Gases
Chapter 5
What you need to know…
•
PV = nRT for gas stoichiometry
•
Partial pressures for kinetics and equilibrium later
•
Water vapor pressure calculations
•
KMT for explaining behavior of atoms/molecules in
•
Gas laws (esp. graham’s law)
•
Differences between real and ideal gases (spec. what
causes deviations from ideal behavior)
Pressure & Temperature

Force per unit of area

Standard pressure is 1 atm (760 mmHg, 760 torr,
101.325 kPa)

Standard temp is 0oC (273 K)

ALL gas calculation must be done in K!!!
Gas Laws

Boyle’s: P1V1 = P2V2; as pressure goes up, volume
goes down (T & n stay constant)

Charles’: V1/T1 = V2/T2; as temp goes up, volume
goes up (P & n stay constant)

Gay-Lussac’s: P1/T1 = P2/T2; as temp goes up,
pressure goes up (V & n stay constant)

Avogadro’s: V1/n1 = V2/n2; as number of moles goes
up, volume goes up (P & T stay constant)
More gas laws

Avogadro’s other law: one mole of any gas at STP
will have a volume of 22.4 L

Combined: P1V1/T1 = P2V2/T2 (n stays constant)

One final law…
Ideal Gas Law
PV = nRT or PVM = mRT or MP = DRT
Where:
P = pressure (atm)
V = volume (L)
n = number of moles (mol)
R = ideal gas constant (0.0821 L atm/mol K
T = temp (K)
M = molar mass (g/mol)
m = mass (g)
D = density (g/L)
Ideal v. Real Gases
•
Ideal gas law is only an approximation of gas
behavior b/c there is no such thing as an ideal gas
•
Most gases behave close to ideal when the pressure is
below 1 atm and the temp is above 25oC
•
non-polar gases behave more ideal than polar
•
Smaller gases behave more ideal than larger ones
Ideal Practice
Gasoline is a mixture of many hydrocarbon
compounds, but its chemical formula can be
approximated as C8H18. How many liters of carbon
dioxide gas are formed at 25.0oC and 712 torr when
3.80 L of liquid gasoline is burned in excess oxygen?
Liquid gasoline has a density of 0.690 g/mL.
Partial Pressures

Dalton figured out that because gas particles are so
spread out, even when mixed with other gases they
don’t really interact, so their respective pressures
simply add up.

Ptotal = P1 + P2 + P3 + …

There’s also mole fraction: X1 = n1/nt

and ideal gas: P1 = n1RT/V

and partial pressure again: P1 = Pt(n1/nt)
What was all that stuff
again?

Mole fraction – ratio of moles of a specific gas to
total moles of gas in a mixture

Why is pressure the only thing affected by all these
gases?

Because volume and temp are the same for all gases in
the same container, only pressure adds up
Partial Pressures practice
A mixture of 9.00 g of oxygen, 18.0 g of argon, and
25.0 g of carbon dioxide exert a pressure of 2.54
atm. What is the partial pressure of each gas in the
mixture?
Water Vapor Pressure

The easiest way to collect gas in the lab is over water,
but this causes water vapor to be mixed in with the
gas.

To cancel this out, the water vapor pressure must be
added into the mix

To figure out the pressure of the gas collected: Patm =
Pwater + Pgas
Practice
Hydrogen is produced by the action of sulfuric acid on
zinc metal and collected over water in a 255 mL
container at 24.0oC and 718 torr. The vapor pressure
of water under these conditions is 22.38 torr. How
many moles of hydrogen gas are produced and how
many grams of zinc react?
Kinetic Molecular Theory

Know the 5 points of the KMT

Pressure is caused by gas particles hitting the walls of
the container (how often and how hard)

Absolute temp is measure if the kinetic energy of the
gas particles
Effusion and Diffusion

Effusion is gas escaping through a tiny hole

Diffusion is random mixing of gases through
space/another medium

Graham’s law inversely relates effusion rate and
molecular mass (heavier gases effuse/diffuse more
slowly)
r1/r2 = √(M1/M2)
where r is rate at which gas effuses (mol/time)
Effusion Practice
At a particular temperature and pressure, neon gas
effuses at a rate of 16.0 mol/s.

What is the rate of effusion for argon under the same
conditions?

Under a different set of conditions, 3.0 mol of argon
effuse in 49.0 seconds. How long will it take and equal
amount of helium to effuse?
van der Waals

van der Waals equation predict the behavior of real
gases at low temp &/or high pressure.

you do not need to know the equation, just that it
implies more deviation from ideal behavior under the
following conditions:

large molecular mass

low volume/high pressure

low temperature
More Practice
Arrange the following gases in order of increasing
deviation from ideal behavior: H2O, CH4, Ne. Justify
your reasoning.