Chapter 12 pp. 470-508

1
Gases

• Chapter 12 pp. 470-508

2
General properties kinetic theory

• Gases are made up of particles that have
  (relatively) large amounts of energy.
• A gas has no definite shape or volume and will
  spread out to fill as much space as possible.
• A gas will exert a pressure on the walls of any
  container it is held in.
• As a result gases are easily compressed.

3
Pressure

• A pressure is exerted when the gas particles
  collide with the walls of the container. Pressure
  can be measured in a number of units.

1 atm 760 mmHg 760 torr 101325 Pa 101325
N/m2
4
Example 1

• Use the factor labeling method to perform the
  following conversions
• 1. 1,657 mmHg to N/m2
• 2. 832 torr to atmospheres
• 3. 17.8 kPa to atmospheres
• 4. 120,000 Pa to mmHg

5
Kinetic theory

• The kinetic theory can be summarized by the five
  postulates below
• 1. Gases are composed of tiny atoms or molecules
  (particles) whose size is negligible compared to
  the average distance between them. This means
  that the volume of the individual particles in a
  gas can be assumed to be negligible (close to
  zero).
• 2. The particles move randomly in straight lines
  in all directions and at various speeds.

6
The Rest of the Post

• 3. The forces of attraction or repulsion between
  two particles in a gas are very weak or
  negligible (close to zero), except when they
  collide.
• 4. When particles collide with one another, the
  collisions are elastic (no kinetic energy is
  lost). The collisions with the walls of the
  container create the gas pressure.
• 5. The average kinetic energy of a molecule is
  proportional to the Kelvin temperature and all
  calculations should be carried out with
  temperatures converted to K.

7
Pressure and Volume relationships Boyles Law

• Boyles Law states that, at constant temperature,
  pressure is inversely proportional to volume.
  This means that as the pressure increases the
  volume decreases and visa-versa.
• P1V1 P2V2

8
Example 2

• If a 1.25 L sample of a gas at 56 torr is
  pressurized to 250 torr at a constant temperature
  what is the new volume?
• 2. The pressure on a 415 mL sample of gas is
  decreased form 823 mmHg to 791 mmHg. What will
  the new volume of the gas be?

9
Volume and Temperature relationships Charless
Law

• Charless Law states that, at constant pressure,
  volume is directly proportional to temperature.
  This means the volume of a gas increases with
  increasing temperature and visa-versa.
• V1T2 V2T1

10
Example 3

• 1. A 12.0L sample of air is collected at 296K and
  then cooled by 15K. The pressure is held constant
  at 1.2 atm. Calculate the new volume of the air.
• 2. A gas has a volume of 0.672L at 35oC and 1 atm
  pressure. What is the temperature of a room where
  this gas has a volume of 0.535L at 1 atm?

11
Volume and Moles relationships Avogadros Law

• Avogadros Law states that, at constant
  temperature and pressure, volume is directly
  proportional to the number of moles of gas
  present. This means the volume of a gas increases
  with increasing number of moles and visa-versa.
• V1n2 V2n1

12
Example 4

• 1. A 13.3 L sample of 0.5 moles of oxygen gas is
  at a pressure of 1 atm and 25ºC. If all of the
  oxygen is converted to ozone (O3) what will be
  the volume of ozone produced?
• 2. If 2.11g of Helium gas occupies a volume of
  12.0L at 28ºC, what volume will 6.50g occupy
  under the same conditions?

13
The Ideal Gas Law

• The combination of Boyles, Charless
  Avogadros Laws leads to the formulation of the
  Ideal Gas Law.
• Most gases obey this law at temperatures above
  0ºC and at pressures of 1 atm or lower.
• PV nRT
• R 0.08206 Latm / molK

14
Different forms of Ideal GL

• n mass / MW so
• PV (m/MW)RT
• Density mass / V so
• D PMW / RT

15
The General Gas equation

• P1V1n2T2 P2V2n1T1
• If the number of moles of gas are constant in a
  problem, then we have the combined gas law
• P1V1T2 P2V2T1

16
Example 5

• 1. Assuming that the gas behaves ideally, how
  many moles of hydrogen gas are in a sample of H2
  that has a volume of 8.16L at a temperature of
  0ºC and a pressure of 1.2 atm?
• 2. A sample of aluminum chloride weighing 0.1g
  was vaporized at 350ºC and 1 atm pressure to
  produce 19.2cm3 of vapor. Calculate a value for
  the MW of aluminum chloride.

17
Deviations from ideal behavior

• At high pressures and low temperatures gas
  particles come close enough together to make the
  kinetic theory assumptions below become invalid
• Gases are composed of tiny particles whose size
  is negligible compared to the average distance
  between them, and
• The forces of attraction or repulsion between two
  particles in a gas are very weak or negligible
  (close to zero)

18
Non-Ideality (cont)

• At this point gases are said to behave
  non-ideally or like real gases. This has two
  consequences.

