Unit 4
Gases
STP
Standard Temperature and Pressure
• Standard Temperature
– 0°C or 273 K
• Standard Pressure
– 1 atm, 760 mmHg, or 101.3 kPa
• Remember that these can be used for pressure
conversions
• Remember, at STP
1 mole of a gas occupies 22.4 L
Assumptions of the Kinetic
Molecular Theory
• The kinetic energy of an ideal gas is
directly proportional to its Kelvin
temperature.
• The volume of an ideal gas particle is
insignificant when compared with the
volume of the gas.
• There are no forces of attraction between
the gas molecules in an ideal gas.
• Gas molecules are in constant motion.
Kinetic Energy of Gases
• KE directly proportional to Kelvin temp
– The greater the temperature, the greater the
KE
• If Kelvin temp doubles, the KE doubles
• If several gases are present at the same
temperature, the gases will have the same
KE
– The average KE of a gas depends only on the
Kelvin temperature, not on the identity of the
gas
Two formulas
(you may need these formulas for an AP test)
• Total KE of a gas sample
KE = 3/2nRT
n = # moles
R = gas constant; 8.31J/mol·K
T = Kelvin temperature
• The Average KE of a single gas particle
KE = ½ mv2 m = mass in kg
v = speed in m/s
Initial/Final Conditions
• Any time you are given a problem with
initial/final conditions, you will need all or
part of the combined gas law (I have
added moles to the formula)
P1V1 P2V2
=
n1T1 n2T2
Individual Laws
• Any of the individual laws (Boyle’s Law,
Charles’ Law, Gay-Lussac’s Law, or
Avogadro’s Law) can be derived from this
law by throwing out the variable(s) that are
constant.
Boyle’s Law
• Use if temperature and # of moles are constant
• Pressure is inversely proportional to volume.
– If volume decreases, the pressure increases
– If volume increases, the pressure decreases
P1V1 = P2V2
Charles’ Law
• Use if pressure and # of moles are constant
• Volume is directly proportional to temperature.
– If temperature increases, the volume increases
– If temperature decreases, the volume decreases
V1 V2
=
T1 T2
Gay-Lussac’s Law
• Use if volume and # of moles are constant
• Pressure is directly proportional to temperature.
– If temperature increases, the pressure increases
– If temperature decreases, the pressure decreases
P1 P2
=
T1 T2
Avogadro’s Law
• Use if pressure and temperature are constant
• Volume is directly proportional to # of moles.
– As # moles increase, the volume increases.
– As # moles decrease, the volume decreases.
V1 V2
=
n1 n2
Something else to think about!
• When two or more gases are at the same
temperature and pressure AND have the
same volume, it means that they contain
the same number of particles
– which means that they contain the same
number of moles)
• They also have the same kinetic energy
– But, each gas has its own velocity (speed)
– Each gas has its own mass
How to solve these problems
• They will be word problems
• They will involve initial/final conditions
• Read the problem and pick out the given
information
• Pick out the variable you are trying to find
• Go find the formula needed
• Plug in and solve
Example
If 502 mL of a gas are collected at 29ºC and 96.0 kPa, what
is the volume at STP?
Ideal Gas Law
PV = nRT
P = pressure (atm, kPa, or mmHg)
V = volume (Liters or dm3)
n = # of moles
T = Kelvin temperature (must change ºC)
R = Ideal Gas Constant (depends on P unit)
Conditions for Ideal Gas Law
• You are assuming the particles are far apart
• The temperature should be high enough to
inhibit condensing action
• The pressure should be low enough to inhibit
condensing action
• They have no attractive or repulsive forces
interfering
– Therefore nonpolar gases will act more ideal
than a polar gas
Related Formulas
You need to be able to create these formulas
• Molecular mass
• Density of gas at other than STP
Example
How many moles of a gas will be in a 1250 mL flask
at 35ºC and a pressure of 95.4 kPa?
Density example
What is the density of chlorine gas at 298 K
and 3.50 atm?
Molecular Mass example
What is the molecular mass of a compound
if 300.0 mL of the gas has a mass of .855 g
at 270ºC and 755 mmHg?
Density of a gas at STP
• Density of any gas at STP can be determined
using the following formula
mass of one mole of gas
Density =
volume of one mole of gas
• What is the density of xenon gas at STP?
Example Density of gas @STP
What is the density of Xenon gas at STP?
Dalton’s Law of Partial Pressures
• Dalton’s law states that the total pressure
of a mixture of gases is just the sum of all
the partial pressures of the individual
gases in the mixture.
Ptotal = Pa + Pb + Pc + …
Several different scenarios
1. Given total pressure and all partial
pressures but one
2. Gas collected over water.
3. Given total pressure and percent
abundance information
4. Given total pressure and mole ratio
information (ie. Mole fraction…see next
slide)
Partial Pressure cont.
• You should also note that the partial
pressure of a gas is directly proportional to
the number of moles of that gas present in
the mixture.
– So it 25% of the gas in a mixture is helium,
then the partial pressure due to helium will be
25% of the total pressure.
Xa = mole fraction of gas
Pa = (Ptotal)(Xa)
Example 1
Determine the partial pressure of oxygen gas
collected over water if the temperature is 28ºC
and the total gas pressure is 98.74 kPa.
PH 2O at 28o C = 3.81kPa
Example 2
What is the partial pressure of hydrogen gas in a mixture of
hydrogen and oxygen gases if there are 3.8 moles of
hydrogen mixed with 4.9 moles of oxygen gas? The total
pressure is 845 mmHg.
Graham’s Law
• At a given temperature, lighter molecules
move faster than heavier molecules.
r1
M2
=
r2
M1
r = rate of effusion of a gas
or average speed of the molecules of a gas
M = molecular mass of the gas
Example
What is the ratio of speed of hydrogen molecules to
the speed of neon atoms when both gases are at the
same temperature and pressure?
What to know for test….
• Any gas law (Boyle, Charles, Gay-Lussac,
Avogadro, combined)
• Ideal Gas Law and related calculations
(density, molar mass)
• Partial pressure
• Graham’s law