Gases: Their Properties and Behavior

1
Chapter 9

• Gases Their Properties and Behavior

2
Properties of Gases

• There are 5 important properties of gases
• Confined gases exerts pressure on the wall of a
  container uniformly
• Gases have low densities
• Gases can be compressed
• Gases can expand to fill their contained
  uniformly
• Gases mix completely with other gases in the same
  container

3
Kinetic Molecular Theory of Gases

• The Kinetic Molecular Theory of Gases is the
  model used to explain the behavior of gases in
  nature.
• This theory presents physical properties of gases
  in terms of the motion of individual molecules
• Average Kinetic Energy ? Kelvin Temperature
• Gas molecules are points separated by a great
  distance
• Particle volume is negligible compared to gas
  volume
• Gas molecules are in rapid random motion
• Gas collisions are perfectly elastic
• Gas molecules experience no attraction or
  repulsion

4
Properties that Describe a Gas

• These properties are all related to one another.
• When one variable changes, it causes the other
  three to react in a predictable manner.

5
Gas Pressure (P)

• Gas pressure (P) is the result of constantly
  moving gas molecules striking the inside surface
  of their container.

6
Atmospheric Pressure

• Atmospheric pressure is the pressure exerted by
  the air on the earth.

• Evangelista Torricelli invented the barometer in
  1643 to measure atmospheric pressure.
• Atmospheric pressure is 760 mm of mercury or 1
  atmosphere (atm) at sea level.

What happens to the atmospheric pressure as you
go up in elevation?
7
Measurement of Gas Pressure

• Traditionally, the gas pressure inside of a
  container is measured with a manometer

8
Units of Pressure

• Standard pressure is the atmospheric pressure at
  sea level, 760 mm of mercury.
• Here is standard pressure expressed in other
  units

9
Gas Pressure Conversions

• The barometric pressure is 697.2 torr. What is
  the barometric pressure in atmospheres? In mm Hg?
  In Pascals (Pa)?

10
Gas Law Problems
11
Boyles Law (V and P)

• Boyles Law states that the volume of a gas is
  inversely proportional to the pressure at
  constant temperature.

• Mathematically, we write
• For a before and after situation

P1V1 P2V2
12
Boyles Law Problem

• A 1.50 L sample of methane gas exerts a pressure
  of 1650 mm Hg. What is the final pressure if the
  volume changes to 7.00 L?

(1650 mm Hg )(1.50 L)
354 mm Hg
7.00 L
13
Charles Law (V and T)

• In 1783, Jacques Charles discovered (while hot
  air ballooning) that the volume of a gas is
  directly proportional to the temperature in
  Kelvin.

• Mathematically, we write
• For a before and after situation

T ? V
14
Charles Law Problem

• A 275 L helium balloon is heated from 20?C to
  40?C. What is the final volume at constant P?

V1 T2
V2
rearranges to

T1
15
Gay-Lussacs Law (P and T)

• In 1802, Joseph Gay-Lussac discovered that the
  pressure of a gas is directly proportional to the
  temperature in Kelvin.

• Mathematically, we write
• For a before and after situation

T ? P
16
Gay-Lussacs Law Problem

• A steel container of nitrous oxide at 15.0 atm is
  cooled from 25?C to 40?C. What is the final
  volume at constant V?

P1 T2
P2
rearranges to
T1
(15.0 atm)(298 K)
11.7 atm
233 K
17
Avogadros Law (n and V)

• In the previous laws, the amount of gas was
  always constant.
• However, the amount of a gas (n) is directly
  proportional to the volume of the gas, meaning
  that as the amount of gas increases, so does the
  volume.

• Mathematically, we write
• For a before and after situation

n ? V
18
Avogadros Law Problem

• A steel container contains 2.6 mol of nitrous
  oxide with a volume 15.0 L. If the amount of
  nitrous oxide is increased to 8.4 mol, what is
  the final volume at constant T and P?

V1 n2
rearranges to
V2
n1
(15.0 L)(8.4 mol)
48.5 L
2.6 mol
19
Combined Gas Law

• When we introduced Boyles, Charles, and
  Gay-Lussacs Laws, we assumed that one of the
  variables remained constant.
• Experimentally, all three (temperature, pressure,
  and volume) usually change.
• By combining all three laws, we obtain the
  combined gas law

20
Combined Gas Law Problem

• Oxygen gas is normally sold in 49.0 L steel
  containers at a pressure of 150.0 atm. What
  volume would the gas occupy if the pressure was
  reduced to 1.02 atm and the temperature raised
  from 20oC to 35oC?

21
Molar Volume and STP

• Standard temperature and pressure (STP) are
  defined as 0?C and 1 atm.
• At standard temperature and pressure, one mole of
  any gas occupies 22.4 L.
• The volume occupied by one mole of gas (22.4 L)
  is called the molar volume.

