = 𝑘𝑇
(at constant V and n)
• Avogadro’s law
𝑉 = 𝑘𝑛
(at constant T and P)

You may think a small gas molecule would take up less space than a large gas molecule,
but it doesn’t at the same temperature and pressure!

The gas laws discussed previously describe how gases
behave but not why they behave as they do
• Why does a gas expand when heated at constant pressure?
• Why does the pressure increase when a gas is compressed at constant
temperature?



More specifically, the four gas laws account for the
observed behavior of an ideal gas
To understand the physical properties of gases, we need a
model that helps us picture what happens to gas particles
when conditions such as pressure or temperature change
This model is known as the kinetic-molecular theory of
gases
Gasses consist of large number of particles are in
constant, random motion
 The combined volume of all the particles of a gas is
negligible relative to the total volume in which the
gas is contained
 Attractive and repulsive forces between gas
molecules are negligible
 All collisions between particles are perfectly elastic

• Energy is completely transferred between particles during
collisions
• However, the average kinetic energy of the particles do not
change with time (at constant temperature)

The average kinetic energy of the molecules is
proportional to its Kelvin temperature
• At any given temperature, the particles of all gases have the
same average kinetic energy
 If
the volume is decreased that means that the
gas particles will hit the wall more often
 Pressure is increased!
 When
a gas is heated,
the speed of its
particles increase
and thus, hit the walls
more often and with
more force
 Only way to keep pressure
constant is to INCREASE
the VOLUME of the
container!
 When
the
temperature of a gas
increases, the
speeds of its particles
increase
 The particles are hitting
the wall with greater
force and greater
frequency
 Since the volume remains
the same, this would result
in INCREASED gas
pressure
 An
increase in the number of particles at
the same temperature would cause the
pressure to increase if the volume were
held constant
 The only way to keep constant pressure is to vary the
volume!

The previous 4 relationships, which show how the volume of a gas
depends on pressure, temperature, and number of moles of gas
present, can be combined as follows:
Tn
V=R
P
• R is the combined proportionality constant called the universal gas constant
 Always use the value

0.08206 (0.0821)
𝐿∙𝑎𝑡𝑚
for R
𝐾∙𝑚𝑜𝑙
Equation can be rearranged to yield the more familiar ideal gas
law:
PV = nRT

The ideal gas law is an equation of state for a gas
• State of a gas is its condition at a given time

A gas that obeys this equation is said to behave ideally
• Expresses behavior that real gases approach at low pressures
and high temperatures
 Thus, an ideal gas is a hypothetical substance
 However, most gases obey the ideal gas equation closely enough at
pressure below 1 atm so assume ideal behavior unless stated otherwise
A
sample of hydrogen gas (H2) has a
volume of 8.56 L at a temperature of 0°C
and a pressure of 1.5 atm.
• Calculate the moles of H2 molecules present in
the sample.
A
sample of diborane gas (B2H6), a
substance that bursts into flame when
exposed to air, has a pressure of 345 torr at
a temperature of -15°C and a volume of 3.48
L.
• Calculate moles of diborane gas.
• If conditions are changed so that the temperature is
36°C and the pressure is 468 torr, what will be the
volume of the sample?


One very important use of the ideal gas law is the
calculation of the molar mass of a gas from its measured
density
Recall that:
grams of gas
mass
m
n=
=
=
molar mass
molar mass molar mass


Substituting the above into the ideal gas equation gives:
m
RT
nRT
m(RT)
molar
mass
P=
=
=
V
V
V(molar mass)
However, m/V is the gas density (d) in units of g/L
 Substituting
and rearranging for molar
mass:
dRT
Molar mass =
P
“Molar Mass Kitty Cat”
All good cats put dirt
[dRT] over their pee [P]
 The
density of a gas was measured at
1.50 atm and 27°C and found to be 1.95
g/L.
• Calculate the molar mass of the gas and give its
identity.
 Use
PV = NRT to solve for the volume of one
mole of gas at STP:
 Look
familiar? This is the molar volume of
a gas at STP

The volume that one mole of any gas takes up at 0°C
(273 K) and 1 atm
 Use
PV = nRT to solve for the volume of
one mole of gas at standard lab
conditions (SLC)
 This is the molar volume of a gas at
standard lab conditions (SLC)
 The volume that one mole of any gas takes up at 25°C
(298 K) and 1 atm
 Notice, the
STP!
volume increased from that at
• Satisfies Charles’s Law
 You
may use the molar volumes of a gas
at STP or SLC as a conversion factor when
doing stoichiometry
• Use stoichiometry to solve gas problems only if
gas is at STP or SLC conditions
• Use the ideal gas law to convert quantities that
are NOT at STP or SLC
 Quicklime
(CaO) is produced by the
thermal decomposition of calcium
carbonate (CaCO3).
• Calculate the volume of CO2 at STP produced
from the decomposition of 152 g CaCO3 by the
reaction:
CaCO3 s → CaO s + CO2 (g)
A
sample of methane gas (CH4) having a
volume of 2.80 L at 25°C and 1.65 atm
was mixed with a sample of oxygen gas
having a volume of 35.0 L at 31°C and
1.25 atm. The mixture was then ignited to
form carbon dioxide and water.
• Calculate the volume of CO2 formed at a
pressure of 2.50 atm and a temperature of 125°C