Gases

1
Chapter 10

• Gases

2
Teacher Note

• The solutions to many of the calculations are
  worked out in a packet in the folder for Chapter
  10.

3
Barometers and Standard Atmospheric Pressure
4
Barometers and Standard Atmospheric Pressure

• Standard atmospheric pressure defined as the
  pressure sufficient to support a mercury column
  of 760mm (units of mmHg, or torr).

5
Barometers and Standard Atmospheric Pressure

• Standard atmospheric pressure defined as the
  pressure sufficient to support a mercury column
  of 760mm (units of mmHg, or torr).
• Another unit was introduced to simplify things,
  the atmosphere (1 atm 760 mmHg).

6
Barometers and Standard Atmospheric Pressure

• Standard atmospheric pressure defined as the
  pressure sufficient to support a mercury column
  of 760mm (units of mmHg, or torr).
• Another unit was introduced to simplify things,
  the atmosphere (1 atm 760 mmHg).
• 1 atm 760 mmHg 760 torr 101.325 kPa (page
  262).

7
STP standard temperature and pressure

• Standard temperature 0C or 273 K
• Standard pressure 1 atm (or equivalent)

8
Boyle's Law

• Pressure varies inversely with volume
• Volume varies inversely with pressure

The volume of a sample of gas is inversely
proportional to its pressure, if temperature
remains constant.
9
Boyles Law
10
Boyles Law Pressure Volume (Figure 10.6 (a)
page 263)
11
Boyles Law Pressure-Volume Relationships
1800 mL
12
Boyles Law Pressure-Volume Relationships
503 mm Hg
13
Charles' Law

• Effects of temperature on a gas
• Volume varies directly with Temperature

The volume of a quantity of gas, held at
constant pressure, varies directly with the
Kelvin temperature.
14
Charless Law
a
15
Charles Law Volume and Temperature (Figure 10.8
Page 266)
16
Charles Law and Absolute Zero

• Extrapolation to zero volume gives a temperature
  of
• -273C or 0 K

17
Charless Law Temperature-Volume Relationships
2.98 L
18
Charless Law Temperature-Volume Relationships
-167C
19
Pressure vs. Temperature

• Pressure varies directly with Temperature
• If the temperature of a fixed volume of gas
  doubles its pressure doubles.

20
Pressure vs. Temperature

• The pressure exerted by a gas is directly related
  to the Kelvin temperature.
• V is constant.

21
Pressure vs. Temperature
22
Example

• A gas has a pressure of 645 torr at 128C. What
  is the
• temperature in Celsius if the pressure increases
  to 1.50 atm?
• Pi 645 torr Pf 1.50 atm 760 torr
  1140 torr
• 1 atm
• Ti 128C 273
• 401 K Tf ?K

23
Solution

• T2 401 K x 1140 torr 709K
• 645 torr
• 709K - 273 436C

24
Combined Gas Law Problem

• A sample of helium gas has a volume of 0.180 L,
  a pressure of 0.800 atm and a temperature of
  29C. What is the new temperature(C) of the
  gas at a volume of 90.0 mL and a pressure of 3.20
  atm?

25
Combined Gas Law Problem

• A sample of helium gas has a volume of 0.180 L,
  a pressure of 0.800 atm and a temperature of
  29C. What is the new temperature(C) of the
  gas at a volume of 90.0 mL and a pressure of 3.20
  atm?

x 3.20 atm x 90.0 mL 0.800 atm
180.0 mL 604 K - 273
331 C
302 K
604 K
26
Combined Gas Law

• A 10.0 cm3 volume of gas measured 75.6 kPa and
  60.0?C is to be corrected to correspond to the
  volume it would occupy at STP.

6.12 cm3
27
Gay-Lussacs Law
Gay-Lussacs Law of combining volumes at a
given temperature and pressure, the volumes of
gases which react are ratios of small whole
numbers.
28
How many liters of steam can be formed from 8.60L
of oxygen gas?
17.2 L
29
How many liters of hydrogen gas will react with
1L of nitrogen gas to form ammonia gas?

