Gas Laws
Chapter 10
Boyle’s Law
The volume of a fixed quantity of gas at
constant temperature is inversely proportional
to the pressure.
P and V are
inversely proportional
• A plot of V versus P
results in an inverse
graph
• Therefore is the
pressure is doubled,
the volume will be
halved.
Boyle’s Law Practice Problem
• If I have 5.6 liters of gas in a piston at a
pressure of 1.5 atm and compress the gas
until its volume is 4.8 L, what will the new
pressure inside the piston be?
P1V1 = P2V2
(1.5 atm)(5.6 L) = (x)(4.8 L)
x = 1.8 atm
Charles’s Law
• The volume of a fixed
amount of gas at
constant pressure is
directly proportional to its
absolute temperature in
Kelvins.
• i.e.,
V =k
T
A plot of V versus T will be a straight line.
Charles’s Law Practice Problem
• If I have 45 liters of helium in a balloon at
250 C and increase the temperature of the
balloon to 550 C, what will the new volume
of the balloon be?
45L
x

298K 328K
x  50 L
Avogadro’s Law
• The volume of a gas at constant temperature
and pressure is directly proportional to the
number of moles of the gas.
• V1/n1 = V2/n2
• Mathematically, this means V = kn
Avagadro’s Law Practice
Problem
A 6.0 L sample at 25 °C and 2.00 atm of
pressure contains 0.5 moles of a gas. If an
additional 0.25 moles of gas at the same
pressure and temperature are added, what
is the final total volume of the gas?
Vf = (6.0 L x 0.75 moles)/0.5 moles
Vf = 4.5 L/0.5 Vf = 9 L
Ideal-Gas Equation
• So far we’ve seen that
V  1/P (Boyle’s law)
V  T (Charles’s law)
V  n (Avogadro’s law)
• Combining these, we get
nT
V
P
Ideal-Gas Equation
The constant of
proportionality is
known as R, the
gas constant.
Ideal-Gas Equation
The relationship
nT
V
P
then becomes
nT
V=R
P
or
PV = nRT
Ideal Gas Law Practice Problem
• If I have 4 moles of a gas at a pressure of
5.6 atm and a volume of 12 L, what is the
temperature?
PV=nRT
205 K
Densities of Gases
If we divide both sides of the ideal-gas
equation by V and by RT, we get
n
P
=
V
RT
Densities of Gases
• We know that
– moles  molecular mass = mass
n=m
• So multiplying both sides by the
molecular mass ( ) gives
m P
=
V RT
Densities of Gases
• Mass  volume = density
• So,
m P
d=
=
V RT
• Note: One only needs to know the
molecular mass, the pressure, and the
temperature to calculate the density of
a gas.
Molecular Mass
We can manipulate the density equation
to enable us to find the molecular mass
of a gas:
P
d=
RT
Becomes
dRT
= P