1 mole Gas 22.4 L
22
Molar Volume Calculation Volume to Moles

• A sample of methane, CH4, occupies 4.50 L at STP.
  How many moles of methane are present?

23
Mole Unit Factors

• We now have three interpretations for the mole
• 1 mol 6.02 1023 particles
• 1 mol molar mass
• 1 mol 22.4 L (at STP for a gas)
• This gives us 3 unit factors to use to convert
  between moles, particles, mass, and volume.

24
Mole Calculation - Grams to Volume

• What is the mass of 3.36 L of ozone gas, O3, at
  STP?

25
Mole Calculation Molecules to Volume

• How many molecules of hydrogen gas, H2, occupy
  0.500 L at STP?

1.34 1022 molecules H2
26
Gas Density and Molar Mass

• The density of a gas is much less than that of a
  liquid.
• We can calculate the density of any gas at STP
  easily.
• You can rearrange this equation to find the Molar
  mass of an unknown gas too!

molar mass in grams (MM)
density, g/L
molar volume in liters (MV)
27
Calculating Gas Density

• What is the density of ammonia gas, NH3, at STP?
• 1.96 g of an unknown gas occupies 1.00 L at STP.
  What is the molar mass?

28
The Ideal Gas Law

• When working in the lab, you will not always be
  at STP.
• The four properties used in the measurement of a
  gas (Pressure, Volume, Temperature and moles) can
  be combined into a single gas law
• Here, R is the ideal gas constant and has a value
  of
• Note the units of R. When working problems with
  the Ideal Gas Law, your units of P, V, T and n
  must match those in the constant!

PV nRT
0.0821 atm?L/mol?K
29
Ideal Gas Law Problem

• Sulfur hexafluoride (SF6) is a colorless,
  odorless, very unreactive gas. Calculate the
  pressure (in atm) exerted by 1.82 moles of the
  gas in a steel vessel of volume 5.43 L at 69.5C.

30
Ideal Gas Law and Molar Mass

• Density and Molar Mass Calculations
• You can calculate the density or molar mass (M)
  of a gas.
• The density of a gas is usually very low under
  atmospheric conditions.

31
Ideal Gas Law and Molar Mass

• What is the molar mass of a gas with a density of
  1.342 g/L1 at STP?
• What is the density of uranium hexafluoride, UF6,
  (MM 352 g/mol) under conditions of STP?
• The density of a gaseous compound is 3.38 g/L1
  at 40C and 1.97 atm. What is its molar mass?

32
Gases in Chemical Reactions

• Gases are involved as reactants and/or products
  in numerous chemical reactions.
• Typically, the information given for a gas in a
  reaction is its Pressure (P), volume (V) (or
  amount of the gas (n)) and temperature (T).
• We use this information and the Ideal Gas Law to
  determine the moles of the gas (n) or the volume
  of the gas (V).
• Once we have this information, we can proceed
  with the problem as we would any other
  stoichiometry problem.

A (g) X (s) ? B (s) Y (l)
33
Reaction with a Gas

• Hydrogen gas is formed when zinc metal reacts
  with hydrochloric acid. How many liters of
  hydrogen gas at STP are produced when 15.8 g of
  zinc reacts?
• Zn (s) 2HCl (aq) ? H2 (g) ZnCl2 (aq)

Can use because at STP!
34
Reaction with a Gas

• Hydrogen gas is formed when zinc metal reacts
  with hydrochloric acid. How many liters of
  hydrogen gas at a pressure of 755 atm and 35C
  are produced when 15.8 g of zinc reacts?
• Zn (s) 2HCl (aq) ? H2 (g) ZnCl2 (aq)

Use because not at STP!
35
Daltons Law of Partial Pressures

• In a mixture of gases the total pressure, Ptot,
  is the sum of the partial pressures of the gases
• Daltons law allows us to work with mixtures of
  gases.

Ptot P1 P2 P3 etc.
36
Daltons Law of Partial Pressures

• For a two-component system, the moles of
  components A and B can be represented by the mole
  fractions (XA and XB).
• What is the mole fraction of each component in a
  mixture of 12.45 g of H2, 60.67 g of N2, and 2.38
  g of NH3?

n
n




1









B
A
X
X
X
X
B
A
B
A


n
n
n
n
B
A
B
A
37
Daltons Law of Partial Pressures

• Mole fraction is related to the total pressure
  by
• On a humid day in summer, the mole fraction of
  gaseous H2O (water vapor) in the air at 25C can
  be as high as 0.0287. Assuming a total pressure
  of 0.977 atm, what is the partial pressure (in
  atm) of H2O in the air?

