Gases

1
Unit 5
Gases
2

• Day 2

3
Kinetic Theory

• All matter us made up of atoms
• These small particles are in constant motion and
  travel in straight lines
• All collisions are perfectly elastic

4

• Gases are in constant random motion.
• Volume of molecules is negligible compared to
  volume of container.
• No attractive or repulsive forces between
  molecules.
• Collisions are perfectly elastic.
• Average KE is proportional to absolute
  temperature of molecules

5
Characteristics of Gases

• Expand to fill their container
• Volume of gas volume container.
• Highly compressible
• Adding pressure shrinks volume
• Form homogenous mixtures with each other.

6

• These characteristics are a result of molecules
  being far apart.
• They behave as if other molecules are not
  present.
• Molecules of liquids and solids are closer
  together and occupy much more of the available
  space.

7
Absolute Temperature of a gas

• A measure of the average kinetic energy of the
  gas molecules.
• Molecular motion increases with increasing
  temperature.

8

• Under ordinary conditions (pressure
  temperature) many molecular compounds exist as
  gases.
• Liquids and solids can exist as gas under
  different circumstances.
• These are called vapors

9
Pressure

• Pressure (P) is a force (F) that acts on a given
  area (A).
• Gases exert a pressure on any surface they
  contact.

10
Atmospheric pressure and Barometer

• Atmospheric pressure is measured in N/m2, or
  Pascal (Pa), mmHg, or Torr.
• 1Pa 1 N/m2

11
Standard Atmospheric Pressure

• Typical pressure at sea level
• 760mm Hg (torr), 1.01325 x 105 Pa (or 101.325
  kPa), and 1 atmosphere (atm).
• Pa is the SI unit for pressure.

12
Mercury Barometers

• Glass tube more than 760 mm long and closed at
  one end.
• Invert into liquid mercury.
• Area in tube above mercury is a vacuum.

13
Pressure Manometers

• Manometer
• Device used in a lab to
  measure pressure of an
  enclosed gas.
• Works similar to a barometer

14
Determining Pressure of a Gas

• Closed manometer (see page 380)
• ?h Pgas
• Open Manometer (see page 380)
• Pgas Patm h vs Patm Pgas h

15

• Day 3

16
Gas Mixtures and partial pressures

• Daltons Law of partial pressures.
• The total pressure of a mixture of gases equals
  the sum of the pressures that each would exert if
  it were present alone.

17

• Each gas in a mixture behaves independently from
  the others.
• Total pressure at a constant T and V is
  determined by the total number of moles present.

18
Partial Pressure Mole Fractions

• Mole fraction is a number that expresses the
  ratio of the number of moles of one component to
  the total number of moles in a mixture of gases.

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• The partial pressure of a gas in a mixture is its
  mole fraction times the total pressure.
• P1 is pressure of gas 1 (n1 is moles)
• Pt is total pressure (nt is total moles)

20
Collecting gases

• Collecting gas over water you can find the gas
  pressure by using the equation
• Ptotal Pgas PH2O
• Partial pressure of water can be found in tables
  (appendix B)

21

• Day 4-5

22
The Gas Laws

• 4 Variables needed to describe state of a gas
• Temperature (T)
• Pressure (P)
• Volume (V)
• Number of moles (n)

23
Boyles Law(Pressure- Volume relationship)

• The volume of a fixed quantity of gas at a
  constant temperature is inversely proportional to
  the pressure.

24

• Volume versus pressure graph shows inverse
  relationship.
• The Volume versus 1/P is a linear relationship.

V
V
P
1/P
25

• A common way to express Boyles Law is
• P1V1P2V2

26
Charles Law

• The Temperature-Volume relationship.
• The volume of a fixed amount of gas at a constant
  pressure is directly proportional to its absolute
  temperature.

27
Charles Law

• Commonly expressed as

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Avogadro's Law

• The quantity-volume relationship
• The volume of a gas maintained at constant
  temperature and pressure is directly proportional
  to the number of moles of the gas.

29
The Ideal-Gas Equation

• We can combine the 3 laws into the ideal-gas
  equation

30

• R is the gas constant
• Units are dependent upon units of P, V, n.
• T must always be expressed as absolute
  temperature (K).
• n is usually expressed in moles
• Units for V and P are usually liters and atm.

31
STP
1atm 0ºC

• Standard temperature and pressure.
• T 0C (273.15K) 1 atm.
• Molar volume of an ideal gas at STP

22.41 L
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• The ideal gas equation does not always accurately
  describe gas behavior.
• Usually the difference between the ideal value
  and the real value is so small that we can ignore
  variations.

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• Calcium carbonate decomposes upon heating to give
  calcium oxide and CO2 gas. A sample of calcium
  carbonate is decomposed and the carbon dioxide is
  collected in a 250mL flask. The gas has a
  pressure of 1.3atm. at 31C. How many moles of
  CO2 were generated?

