Section 13.2
Using Gas Laws to Solve Problems
Learning Goal: I will be able to…
… solve gas problems using the ideal gas law or
any other gas law.
Section 13.2
Using Gas Laws to Solve Problems
A. The Ideal Gas Law
• Boyle’s Law
• Charles’s Law
• Avogadro’s Law
Combined gas law: PV/T = k
PV = k (at constant T and n)
V/T = b (at constant P and n)
V/n = a (at constant T and P)
Volume depends on T, P, and n: V = R(Tn/P)
Combining and rearranging the equation gives the
ideal gas law:
PV = nRT
universal gas constant R = 0.08206 L atm/K mol
units must be P in atm, V in L, T in K
Section 13.2
Using Gas Laws to Solve Problems
The Ideal Gas Law
• Most gases obey this equation closely / behave ideally
at pressures of ~1 atm or lower, and ~0oC or higher.
• You should assume ideal gas behavior when working
your chemistry problems.
• This equation can be used to solve all types of gas law
problems:
1. List the initial and final conditions of the gas
2. If needed, convert P to atm, V to L, T to K
3. Rearrange the equation so that the quantities that
change are on one side and the quantities that
remain constant are on the other side; this will
simplify the equation: ex.: you may end up with
Boyle’s equation or Charles’ equation
Section 13.2
Using Gas Laws to Solve Problems
Example:
Initial Conditions
P1 = 0.454 atm
V1 = 3.48 L
T1 = 258 oK
Final Conditions
P2 = 0.616 atm
V2 = ?
T2 = 309 oK
(oK = oC + 273)
Notice that n is not given, but we know it has not changed.
PV = nRT should be rearranged as:
Change
Constant
PV
=
nR
T
which leads to P1V1 = nR = P2V2 and P1V1 = P2V2
T1
T2
T1
T2
Solving for V2 will give us the answer:
V2 = P1V1 T2 = 3.07 L
T1P2
Section 13.2
Using Gas Laws to Solve Problems
C. Gas Stoichiometry (covered before)
Molar Volume
• Standard temperature and pressure (STP)
– 0oC and 1 atm
• For one mole of a gas at STP
• Molar volume of an ideal gas at STP = 22.4 L
• Mole-mole ratio = liter-liter ratio for gases
Section 13.2
Using Gas Laws to Solve Problems
B. Dalton’s Law of Partial Pressures
• What happens to the pressure of a gas as we mix different
gases in the container?
• For a mixtures of gases in a container, the total pressure
exerted is the sum of the partial pressures of the gases
present.
Ptotal = P1 + P2 + P3
• The pressure of the gas is affected by the number of
particles
• The pressure is independent of the nature of the particles
Section 13.2
Using Gas Laws to Solve Problems
B. Dalton’s Law of Partial Pressures
Therefore:
• The volume of the individual particles is not very important.
• The forces among the particles must not be very important.
Section 13.2
Using Gas Laws to Solve Problems
B. Dalton’s Law of Partial Pressures (not in notes)
Collecting a gas over water
• Total pressure is the pressure of the gas + the vapor
pressure of the water.
Section 13.2
Using Gas Laws to Solve Problems
B. Dalton’s Law of Partial Pressures (not in notes)
Collecting a gas over water
• How can we find the pressure
of the gas collected alone?
13.3
Section 13.2
Using Gas Laws to Solve Problems
B. The Kinetic Molecular Theory of Gases
13.3
Section 13.2
Using Gas Laws to Solve Problems
D. Real Gases
• Gases do not behave ideally under conditions of high
pressure and low temperature. Why?
• At high pressure the volume is decreased
– Molecule volumes become important
– Attractions become important (London disp. forces)