19
Non-Ideality (cont)

• Under these real conditions the actual volume
  occupied by the gas is smaller than one would
  expect when assuming the size of particles is
  negligible. Since in a small volume the size of
  the particles is not negligible, the observed
  volume is larger than it really is. This
  necessitates the need to correct the volume by
  subtracting a factor.

20
Non-Ideality (cont)

• Under these real conditions the actual pressure
  of a gas is higher than one would expect when
  assuming there was no attractive forces between
  the molecules. Because the particles are
  attracted to one another they collide with the
  walls with less velocity and the observed
  pressure is less than it really is. This
  necessitates the need to correct the pressure by
  adding a factor.

21
Van der Waals Equation for Real Gases
(P a(n/V)2)(V-nb) nRT
a and b are constants, where a corrects for
intermolecular forces and b corrects for
molecular volume
22
Example 6

• You want to store 165g of CO2 gas in a 12.5L tank
  at room temperature (25ºC). Calculate the
  pressure the gas would have using (a) the ideal
  gas law and (b) the van der Waals equation. (For
  CO2, a 3.59 atmL2/mol2 and b 0.0427 L/mol)

23
Molar Volume

• We have seen how Avogadro's law states that equal
  volumes of all gases at constant temp and
  pressure will contain equal numbers of moles.
• The volume of one mole of any gas is called its
  molar volume and can be calculated using the
  ideal gas equation.

PVm nRT
24
Molar Volume (cont)

• By applying the data, pressure (P) 1atm, temp
  (T) 273K, the gas constant (R) 0.08206
  Latmmol-1 K-1, number of moles (n) 1 mol, the
  molar volume (Vm) can be found.
• A simple calculation finds its value to be 22.4L.
• That is to say, for one mole of any ideal gas, at
  standard temp and pressure (s.t.p), the volume it
  occupies will be 22.4 L.

25
Example 7

• Calculate the mass of ammonium chloride required
  to produce 22L of ammonia (at s.t.p) in the
  reaction below.
• 2NH4Cl(s) Ca(OH)2(s) ? 2NH3(g) CaCl2(s)
  2H2O(g)

26
Example 8

• What mass of potassium chlorate must be heated to
  give 3.25L of oxygen at s.t.p?
• 2KClO3(s) ? 2KCl(s) 3O2(g)

27
Example 9

• Barium carbonate decomposes according to the
  equation below. Calculate the volume of carbon
  dioxide produced at s.t.p when 9.85g of barium
  carbonate is completely decomposed.
• BaCO3(s) ? BaO(s) CO2(g)

28
Example 10

• What volume of oxygen (at s.t.p.) is required to
  burn exactly 1.5L of methane (CH4)
• CH4(g) 2O2(g) ? CO2(g) 2H2O(g)

29
Distribution of Molecular Speeds

• When considering the kinetic theory postulate 2
  introduces the idea that all of the gas particles
  move at different speeds
• and postulate 5 that the speed (velocity), and
  therefore the kinetic energy, is dependent upon
  the temperature.

30
Greatest number of particles are moving with this
energy
Root Mean Square of the energy of the particles
A typical plot showing the variation in particle
speeds is shown below for hydrogen gas at 273K..
31
Root Mean Square

• The root-mean-square-speed is the square root of
  the averages of the squares of the speeds of all
  the particles in a gas sample at a particular
  temperature.

µrms (3RT / MW)1/2
Where R universal gas constant
8.3145 kgm2/s2 molK, T temperature in
Kelvin, MW molar mass of the gas in kg/mol.
32
Example 11

• Determine the µrms of hydrogen gas at 25ºC.
  Determine the µrms of nitrogen gas at 25ºC.
• Determine the µrms of argon gas at 25ºC.
• Determine the µrms of the gases in questions 1, 2
  and 3 at a temperature of 50ºC.
• What can be said quantitatively about the µrms of
  a gas in relation to its molar mass and its
  temperature?

33
Grahams Law of Effusion and Diffusion

• Effusion is the process in which a gas escapes
  from one chamber of a vessel to another by
  passing through a very small opening.
• Grahams Law of effusion states that the rate of
  effusion is inversely proportional to the square
  root of the density of the gas at constant
  temperature.

34
Grahams Law of Effusion and Diffusion

• Diffusion is the process by which a homogeneous
  mixture is formed by the random motion and mixing
  of two different gases.
• Grahams Law of diffusion states that the rate at
  which gases will diffuse is inversely
  proportional to the square roots of their
  respective densities and molecular masses.

35
Daltons Law of Partial Pressures

• Daltons Law states that in a mixture of gases
  the total pressure exerted by the mixture is
  equal to the sum of the individual partial
  pressures of each gas.
• PT P1 P2 P3 Pn