Section 5
Gases
1
Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General
Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline.
Gas Laws
• In the first part of this chapter we will examine
the quantitative relationships, or empirical
laws, governing gases.
• First, however, we need to understand the
concept of pressure.
2
Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General
Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline.
Pressure
• Pressure - force exerted per unit area of
surface by molecules in motion.
P = Force/unit area
– 1 atmosphere (atm) = 14.7 psi
– 1 atmosphere = 760 mm Hg = 760 Torr
– 1 atmosphere = 101,325 Pascals
– 1 Pascal
= 1 kg/m.s2
–1 atm = 0.101325 MPa = 1.01325 bar
3
Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General
Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline.
A mercury
barometer.
4
Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General
Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline.
Pressure Conversions
The pressure of gas in a flask is 797.7 mmHg. What is the
pressure in atm?
HW 37
Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General
Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline.
5
The Empirical Gas Laws
• Boyle’s Law: The volume of a sample of gas
at a constant temperature varies inversely
with the applied pressure.
V a 1/P [constant moles (n) and T]
or
P1  V1  P2  V2
6
Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General
Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline.
A Problem to Consider
• A sample of chlorine gas has a volume of 1.8 L
at 1.0 atm. If the pressure increases to 4.0 atm
(at constant temperature), what would be the
new volume?
HW 38
Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General
Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline.
7
The Empirical Gas Laws
• Charles’s Law: The volume occupied by any
sample of gas at constant pressure is directly
proportional to its absolute temperature.
V a Tabs
(constant moles and P)
or
V1
T1

V2
T2
8
Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General
Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline.
A Problem to Consider
• A sample of methane gas that has a volume
of 3.8 L at 5.0°C is heated to 86.0°C at
constant pressure. Calculate its new volume.
HW 39
Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General
Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline.
9
The Empirical Gas Laws
• Gay-Lussac’s Law: The pressure exerted by
a gas at constant volume is directly
proportional to its absolute temperature.
P a Tabs
(constant moles and V)
or
P1
T1

P2
T2
10
Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General
Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline.
A Problem to Consider
• An aerosol can has a pressure of 1.4 atm at
25°C. What pressure would it attain at 1200°C,
assuming the volume remained constant?
HW 40
Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General
Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline.
11
The Empirical Gas Laws
• Combined Gas Law: In the event that all
three parameters, P, V, and T, are changing,
their combined relationship is defined as
follows (at constant n):
P1V1
T1

P2V2
T2
12
Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General
Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline.
A Problem to Consider
• A sample of carbon dioxide gas occupies 4.5
L at 30°C and 650 mm Hg. What volume
would it occupy at 800 mm Hg and 200°C?
HW 41
Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General
Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline.
13
The Empirical Gas Laws
• Avogadro’s Law: Equal volumes of any two gases at
the same temperature and pressure contain the
same number of molecules.
Vn
at constant T & P
• The volume of one mole of gas is called the
molar gas volume, Vm.
• Volumes of gases are often compared at
standard temperature and pressure (STP),
chosen to be 0 oC (273 K) and 1 atm
pressure.
14
Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General
Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline.
The Empirical Gas Laws
• Avogadro’s Law
– At STP, the molar volume, Vm, that is, the
volume occupied by one mole of any gas, is
22.4 L/mol
at STP, 1 mol of any gas = 22.4 L
HW 42
Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General
Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline.
15
The Ideal Gas Law
• From the empirical gas laws, we See that volume
varies in proportion to pressure, absolute
temperature, and moles.
V  1/P
V  Tabs
Boyle' s Law
Charles' Law
Vn
Avogadro' s Law
V  nTabs /P
Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General
Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline.
16
The Ideal Gas Law
• This implies that there must exist a proportionality
constant governing these relationships.
V  nTabs /P
V " R" (
nTabs
P
)
where “R” is the proportionality constant referred
to as the ideal gas constant (independent of
gas).
Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General
Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline.
17
The Ideal Gas Law
• At STP, only missing “R”:
1 mol, 22.4 L, 273 K, 1 atm
R