• 3L H2

30
A
31
A
How many mL of hydrogen are needed to produce
13.98 mL of ammonia?
20.97 ml NH3
32
Avogadros Law Equal volumes of gases at the
same temperature and pressure contain the same
number of particles.
33
The molar volume of a gas at STP 22.4L
22.4 L
34
Ideal Gas

• An ideal gas is defined as one for which both the
  volume of molecules and forces of attraction
  between the molecules are so small that they have
  no effect on the behavior of the gas.

35
Ideal Gas Equation

• PVnRT

36
R values

A
a

I

• R values for atm and kPa on Page 272 in book.

37
Calculate the volume occupied by 0.845 mol of
nitrogen gas at a pressure of 1.37 atm and a
temperature of 315 K.
15.9 L
38
Find the pressure in millimeters of mercury of a
0.154 g sample of helium gas at 32C and
contained in a 648 mL container.
1130 mm Hg
39
An experiment shows that a 113 mL gas sample has
a mass of 0.171 g at a pressure of 721 mm Hg and
a temperature of 32C. What is the molar mass
(molecular weight) of the gas?
40.0 g/mol
40
Can the ideal gas equation be used to determine
the molar mass of a liquid?
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Homework

• Do the lab summary for The Molecular Mass of a
  Volatile Liquid. It is due ____.
• Attempt the pre-lab for The Molecular Mass of a
  Volatile Liquid. It is due ____.

43
Problem A volatile liquid is placed in a flask
whose volume is 590.0 ml and allowed to boil
until all of the liquid is gone, and only vapor
fills the flask at a temperature of 100.0 oC and
736 mm Hg pressure. If the mass of the flask
before and after the experiment was 148.375g and
149.457 g, what is the molar mass of the liquid?
57.9 g/mol
44
What is the density of methane gas (natural gas),
CH4, at 125oC and 3.50 atm?
1.71 g/L
45
Calculate the density in g/L of O2 gas at STP.

• 1.43 g/L

46
Daltons Law of Partial Pressure

• The total pressure in a container is the sum of
  the partial pressures of all the gases in the
  container.
• In a gaseous mixture, a gass partial pressure is
  the one the gas would exert if it were by itself
  in the container.
• Ptotal P1 P2 P3
• Ptotal 100 KPa 250 KPa 200 KPa 550
  KPa

47
Two 1.0 L containers, A and B, contain gases with
2.0 atm and 4.0 atm, respectively. Both gases are
forced into Container B. Find the total pressure
of the gas mixture in B.
P V Vmixture P
A 2.0 atm 1.0 L 2.0 atm
B 4.0 atm 1.0 L 4.0 atm
1.0 L
Total 6.0 atm
48
Daltons Law Problem

• Air contains oxygen, nitrogen, carbon dioxide,
  and trace amounts of other gases. What is the
  partial pressure of oxygen at standard conditions
  if the partial pressure of nitrogen, carbon
  dioxide, and other gases are 79.1 KPa, 0.04 KPa,
  and 0.94 KPa respectively?
• Ptotal PO2 PN2 PCO2 POther gases
• 101.3 KPa PO2 79.1 KPa 0.04 KPa
  0.94KPa
• PO2 101.3 KPa (79.1 KPa 0.04 KPa
  0.94KPa)
• PO2 21.2 KPa