38
Daltons Law of Partial Pressures

• Exactly 2.0 moles of Ne and 3.0 moles of Ar were
  placed in a 40.0 L container at 25C. What are
  the partial pressures of each gas and the total
  pressure?
• A sample of natural gas contains 6.25 moles of
  methane (CH4), 0.500 moles of ethane (C2H6), and
  0.100 moles of propane (C3H8). If the total
  pressure of the gas is 1.50 atm, what are the
  partial pressures of the gases?

39
Kinetic Molecular Theory of Gases

• The Kinetic Molecular Theory of Gases is the
  model used to explain the behavior of gases in
  nature.
• This theory presents physical properties of gases
  in terms of the motion of individual molecules.
• Average Kinetic Energy ? Kelvin Temperature
• Gas molecules are points separated by a great
  distance
• Particle volume is negligible compared to gas
  volume
• Gas molecules are in rapid random motion
• Gas collisions are perfectly elastic
• Gas molecules experience no attraction or
  repulsion

40
Kinetic Molecular Theory of Gases
41
Kinetic Molecular Theory of Gases

• Average Kinetic Energy (KE) is given by

42
Kinetic Molecular Theory of Gases

• The RootMeanSquare Speed (uRMS) is a measure
  of the average molecular speed of a particle of
  gas.

Taking square root of both sides gives the
equation
R 8.314 J/mol K
43
Kinetic Molecular Theory of Gases

• Calculate the rootmeansquare speeds (uRMS) of
  helium atoms and nitrogen molecules in m/s at
  25C.

44
Grahams Law Diffusion and Effusion

• Diffusion is the mixing of different gases by
  random molecular motion and collision.

• Effusion is when gas molecules escape without
  collision, through a tiny hole into a vacuum.

45
Grahams Law Diffusion and Effusion

• Grahams Law The rate of effusion is
  proportional to its RMS speed (uRMS).
• For two gases at same temperature and pressure

Rate ?
46
Grahams Law Diffusion and Effusion

• Under the same conditions, an unknown gas
  diffuses 0.644 times as fast as sulfur
  hexafluoride, SF6 (MM 146 g/mol). What is the
  identity of the unknown gas if it is also a
  hexafluoride?
• What are the relative rates of diffusion of the
  three naturally occurring isotopes of neon 20Ne,
  21Ne, and 22Ne?

47
Behavior of Real Gases

• Deviations from Ideal behavior result from two
  key assumptions about ideal gases.
• Molecules in gaseous state do not exert any
  force, either attractive or repulsive, on one
  another.
• Volume of the molecules is negligibly small
  compared with that of the container.
• These assumptions breakdown at high pressures,
  low volumes and low temperatures.

48
Behavior of Real Gases

• At STP, the volume occupied by a single molecule
  is very small relative to its share of the total
  volume
• For example, a He atom (radius 31 pm) has
  roughly the same space to move about as a pea in
  a basketball
• Lets say we increase the pressure of the system
  to 1000 atm, this will cause a decrease in the
  volume the gas has to move about in
• Now our He atom is like a pea in a ping pong ball
• Therefore, at high pressures, the volume occupied
  by the gaseous molecules is NOT negligible and
  must be considered.
• So the space the gas has to move around in is
  less than under Ideal conditions!

VReal gt VIdeal
49
Behavior of Real Gases

• At low volumes, particles are much closer
  together and attractive forces become more
  important than at high volumes.
• This increase in intermolecular attractions pulls
  the molecules away from the walls of the
  containers, meaning that they do not hit the wall
  with as great a force, so the pressure is lower
  than under ideal conditions.

PReal lt PIdeal
50
Behavior of Real Gases

• A similar phenomenon is seen at low temperatures
  (aka. The Flirting Effect)
• As molecules slow down, they have more time to
  interact therefore increasing the effect of
  intermolecular forces.
• Again, this increase in intermolecular
  attractions pulls the molecules away from the
  walls of the containers, meaning that they do not
  hit the wall with as great a force, so the
  pressure is lower than under ideal conditions.

PReal lt PIdeal
51
Behavior of Real Gases
52
Behavior of Real Gases

• Corrections for non-ideality require the van der
  Waals equation.

Correction for Intermolecular Attractions
Correction for Molecular Volume
VReal gt VIdeal
PReal lt PIdeal
n moles of gas a and b are constants given in
the problem
53
Behavior of Real Gases

• Given that 3.50 moles of NH3 occupy 5.20 L at
  47C, calculate the pressure of the gas (in atm)
  using
• (a) the ideal gas equation
• (b) the van der Waals equation. (a 4.17, b
  0.0371)
• Calculate the pressure exerted by 4.37 moles of
  molecular chlorine confined in a volume of 2.45 L
  at 38C. Compare the pressure with that
  calculated using the ideal gas equation. (a
  6.49 and b 0.0562)