VP
R  nT
(22.4 L)(1.00 atm)
(1.00 mol)(273 K)
Latm
0.0821 mol K
Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General
Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline.
18
The Ideal Gas Law
• Thus, the ideal gas equation, is usually
expressed in the following form:
PV  nRT
P is pressure (in atm)
V is volume (in liters)
n is number of atoms (in moles)
R is universal gas constant - 0.0821 L.atm/K.mol
T is temperature (in Kelvin)
19
Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General
Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline.
A Problem to Consider
• An experiment calls for 3.50 moles of chlorine
gas, Cl2. What volume would this be if the gas
volume is measured at 34°C and 2.45 atm?
HW 43
Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General
Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline.
20
Molecular Weight Determination
• In section 3 we showed the relationship
between moles and mass.
moles 
mass
molecular mass
or
n
m
Mm
21
Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General
Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline.
Molecular Weight Determination
• If we substitute this in the ideal gas equation,
we obtain
PV 
m
( Mm )RT
If we solve this equation for the molecular
mass, we obtain
mRT
Mm 
PV
Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General
Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline.
22
A Problem to Consider
• A 9.25 gram sample of an unknown gas
occupied a volume of 5.75 L at 25°C and a
pressure of 1.08 atm. Calculate its molecular
mass. Which of the following gases is most
likely to be the unknown gas - N2, O2, or HCl?
23
Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General
Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline.
Density Determination
• If we look again at our derivation of the
molecular mass equation,
PV 
m
( Mm )RT
we can solve for m/V, which represents
density.
m PM m
D 
V
RT
Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General
Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline.
24
A Problem to Consider
• Calculate the density of ozone gas, O3 (Mm =
48.0g/mol), at 50°C and 1.75 atm of pressure.
HW 44
Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General
Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline.
25
Stoichiometry Problems Involving Gas
Volumes
2 KClO3 (s)  2 KCl(s)  3 O 2 (g )
• Suppose you heat 0.0100 mol of potassium chlorate,
KClO3, in a test tube. How many liters of oxygen can you
produce at 298 K and 1.02 atm?
26
Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General
Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline.
Stoichiometry Problems Involving
Gas Volumes
Many air bags are inflated with N2 gas by the following rxn:
6NaN3 (s) + Fe2O3 (s)  3 Na2O (s) + 2Fe (s) + 9N2 (g)
How many grams of NaN3 would be needed to provide 75.0 L of
N2 gas at 25oC and 748 mmHg?
Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General
Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline.
HW 45
27
Partial Pressures of Gas Mixtures
• Dalton’s Law of Partial Pressures: the sum
of all the pressures of all the different gases
in a mixture equals the total pressure of the
mixture.
Ptot  Pa  Pb  Pc  ....
28
Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General
Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline.
Partial Pressures of Gas Mixtures
• The composition of a gas mixture is often
described in terms of its mole fraction.
– The mole fraction of a component gas is the
fraction of moles of that component in the total
moles of gas mixture.
n A PA
 A  Mole fraction of A 

n tot Ptot
29
Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General
Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline.
Partial Pressures of Gas Mixtures
• The partial pressure of a component gas, “A”,
is then defined as
PA   A  Ptot
– Applying this concept to the ideal gas equation,
we find that each gas can be treated
independently.
PA V  n A RT
30
Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General
Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline.
A Problem to Consider
A 10.0 L flask contains 1.031 g O2 and 0.572 g CO2 gases
at 18oC. What are the partial pressures of O2 and CO2?
What is the total pressure? What is the mole fraction of
O2 in the mixture?
Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General
Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline.
HW 46
31
Collecting Gases “Over Water”
• A useful application of partial pressures
arises when you collect gases over water.
– As gas bubbles through the water, the gas becomes
saturated with water vapor.
– The partial pressure of the water in this “mixture”
depends only on the temperature (vapor pressure of
water).
32
Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General
Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline.
A Problem to Consider
• Suppose a 156 mL sample of H2 gas was
collected over water at 19oC and 769 mm Hg.
What is the mass of H2 collected?
33
Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General
Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline.
34
Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General
Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline.
HW 47 & 48
Kinetic-Molecular Theory
of gases
A simple model based on the actions of individual atoms
• Volume of particles can be neglected but volume of
container cannot.
• Particles are in constant motion; move in straight
lines in all directions and at various speeds (smaller
mass, faster it moves).
• No inherent attractive or repulsive forces
• When molecules collide, the collisions are elastic
(total KE remains constant).
• The average kinetic energy of a collection of particles
is proportional to the temperature (K) – higher T,
greater KE
35
Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General
Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline.
Molecular Speeds; Diffusion and Effusion
• The root-mean-square (rms) molecular
speed, u – m/s, is a type of average
molecular speed, equal to the speed of a
molecule having the average molecular
kinetic energy. It is given by the following
formula:
3RT
u
Mm
36
Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General
Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline.
Molecular Speeds; Diffusion and Effusion
• Diffusion is the transfer of a gas through space or
another gas over time.
• Effusion is the transfer of a gas through a membrane
or orifice.
– The equation for the rms velocity of gases
shows the following relationship between rate of
effusion and molecular mass (inversely
proportional). Graham’s Law:
1
Rate of effusion 
Mm
Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General
Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline.
37
The rate of effusion of molecules from a container depends on
three factors:
1.) cross-sectional area of the hole (the larger it is; the more likely
molecules are to escape)
2.) the number of molecules per unit volume (conc of gas).
3.) the average molecular speed (affected by temp and molar
mass)
Therefore, temp, conc., molar mass, and size of hole affects rate
of effusion.
38
Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General
Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline.
Molecular Speeds; Diffusion and Effusion
• According to Graham’s law, the rate of
effusion or diffusion is inversely proportional
to the square root of its molecular mass. (for
same container at constant T & P). Following
relationship allows for comparison of gases:
Rate of effusion of gas " A"
M m of gas B

Rate of effusion of gas " B"
M m of gas A
39
Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General
Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline.
A Problem to Consider
• How much faster would H2 gas effuse through
an opening than methane, CH4?
Rate of H 2
M m (CH4 )

Rate of CH 4
M m (H 2 )
Rate of H 2
16.0 g/mol

 2.8
Rate of CH 4
2.0 g/mol
So hydrogen effuses 2.8 times faster than CH4
Material was developed by combining Janusa’s material with the lecture outline provided with Ebbing, D. D.; Gammon, S. D. General
Chemistry, 8th ed., Houghton Mifflin, New York, NY, 2005. Majority of figures/tables are from the Ebbing lecture outline.
HW 49
40