34
0.013 mol of CO2
35

• A tennis ball has a volume of 144cm3 and contains
  0.33 g of nitrogen gas. What is the pressure
  inside the ball at 24C?

36
Solution
2.0 atm
37
Using the Gas Laws
P1V1P2V2
Combined gas law
n constant
38

• What is the volume in liters occupied by 49.8 g
  of HCl at STP?

30.6 L

• A gas initially occupies 4.0 L, 66ºC 1.2atm
  undergoes a change so final volume is 1.7 L at
  42ºC. What is its final pressure? Assume the
  quantity is unchanged.

2.6 atm
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Using the Gas Laws
P1V1P2V2
Combined gas law
n constant
40

• A sample of oxygen gas initially at 0.97atm is
  cooled from 21ºC to -68ºC at a constant volume.
  What is its final pressure (in atm)?

0.68 atm
41

• Day 7

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Gas Densities and Molar Mass

• We can use the ideal gas equation to find the
  molar mass.
• Rearrange the equation

n/V has units of Moles per liter
43

• If you multiply both sides of the equation by the
  molar mass the units on the left become grams/ L
  (density).

44

• The density of a gas depends on the pressure,
  molar mass, and temperature of the gas.

45

• What is the density of Carbon tetrachloride vapor
  at 714 torr and 125ºC?

46
Solution
4.43 g/L
47

• What is the density of uranium hexaflouride at
  779 mmHg and 62ºC?

48
Solution
13.1 g/L
49
Volumes of Gases in Reactions

• Using the coefficients from balanced chemical
  equations we can find volumes of gases consumed
  or produced in a chemical reaction.

50

• Calculate the volume of O2 (in liters) required
  to complete the combustion of 14.9 L of butane at
  STP.

0.665 mol of butane
51

• What is the total pressure exerted by a mixture
  of 2.00g of hydrogen gas and 8.00g of nitrogen
  gas at 273 K in a 10.0 L container?

2.87 atm
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Daltons Law of Partial Pressure
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• Day 9

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• Molecules in a gas sample have an average KE and
  therefore an average speed.
• The individual molecules themselves have varying
  speeds.
• Average KE of the molecules

55
Distribution of molecular speed for N2 At 0ºC and
100ºC
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Application to Gas Laws

• Effect of volume increase at constant
  temperature.
• Same rms speed (fewer collisions with container)
• Temperature increase at constant volume.
• Increase in rms speed. (more collisions)

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• How is the rms speed of N2 gas changed by
• Increase in temperature
• Increase in volume
• Mixing with a sample of Ar at the same
  temperature.

a) Increase b) c) no effect
58
Effusion and Diffusion

• Average KE of any collection of gas molecules ½
  mu2, at a given Temperature.
• Lighter particles and heavier particles will have
  the same average KE.
• Lighter particles have higher rms.

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Effusion

• Escape of gas molecules through a tiny hole into
  an evacuated space. (see page 377)
• Diffusion
• spread of 1 substance throughout a space or
  another substance.

60
Grahams Law of Effusion

• Effusion rate of a gas is inversely proportional
  to the square root of its molar mass.

61

• The rate of effusion of a gas is inversely
  proportional to the time for the gas to effuse
  through a barrier.

62

• Compare the effusion rates of helium and
  molecular oxygen at the same temperature and
  pressure.

He effuses 2.827 times faster
63

• Compare the effusion rates of hydrogen and Xenon
  at the same temperature and pressure.

Hydrogen effuses 8.07 times faster
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• A flammable gas is made up of only hydrogen and
  carbon. A pure sample of the gas is found to
  effuse through a porous barrier in 1.50 minutes.
  Under identical conditions of temperature and
  pressure, it takes an equal volume of bromine gas
  4.73 minutes to effuse through the same barrier.
• Calculate the molar mass of the gas and suggest
  what the gas might be.

65
16.1g/mol
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Diffusion and Mean Free Path

• Diffusion is faster for lighter molecules.
• Follows Grahams Law
• Molecular collisions make diffusion more
  complicated than effusion.

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• Molecular collisions cause the direction of
  motion of the gas molecules to constantly change.
• Mean Free Path
• The average distance traveled by a molecule
  between collisions.

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Deviations from ideal behavior

• High Pressure causes deviation from ideal
  behavior.

69

• Temperature also affects ideal behavior.
• As temperature increases, properties of gases
  approach ideal behavior.

70

• Ideal gas molecules are assumed to occupy no
  space and have no attractions for one another.
• Real molecules have finite volumes and do attract
  one another.

71

• As pressure increases molecules are forced to be
  closer together. Increasing the effect of
  attractive forces. This causes a decrease the
  force with which the molecules hit the wall.
• Decreasing temperature takes away the energy
  needed for gas molecules to overcome their
  mutually attractive forces.