49
Two 1.0 L containers, A and B, contain gases
with 2.0 atm and 4.0 atm, respectively. Both
gases are forced into Container Z (vol. 2.0 L).
Find the total pressure of mixture in Z.
50
Two 1.0 L containers, A and B, contain gases
with 2.0 atm and 4.0 atm, respectively. Both
gases are forced into Container Z (vol. 2.0 L).
Find the total pressure of mixture in Z.
PX VX VZ PX,Z
A 2.0 atm 1.0 L 2.0 L 1.0 atm
B 4.0 atm 1.0 L 2.0 L 2.0 atm
Total 3.0 atm
51
Find total pressure of the gas mixture in
Container Z.
1.3 L 2.6 L 3.8 L 2.3 L 3.2
atm 1.4 atm 2.7 atm X atm
52
Find total pressure of the gas mixture in
Container Z.
1.3 L 2.6 L 3.8 L 2.3 L 3.2
atm 1.4 atm 2.7 atm X atm
PX VX VZ PX,Z
A 3.2 atm 1.3 L 2.3 L 1.8 atm
B 1.4 atm 2.6 L 2.3 L 1.6 atm
C 2.7 atm 3.8 L 2.3 L 4.5 atm
Total 7.9 atm
53
Daltons Law
Zumdahl, Zumdahl, DeCoste, World of Chemistry
2002, page 422
54
Daltons Partial Pressures
Zumdahl, Zumdahl, DeCoste, World of Chemistry
2002, page 421
55
Daltons Law of Partial Pressures
The mole ratio in a mixture of gases determines
each gass partial pressure.
Total pressure of mixture (3.0 mol He and 4.0 mol
Ne) is 97.4 kPa. Find partial pressure of each
gas


56
Daltons Law of Partial Pressures
Total pressure of mixture (3.0 mol He and 4.0 mol
Ne) is 97.4 kPa. Find partial pressure of each
gas.


57
80.0 g each of He, Ne, and Ar are in a container.
The total pressure is 780 mm Hg. Find each gass
partial pressure.
58
80.0 g each of He, Ne, and Ar are in a container.
The total pressure is 780 mm Hg. Find each gass
partial pressure.
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61
Example A student generates oxygen gas and
collects it over water. If the volume of the gas
is 245 mL and the barometric pressure is 758.0
torr at 25oC, what is the volume of the dry
oxygen gas at STP? (Pwater 23.8 torr at 25oC)

• PO2 PT - Pwater 758.0 torr - 23.8 torr
  734.2 torr

62
Find the molar mass of an unknown gas if a 0.16 g
sample of the gas is collected over water and
equalized to a pressure of 781.7 torr and a
volume of 90.0 mL at a temperature of 28C .
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Find the molar mass of an unknown gas if a 0.16 g
sample of the gas is collected over water and
equalized to a pressure of 781.7 torr and a
volume of 90.0 mL at a temperature of 28C .

• 44 g/mol

65
Homework

• Do the AP sample problem (1999 Test question 5)
  in notebook. It will be included as part of your
  homework.
• Dont forget the pre-lab and lab summary for The
  Molecular Mass of a Volatile Liquid.

66
Gas Diffusion and Effusion
Graham's Law governs the rate of effusion
and diffusion of gas molecules.
67
Stink or Die
a
68
The Root Mean Square Speed Fig. 10.17 Page 285
69
To use Grahams Law, both gases must be at same
temperature.
diffusion particle movement from high to low
concentration
effusion diffusion of gas particles
through an opening
For gases, rates of diffusion effusion obey
Grahams law more massive slow less massive
fast
70
Gas Diffusion and Effusion
Graham's Law governs the rate of effusion
and diffusion of gas molecules.
Rate of diffusion/effusion is inversely
proportional to its molar mass.
71
Grahams Law

• Determine the relative rate of diffusion
  for krypton and bromine.

The lightest gas is Gas A and the heavier gas
is Gas B. Relative rate means find the ratio
vA/vB.
Kr diffuses 1.381 times faster than Br2.
72
Grahams Law

• A molecule of oxygen gas has an average speed
  of 12.3 m/s at a given temp and pressure. What
  is the average speed of hydrogen molecules at the
  same conditions?

73
Grahams Law
1
H2
2.0

• An unknown gas diffuses 4.0 times faster than
  O2. Find its molar mass.

