The Gaseous State

1

• Chapter 6
• The Gaseous State

2
Solid Phase

• A solid has fixed shape and volume.

Solid Br2 at low temperature
3
Liquid Phase

• A liquid has fixed volume but no definite shape.
• The density of a solid or a liquid is given in
  g/mL.

Liquid Br2
4
Gas Phase

• A gas has no fixed volume or definite shape.
• The density of a gas is given in g/L whereas
  liquids and solids are in g/mL.

Gaseous Br2
5
Pressure of a Gas

• Pressure is the force per unit area exerted on a
  surface.
• The pressure of the atmosphere is measured with a
  barometer.

6
Manometers

• Both open and closed end manometers measure
  pressure differences.

7
Units of Pressure

• One atmosphere of pressure (1 atm) is the normal
  pressure at sea level. The SI unit of pressure
  is the pascal (Pa), but is a very small unit and
  is not used frequently by chemists.

1 atm 760 mm Hg 1 atm 101.3 kPa 1 atm
760 torr 1 atm 1.01 bar 1 torr 133.3
Pa 1 atm 29.9 in Hg 1 atm 14.7 psi
8
Boyles Law

• Increasing the pressure on a gas sample, by
  addition of mercury to an open ended manometer,
  causes the volume to decrease.

9
Boyles Law

• A plot of volume versus 1/P is a straight line.
• V k1 x

10
Example Changing P and V

• A sample of a gas occupies 5.00 L at 0.974 atm.
  Calculate the volume of the gas at 1.00 atm, when
  the temperature held is constant.

11
Charless Law

• A plot of volume versus temperature is a straight
  line.
• Extrapolation to zero volume yields absolute zero
  in temperature
• -273o C.
• V k2 x T, where T is given in units of kelvin.

12
Avogadros Hypothesis

• Equal volumes of gases at constant T and P
  contain the same number of particles.
• The pressure in both containers is the same,
  but the mass of the gases is different.

13
Avogadros Law

• A plot of the volume of all gas samples, at
  constant T and P, vs. the number of moles (n) of
  gas is a straight line.
• V k3 x n

14
Example Changing P, T and V

• A sample of a gas occupies 4.0 L at 25o C and
  2.0 atm of pressure. Calculate the volume at STP
  (T 0 oC, P 1 atm).

15
Test Your Skill

• A sample of a gas occupies 200 mL at 100o C. If
  the pressure is held constant, calculate the
  volume of the gas at 0o C.

16
Ideal Gas Law

• The ideal gas law combines the three gas laws
  into a single equation
• PV nRT
• where R 0.08206 L.atm/mol.K
• The volume of one mole of an ideal gas at STP is
  22.4 L

17
Ideal Gas Law Calculation

• Calculate the number of moles of argon gas in a
  30 L container at a pressure of 10 atm and
  temperature of 298 K.

18
Ideal Gas Law Calculation

• Calculate the number of moles of argon gas in a
  30 L container at a pressure of 10 atm and
  temperature of 298 K.
• PV nRT
• n
• n 12 mol

19
Molar Mass and Density

• The ideal gas law can be used to calculate
  density (mass/volume) and molar mass (mass/moles)
  of a gas.
• At constant pressure and temperature the density
  of a gas is proportional to its molar mass, so
  the higher the molar mass, the greater the
  density of the gas.

20
Example Molar Mass

• Calculate the molar mass of a gas if a 1.02 g
  sample occupies 220 mL at 95o C and a pressure of
  750 torr.

21
Gases and Chemical Equations

• The ideal gas law can be used to determine the
  number of moles, n, for use in problems involving
  reactions.
• The ideal gas law relates n to the volume of gas
  just as molar mass is used with masses of solids
  and molarity is used with volumes of solutions.

22
Example Gases with Equations

• Calculate the volume of O2 gas formed in the
  decomposition of 2.21 g of KClO3 at STP.
  2KClO3(s) 2KCl(s) 3O2(g)

23
Gas Volumes in Reactions

24
Example Gas Volumes in Reactions

• Calculate the volume of NH3 gas produced in the
  reaction of 4.23 L of H2 with excess N2 gas.
  Assume the volumes are measured at the same
  temperature and pressure.

25
Daltons Law of Partial Pressure

• The pressure exerted by each gas in a mixture is
  called its partial pressure.
• For a mixture of two gases A and B, the total
  pressure, PT, is PT PA PB

26
Pressure of a Mixture of Gases

27
Example Partial Pressures

• Calculate the pressure in a container that
  contains O2 gas at a pressure of 3.22 atm and N2
  gas at a pressure of 1.29 atm.

28
Mole Fraction

• Mole fraction (c, chi) is the number of moles of
  one component of a mixture divided by the total
  number of moles of all substances present in the
  mixture.
• cA cB cC 1
• The partial pressure of any gas, A, in a mixture
  is given by PA cA x PT

29
Mole Fraction

• Mole fraction of the yellow gas is 3/12 0.25
  and the mole fraction of the red gas is 9/12
  0.75

30
Example Partial Pressure

• Calculate the partial pressure of Ar gas in a
  container that contains 2.3 mol of Ar and 1.1 mol
  of Ne and is at a total pressure of 1.4 atm.

31
Collecting Gases over Water

• Water vapor is also present in a sample of O2 gas
  collected over water.

32
Example Collecting Gases

• Sodium metal is added to excess water, and H2 gas
  produced in the reaction is collected over water
  with the gas volume of 1.2 L. If the pressure is
  745 torr and the temperature 26o C, what was the
  mass of the sodium? The vapor pressure of water
  at 26o C is 25 torr. 2Na(s) 2H2O(l) H2(g)
  2NaOH(aq)

33
Kinetic Molecular Theory of Gases

• 1. Gases consist of small particles that are in
  constant and random motion.
• 2. Gas particles are very small compared to the
  average distance that separates them.
• 3. Collisions of gas particles with each other
  and the walls of the container are elastic.
• 4. The average kinetic energy of gas particles
  is proportional to the temperature on the Kelvin
  scale.

34
Average Speed of a Gas

• Gas particles move at different speeds.
• Average speed is called the root mean square
  (rms) speed, urms, and is the square root of the
  average squared speed.

Maxwell-Boltzmann distribution curves
35
Average Speed of a Gas

• R 8.314 J/mol.K molar mass in kilograms per
  mole

36
Effusion and Diffusion

• Effusion - the passage of a gas through a small
  hole into an evacuated space.
• Gases with low molar masses effuse more rapidly.
• Diffusion is the mixing of particles due to
  motion.

37
Deviations from Ideal Behavior

• Gases deviate from the ideal gas law at high
  pressures.

38
Deviations from Ideal Behavior

• The assumption that gas particles are small
  compared to the distances separating them fails
  at high pressures.
• The observed value of PV/nRT will be greater than
  1 under these conditions.

39
Forces of Attraction in Gases

• The forces of attraction between closely spaced
  gas molecules reduce the impact of wall
  collisions.
• These attractive forces cause the observed value
  of PV/nRT to decrease below the expected value of
  1 at moderate pressures.

40
Ideal Gases

• A gas (O2 below) deviates from ideal gas behavior
  at low temperatures (near the condensation point
  ) and high pressures.

41
van der Waals Equation

• The van der Waals equation corrects for
  attractive forces and the volume occupied by the
  gas molecules.
• a is a constant related to the strength of the
  attractive forces.
• b is a constant that depends on the size of the
  gas particles.
• a and b are determined experimentally for each
  gas.