### Dalton`s Law, Graham`s Law & Real vs. Ideal Gases

```Unit 9: Gases
Dalton’s Law of Partial Pressures, Grahams Law,
and Real vs. Ideal Gases
After today you will be able to…
• Describe Dalton’s law of partial
pressures and calculate Ptotal or a
partial pressure
• Explain Graham’s law of effusion
and calculate the rate at which
gases effuse
• Explain what is meant by the
term “real” vs. “ideal” gases
Recall, gas pressure results from
collisions of gas particles.
•Gas pressure depends on the
amount of gas and the KE of its
particles.
•Since particles in a mixture of
gases at the same temperature
contain the same average KE, the
kind of particle is unimportant.
Example: Composition of Dry Air
Component Volume Partial Pressure
Nitrogen
78.08%
79.11 kPa
Oxygen
20.95%
21.22 kPa
Carbon dioxide
0.04%
0.04 kPa
MISC gases
0.93%
0.95 kPa
Total 100.00%
101.32 kPa
“The total pressure
of a mixture of
gases is equal to
the sum of the
individual (partial)
pressures.”
Dalton’s Law of Partial Pressures
Ptotal= P1 + P2 + P3…
Units of pressure must match!
Example: Dalton’s Law
What is the total pressure for a mixture of O2 and
CO2 if PO2= 0.719 atm and PCO2= 423mmHg.
760mmHg
PO2= 0.719atm x
= 546mmHg
1atm
PCO2= 423mmHg
Ptotal=546mmHg + 423mmHg
Ptotal=969mmHg
Thomas Graham (1846)
•Diffusion: Is the tendency of gas
particles to spontaneously spread out
until uniformly distributed.
•Effusion: The escape of a gas through
a tiny pinhole in a container of gas.
–Gases with lower molar masses
effuse more quickly.
“The rate of
effusion of a gas is
inversely
proportional to the
square root of the
gas’s molar mass.”
Graham’s Law of Effusion
Rate A = √MMB
Rate B
√MMA
Always place the larger molar mass
in the numerator!
Example: Graham’s Law
Which gas effuses faster, H2 or Cl2? How much
faster?
Rate H2
√MMCl2
=
Rate Cl2
√MMH2
Rate H2
√(70.90)
=
Rate Cl2
√(2.02)
= 5.92x
H2 effuses
5.92x faster
than Cl2
Real vs. Ideal Gases
•The gas laws we’ve learned in this unit are based
on a gas that behaves “ideally.”
•An ideal gas has:
–No molecular volume
–No attractive forces
•In reality, there are no perfectly ideal gases. But,
under most conditions, real gases will approximate
ideal gas behavior.
•However, under certain conditions, real gases will
deviate from ideal gas behavior.
Real vs. Ideal Gases
•These deviations occur for:
1. High pressure: Gas particles are pushed closer
together, more attractive forces result.
2. Low Temperature: The gas is compressed,
there are more attractive forces.
3. High molar mass: Higher molar mass of the
molecule usually means larger volume.
4. Polar molecules: Unequal sharing of electrons
creates an attraction between molecules.
```