The lightest gas is Gas A and the heavier gas
is Gas B. The ratio vA/vB is 4.0.
Square both sides to get rid of the square root
sign.
74
Kinetic Molecular Theory

• Theory developed to explain gas behavior.
• Theory of moving molecules.
• Assumptions
• Gases consist of a large number of molecules in
  constant random motion.
• Volume of individual molecules negligible
  compared to volume of container.
• Intermolecular forces (forces between gas
  molecules) negligible.
• Energy can be transferred between molecules, but
  total kinetic energy is constant at constant
  temperature.
• Average kinetic energy of molecules is
  proportional to temperature.

75
Kinetic Molecular Theory

• Kinetic molecular theory gives us an
  understanding of pressure and temperature on the
  molecular level.
• Pressure of a gas results from the number of
  collisions per unit time on the walls of
  container.
• Magnitude of pressure given by how often and how
  hard the molecules strike.
• Gas molecules have an average kinetic energy.
• Each molecule has a different energy.

76
Kinetic Molecular Theory
There is a spread of individual energies of gas
molecules in any sample of gas.
As the temperature increases, the average kinetic
energy of the gas molecules increases
77
Kinetic Molecular Theory

• As kinetic energy increases, the velocity of the
  gas molecules increases.
• Root mean square speed, u, is the speed of a gas
  molecules having the certain average kinetic
  energy.
• Average kinetic energy, ?, is related to root
  mean square speed, u

a
78
Kinetic Molecular Theory

• As kinetic energy increases, the velocity of the
  gas molecules increases.
• Root mean square speed, u, is the speed of a gas
  molecules having the certain average kinetic
  energy.
• Average kinetic energy, ?, is related to root
  mean square speed, u

a
79
How does this theory explain Boyles Law?
As the volume of a container of gas increases at
constant temperature, the gas molecules have to
travel further to hit the walls of the container.
There are fewer collisions by the gas molecules
with the walls of the container. Therefore,
pressure decreases. If temperature increases at
constant volume, the average kinetic energy of
the gas molecules increases. Therefore, there
are more collisions with the container walls and
the pressure increases.
80
How does this theory explain Charles Law?
If temperature increases at constant volume, the
average kinetic energy of the gas molecules
increases and they speed up. Therefore, there
are more frequent and more forceful collisions
with the container walls by the gas molecules and
the pressure increases.
81
Ideal Gases vs. Real Gases

• An ideal gas is an imaginary gas made up of
  particles with negligible particle volume and
  negligible attractive forces.

82
Ideal Gases vs. Real Gases

• In a Real Gas the molecules of a gas do have
  volume and the molecules do attract each other.
• Therefore anything that makes gas particles more
  likely to stick together or stay close to one
  another make them behave less ideally.

83
Real Gases Deviations from Ideal Behavior
As the pressure on a gas increases, the molecules
are forced into a smaller volume.

• As the volume becomes smaller, the molecules get
  closer together, and a greater fraction of the
  occupied space is actually taken up by gas
  molecules.
• Therefore, the higher the pressure, the less the
  gas resembles an ideal gas.

84
Real Gases Deviations from Ideal Behavior

• The smaller the distance between gas molecules,
  the more likely attractive forces will develop
  between the molecules.
• As temperature increases, the gas molecules move
  faster and are further apart.
• Also, higher temperatures mean more energy
  available to break intermolecular forces.
• Therefore, the higher the temperature, the more
  ideal the gas.

85
Real Gases and Ideal Behavior

• A real gas typically exhibits behavior closest to
  ideal gas behavior at low pressures and high
  temperatures.

86
Real Gases The van der Waals equation

• We add two terms to the ideal gas equation one to
  correct for volume of molecules and the other to
  correct for intermolecular attractions
• The correction terms generate the van der Waals
  equation
• where a and b are empirical constants.

a corrects for the effect of molecular
attractions (van der Waals forces), and b
corrects for the molecular volume
87
Real Gases The van der Waals equation

• We add two terms to the ideal gas equation one to
  correct for volume of molecules and the other to
  correct for intermolecular attractions
• The correction terms generate the van der Waals
  equation
• You will not be required to solve this equation
  but you should know its form and which variables
  need to be corrected.

a corrects for the effect of molecular
attractions (van der Waals forces), and b
corrects for the molecular volume
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