Chapter 14 Gas Laws

1
Chapter 14Gas Laws
2
Standards
Students know how to apply the gas laws to
relations between the pressure, temperature, and
volume of any amount of an ideal gas or any
mixture of ideal gases.
3
Daltons Law of Partial Pressures

• For a mixture of gases in a container,
• PTotal P1 P2 P3 . . .

This is particularly useful in calculating the
pressure of gases collected over water.
4
Daltons Law of Partial Pressure

• The total pressure in a container is the sum of
  the pressure each gas would exert if it were
  alone in the container.
• The total pressure is the sum of the partial
  pressures.
• PTotal P1 P2 P3 P4 P5 ...
• For each P nRT/V

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Daltons Law Continued

• In the same container R, T and V are the same.
• PTotal n1RT n2RT n3RT ... V
  V V

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The Mole Fraction

• Ratio of moles of the substance to the total
  moles.
• symbol is Greek letter chi c
• c1 n1 P1 nTotal PTotal

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Examples

• The partial pressure of nitrogen in air is 592
  torr. Air pressure is 752 torr, what is the mole
  fraction of nitrogen?
• What is the partial pressure of nitrogen if the
  container holding the air is compressed to 5.25
  atm?

• .

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Gas Density and Molar Mass

• D m/V
• Let M stand for molar mass
• M m/n
• n PV/RT
• M m
• PV/RT
• M mRT m RT DRT PV V
  P P

• PTotal (n1 n2 n3...)RT V
• PTotal (nTotal)RT V

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Examples

• What is the density of ammonia at 23ºC and 735
  torr?
• A compound has the empirical formula CHCl. A 256
  mL flask at 100.ºC and 750 torr contains .80 g of
  the gaseous compound. What is the molecular
  formula?

• .

10
Boyles Law
Pressure is inversely proportional to volume when
temperature is held constant.
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Examples

• 1. 20.5 L of nitrogen at 25ºC and 742 torr are
  compressed to 9.8 atm at constant T. What is the
  new volume?2. 30.6 mL of carbon dioxide at 740
  torr is expanded at constant temperature to 750
  mL. What is the final pressure in kPa?

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A Graph of Boyles Law
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Charless Law

• The volume of a gas is directly proportional to
  temperature, and extrapolates to zero at zero
  Kelvin.
• (P constant)

Temperature MUST be in KELVINS!
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Examples

• 1.What would the final volume be if 247 mL of gas
  at 22ºC is heated to 98ºC , if the pressure is
  held constant?
• 2. At what temperature would 40.5 L of gas at
  23.4ºC have a volume of 81.0 L at constant
  pressure?

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A Graph of Charles Law
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Gay Lussacs Law
The pressure and temperature of a gas
are directly related, provided that the volume
remains constant.
Temperature MUST be in KELVINS!
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Examples

• A sample of nitrogen gas has a pressure of
• 6.58 kPa at 539 K. If the volume does not
  change, what will the pressure be at 211 K ?
• The pressure in a car tire is 198 kPa at
• 27C. After a long drive, the pressure is
  225 kPa. What is the temperature of the air in
  the tire? Assume that the volume is constant.

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A Graph of Gay-Lussacs Law
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The Combined Gas Law
The combined gas law expresses the relationship
between pressure, volume and temperature of a
fixed amount of gas.
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Examples

• A deodorant can has a volume of 175 mL and a
  pressure of 3.8 atm at 22ºC. What volume of gas
  could the can release at 22ºC and 743 torr?

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Ideal Gases
Ideal gases are imaginary gases that perfectly
fit all of the assumptions of the kinetic
molecular theory.

• Gases consist of tiny particles that are far
  apart relative to their size.
• Collisions between gas particles and between
  particles and the walls of the container are
  elastic collisions
• No kinetic energy is lost in elastic collisions

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Ideal Gases (continued)

• Gas particles are in constant, rapid motion.
  They therefore possess kinetic energy, the energy
  of motion
• There are no forces of attraction between gas
  particles
• The average kinetic energy of gas particles
  depends on temperature, not on the identity of
  the particle.

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Real Gases Do Not Behave Ideally
Real gases DO experience inter-molecular
attractions
Real gases DO have volume
Real gases DO NOT have elastic collisions
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Deviations from Ideal Behavior
Likely to behave nearly ideally
Gases at high temperature and low pressure
Small non-polar gas molecules
Likely not to behave ideally
Gases at low temperature and high pressure
Large, polar gas molecules
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IDEAL GAS LAW

• PV nRT
• P pressure in atm, kPa, mm Hg
• ? n number of moles
• ? V volume in Liters
• ? R is the ideal gas constant depends on the
  pressure unit
• ? R 0.0821 L?atm/ K?mol or
• R 8.314 L?kPa/ K?mol or
• R 62.36 L?mmHg/ K?mol

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Examples

• 1.A 47.3 L container containing 1.62 mol of He
  is heated until the pressure reaches 1.85 atm.
  What is the temperature?
• 2.Kr gas in a 18.5 L cylinder exerts a pressure
  of 8.61 atm at 24.8ºC What is the mass of Kr?
• 3.A sample of gas has a volume of 4.18 L at 29ºC
  and 732 torr. What would its volume be at 24.8ºC
  and 756 torr?

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Diffusion

• Diffusion describes the mixing of gases. The
  rate of diffusion is the rate of gas mixing.
• Diffusion is the result of random movement of
  gas molecules
• The rate of diffusion increases with temperature
• Small molecules diffuse faster than large
  molecules

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Grahams Law of Diffusion
M1 Molar Mass of gas 1
M2 Molar Mass of gas 2
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Examples

• Which gas effuses faster hydrogen or
  chlorine, and by what factor?
• 2. Calculate the ratio of the velocity of helium
  atoms to fluorine molecules at the same
  temperature.