CHAPTER 10: GASES
AP Chemistry
Measurements of Gases
A. Volume, V
1. Definition: The amount of space an object or substance occupies
2. Common units: mL, L, cm3, dm3
 1 L = 1 dm3
 1 ml = 1 cm3
B. Amount, moles (n)
1. Definition: the amount of matter that contains 6.022 x 1023 species
2. One mole of an ideal gas has a volume of 22.4 L at STP (1.00 atm
and 0⁰C
C. Temperature, T
1. Definition: The average kinetic energy of the particles in an object or
substance
2. Units: K, ⁰C, or ⁰F
3. Absolute zero is 0 K or -273.15 ⁰C; so to convert from ⁰C to K, add
273.15
Measurements of Gases
D. Pressure, P
1. Definition: the force exerted per unit area
2. Units: mmHg, atm, Pa, kPa, torr, bar, psi
3. 1 atm = 760 mmHg = 760 torr = 14.70 psi = 101.3 kPa = 1.013 bar
Convert 0.95 atm to mmHg
0.95 atm
760 mm Hg
1.00 atm
= 720 mm Hg
Convert 95.9 kPa to atm
95.9 kPa
1.00 atm
101.3 kPa
= 0.947 atm
Measurement of Gases
E. “STP”
1. STP stands of Standard Temperature & Pressure
2. STP conditions: 273.15 K (0⁰C) & 1 atm
F. Manometers
Ideal Gas Laws
Background
1. Volume is directly proportional to absolute (K) temp.
As the temp of gas increases, volume increases
 V1/V2 = T1/T2
2. Volume is inversely proportional to pressure
As the pressure of a gas increases, volume decreases
P1V1 = P2V2
3. Pressure is directly proportional to the absolute (K) temp
As the temperature of gas increases, pressure increases
T1/T2 = P1/P2
4. Volume is directly proportional to the amount (moles)
As the moles of gas increases, volume increases
V1/V2 = n1/n2
Combined Gas Law
• Initial and Final State Problem
• A 1.5 L sample of air is moved from a room temp (25 ⁰C)
to Standard Temp (0 ⁰C). What is the new volume
• 0 ⁰C = 273 K; 25 ⁰C = 298 K
𝑉1
•
𝑉2
𝑇1
=
𝑇2
𝑉𝑇
• V2 = 1 2
𝑇1
• V2 = (1.5 L)(273 K) / 289 K
= 1.4 L
• A 5.00 ml sample of gas is collected in a syringe at STP.
What is the pressure if the volume is decreased to 3.00 ml
• Before
After
V= 5.00 ml
3.00 ml
T = constant
constant
P = 1.00 atm
?
P1V1 = P2V2
P2 =
𝑃1𝑉1
𝑉2
=
1.00 𝑎𝑡𝑚 (5.00 𝑚𝑙)
3.00 𝑚𝑙
= 1.67 atm
• A flask is filled with air at STP. The flask is sealed, then
heated with a Bunsen burner. How hot can the flask get
without exploding, if the maximum pressure the glass can
withstand is 3.00 atm?
• Before
After
•T=
•P=
• A 10.0 L vessel filled with He at STP is moved to a room
•
•
•
•
with a pressure of 765 mm Hg and a temp of 25 C. What
is the new volume?
Before
After
V=
T=
P=
Gas Mixtures, Pressures, Mole Fractions
A. Dalton’s Law
1. Equation: Ptotal = P1 + P2 + … Px
2. Examples
a. The gases in a balloon contribute the following partial
pressures: CO2 = 0.15 atm; O2 = 0.22 atm; N2 = 0.74 atm. Assuming
these are the only three gases in the balloon, what is the total
pressure? (Add them!)
Ptotal =
b. What is the pressure of dry hydrogen collected over water at
25⁰C if the pressure of the wet gas is 250.0 torr and the vapor
pressure is 23.8 torr at that temperature?
• A sample of oxygen gas has been collected over water
•
•
•
•
•
and has a volume of 22.50 ml at STP. What is the volume
of the dry gas at 22.0 C and 775 torr? Use the table in the
Appendix to look up vapor pressure of water.
Before
After
V=
T=
P*=
To get P1 for the dry gas, subtract the water vapor
pressure from P1
• A sample of oxygen gas has been collected over water
•
•
•
•
•
and has a volume of 45.0 ml at 22.0 C and 0.95 atm.
What is the volume of the dry gas at STP? Use the
appendix to look up vapor pressure of water.
Before
After
V=
T=
P=
Subtract the water vapor pressure from P1
Partial Pressure and Mole Fraction
• The mole fraction for a substance is calculated with this
equation:
XA =
𝑛𝐴
𝑛𝑡𝑜𝑡𝑎𝑙
(ntotal = sum of the moles of the mixture)
The mole fraction represents the fraction of the total
number of moles accounted for by the gas “A”
• Relationship between mole fraction and partial pressure
PA = (XA) (Ptotal)
• Example
• A gas mixture is composed of 0.200 moles of nitrogen and 0.450
moles oxygen. Calculate the mole fraction of each gas.
• XN2 =
0.200 𝑚𝑜𝑙
0.650 𝑚𝑜𝑙
= 0.308
• XO2 =
• Find partial pressures for each gas if the total pressure of the gas
mixture is 3.20 atm.
