Properties of Gases
Gases have low densities: the density of air is ~ 0.0012 g/cm3. Remember,
that the density of water is ~ 1 g/cm3. The low density is due to the fact that
the gas molecules are widely spaced. A gas exerts pressure: gases exert a
constant, uniform pressure on the walls of the container. This is a unique
property of gases and is independent of outside influences such as
gravitational forces.
When the gas molecules collide
with the walls of the container or
with each other they do so
without any loss in total kinetic E.
Gasses move rapidly in random straight lines and rarely
bump into each other. Gas molecules behave as if they
were independent particles: attractive forces between
them are negligible
Fig. 4-3, p.94
Gases can be compressed: that is, gases can be made
to occupy a smaller volume. Gases expand to fill the
container: the larger the space, i.e. the lower the force
pushing down on a gas, the more the gas will expand.
Fig. 4-1, p.92
Gases may be mixed together: The same gas or different
gases may be mixed together.
Units of Pressure
• The SI unit of measurement is the Pascal which is one
newton/m2; P = Force/area.
• 1 atm = 1.013 x 105 Pa = 101.3 kPa
• 1 atm = 101.3 bar
• 1 atm = 14.69 psi
• 1 atm = 760 mm Hg = 760 torr
Units of Temperature for gas
calculations
• Always expressed in Kelvin, K
• Remember: Tk = Tc + 273
Boyle’s Law: The Volume-Pressure Law
The pressure of a gas is inversely proportional to the
volume it occupies for a fixed quantity of gas at constant
temperature.
• P = k (1/V)
• For any gas, PV = k, a constant, and it follows that P1V1
= P2V2.
• If pressure increases, volume must decrease. And, if
pressure decreases, volume must increase.
Fig. 4-12c, p.104
Charles’s Law: The Volume-Temperature
Law
The volume of a fixed quantity of a
gas at constant pressure is directly proportional to the
absolute temperature
• V = kT
• For any gas, V/T = k, a constant, and it follows that V1/T1
= V2/T2.
• Since V and T are directly proportional to each other, if
one goes up the other must also go up, and if one goes
down, the other must go down.
Fig. 4-9c, p.100
Avogadro’s Law: Volume and Moles
Equal volumes of gases at the same temperature and
pressure contain the same number of molecules.
• The law follows that V is directly proportional to
n, moles, or
V1/n1 = V2/n2
The Ideal Gas Law
• Charles’s Law, Boyle’s Law and Avogadro’s Law
combine to yield the ideal gas law :
PV = nRT
R = universal gas constant = 0.08206 L atm/mol K
Most gases behave like an ideal gas at low pressure (1 atm
or lower) and high temperature (0 0C or higher)
The Combined Gas Law
• When there is no change in the number of moles
“n”, we can say that
(P1V1)/T1 = nR = (P2V2)/T2
or
(P1V1)/T1 = (P2V2)/T2
This is called the combined gas law. You do not
have to remember this equation, because you
can always use the idea gas equation instead.
Dalton’s Law of Partial Pressures
For a mixture of gases in a container, the total
pressure exerted is the sum of partial
pressures of the gases present.
The partial pressure of a gas is the pressure
that the gas would exert if it were alone in
the container.
Ptotal = P1 + P2 + P3
Ptotal = ntotal(RT/V)
STP: Standard Temperature and
Pressure!
• It is defined as temperature equal to 0 degrees
centigrade or (273 deg K) and a pressure of 1 atm: T =
0 ºC and P = 1 atm.
Then we can use PV = nRT to find that one mole of any
gas has a volume = 22.4 liters, the molar volume of
any ideal gas
V = nRT = (1.00 mol)(0.08206Latm/Kmol)(273K) = 22.4L
P
1.00 atm
At STP, one mole of an ideal gas
occupies exactly 22.4 L of volume
It Doesn’t Stop!!!!!
• Gay-Lussac’s Law: When gases react with
each other, the reacting volumes are always
in the ratio of small whole numbers, if
temperature and pressure are constant.
• 1 liter O2 reacts with 2 liters H2 to form 2 liters
water vapor 2 H2 + O2  2H2O
• Notice: With Gases, volumes can be used
like moles! Thanks to Gay-Lussac’s Law, We
don’t have to convert from liters to moles! We
can (later) do stoichiometry based on Liters
Gay-Lussac’s Law: When gases react with each other, the reacting
volumes are always in the ratio of small whole numbers, if
temperature and pressure are constant.
Fig. 13-1, p. 348
Stoichiometry with gases
• Two ways of doing stoichiometry with gases:
1.
Do the stoichiometry at STP and convert
to new conditions using P1V1/n1T1=P2V2/n2T2
You must remember that 1 mole = 22.4 liters
at STP
2.
Do the stoichiometry to get the moles and
plug moles and knowns into the ideal gas
equation. This is often faster.
Biggest problem with gas stoichiometry:
Juggling too many numbers. When you
have a comparison problem
• Make a
table:
1
Pressure
Volume
moles
Temperature
R
2
Examples
1.
The pressure of a gas is measured to be 2.79 x 105 Pa. Represent this
pressure in atm, torr, and psi.
Ans. 2.75 atm; 2.10 x 103 torr; 40.4 psi
2.
A steel tank of argon gas has a pressure of 34.6 atm. If all of the argon
is transferred to a new tank with a volume 456L, the pressure is
measured to be 2.94 atm. What is the volume of the original container?
Assume constant temperature. Ans. 38.7 L
3.
A sample of methane gas is collected at 285 K and cooled to 245 K. At
245 K the volume of the gas is 75.0 L. Calculate the volume of the
methane gas at 285 K. Assume constant pressure. Ans. 87.2 L
4.
Consider a gas with a volume of 9.25 L at 47 0C and 1 atm pressure. At
what temperature does this gas have a volume of 3.50 L and 1 atm
pressure? Ans. -152 0C (121K)
5.
If 4.35 g of neon gas occupies a volume of 15.0 L at a particular
temperature and pressure, what volume does 2.00 g of neon gas
occupy under the same conditions? Ans. 6.90 L
Additional Examples
1.
A 5.00 mol sample of oxygen gas has a pressure of 1.25 atm at 22 0C.
What volume does this gas occupy? Ans. 96.8 L
2.
Consider a sample of helium gas at 28 0C with a volume of 3.80 L at a
pressure of 3.15 atm. The gas expands to 9.50 L and the gas is heated
to 43 0C. Calculate the new pressure of the gas. Ans. 1.32 atm
3.
Equal masses of oxygen and nitrogen gas present in a container.
Which gas exerts the larger partial pressure? By what factor?
Ans. N2 exerts a partial pressure that is 1.14 times as great as the
partial pressure of O2.
4.
A sample of hydrogen gas occupies a volume of 15.0 L at STP. What
volume will this sample occupy at 22 0C and 2.50 atm. Ans. 6.48 L
5.
When subjected to an electric current, water decomposes to hydrogen
and oxygen gas: 2H2O (l)
2H2(g) + O2(g). If 25 g of water is
decomposed, what volume of oxygen gas is produced at STP?
Ans. 15.5 L
NaN3 → 2 Na + 3 N2 and 10 Na + 2 KNO3 → K2O + 5 Na2O + N2