Ideal Gas Law
• PV = nRT
• Where R = 0.0821 atm L/mol K
Calculations:
1. What is the volume of 1.25 moles of helium gas at STP?
2. If 8.00 g of oxygen has a volume of 3.23 L at 1.50 atm, what is
the temperature?
3. What is the pressure of a 20.54 g sample of CH4 gas at 735 torr
and 25⁰C?
Calculation of Molar Mass and Density
• Use the Ideal Gas law in this form: d = MP/RT
1. What is the density of air at STP if the average molar mass of air
is 29.0 g/mol?
2. If the density of an elemental gas is 0.9002 g/L, what is its
identity?
Volumes of Gases Involved in Reactions
• The coefficients in a balanced chemical equation give the
mole ratios of the reactants and products.
• This law allows us to extend this relationship to volumes
of gases. (Also referred to a Avogadro’s Law)
• The law says that the volumes of different gases involved
in a reaction, if measured at the same temp and pressure,
are in the same ratio as the coefficients as the balanced
equation.
• 1.00 L of hydrogen reacts with the equivalent of nitrogen to
form ammonia gas, NH3. How much nitrogen is needed?
N2(g) + 3H2(g) → 2NH3(g)
1.00 L H2
1 mol H2 1 mol N2
22.4 L H2 3 mol H2
or more simply:
1.00 L H2
1 L N2
3 L H2
22.4 L N2
1 mol N2
= 0.333 L N2
= 0.333 L N2
• How much ammonia is formed from one liter of hydrogen?
Kinetic Theory of Gases (Day 2)
1. Kinetic Theory
1. Gases consist of particles in continuous, random
2.
3.
4.
5.
motion.
Collisions between gas particles are elastic
The volume occupied by the particles is negligibly
small.
Attractive forces between particles have negligible
effect on their behavior.
The average energy of translational motion of a gas
particle is directly proportional to the temperature.
Comparison on Matter in Terms of Kinetic
Energy
Shape
Type of motion
(vibration,
rotation, or
translation
Degree of
movement
Strength of
attractive
forces
compared to
kinetic energy
Constant
Constant
Vibrational
Low
KE<<AF
Constant
Variable
Vibrational,
Rotational
Medium
KE ≈ AF
Variable
Vibrational
rotational
translational
High
KE>>AF
Volume
(variable/
constant
Solid
Liquid
State
Gas
Variable
What happens to a liquid when it boils?
Attractive forces between molecules are broken but no chemical bonds
are affected; aka, the molecule stays intact.
Translational Energy, Et
• Equation – root-mean-square speed (rms)
• Et = mv2/2 = cTv
•
m is mass in kg, c is a constant, and T is in Kelvin
•
(Remember, 1 J = 1 kg m2/s2)
• Example: How much translational energy does an
oxygen molecule have it is moving at 2.0 m/s
• Et =
Average Speeds of Gas Particles
• Equation
• u2 =
3𝑅𝑇
𝑀
• M is molar mass (must be converted to kg/mol), T is in K;
R = 8.31 J/mol K; speed will be in m/s)
• OR
u=
3RT
M
• Example: Find the average (rms) speed of a hydrogen
molecule at 25 C.
•u=
Distribution of Molecular Speeds and
Energies (Day 3)
• Maxwell distribution
Notice that the higher the
average temperature, the
more variation there is in
the kinetic energy.
Diffusion and Effusion; Graham’s Law
1. Definitions:
1. Diffusion – the movement of gas particles through space from an
area of high concentration to an area of lower concentration
2. Effusion – the flow of gas through small spaces, holes, or pores
2. Equation/Explanation for Graham’s Law
1. At a given temp and pressure, the rate of effusion of a gas is
inversely proportional to the square root of its molar mass; it
follows that the heavier the gas, the slower it moves. r is the rate
of effusion and M is the molar mass.
• Which gas has the lowest average molecular speed?
Which has the highest?
• Which has the lowest average kinetic energy?
• Examples
• How many times faster does a hydrogen molecule diffuse than a
carbon dioxide molecule?
•
𝑟1
𝑟2
=
𝑀2/𝑀1 =
• Rank the following gases in order of increasing rate of effusion:
He, Xe, CO, O3, Cl2, Rn
Real Gases
• Theory
• Under ordinary conditions, gases behave ideally, but at extreme
conditions they deviate from the Ideal Gas Law
• At high pressure and low temperature, the gas is closer to the
liquid state. This causes it to deviate from the “ideal.”
• This change occurs because the ideal gas law neglects 2
postulates of kinetic theory: the finite volume of gas particles, and
the attractive forces btw molecules.
• Attractive Forces
• As pressure is increased, so do the attractive forces between particles.
This causes the volume to be smaller than anticipated.
• Particle Volume
• At high pressure the molar volume of gases will decrease from
ideal of 22.4 L/mol.
• The dotted line represents the answers you would get for n
(number of moles) using the ideal gas law at different
pressures; the colored lines represent the REAL values for
4 gases
• The dotted line represents the answers you would get for n
(number of moles) using the Ideal gas law at different
pressures; the colored lines represent three different
temperature conditions for the same gas.