Chapter 5: Gases

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Chapter 5 Gases
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5.1 Measurements on Gases

• Volume- amount of space the gas occupies
• 1 L 1000 mL 1000 cm3 1 x10-3 m3
• Amount most commonly expressed in terms of
  moles (n)
• m MM x n
• Temperature measured in degrees Celsius but
  commonly must convert to Kelvin
• TK tC 273.15
• Pressure gas molecules are constantly colliding
  because of this they exert a force over an
  area
• 1.013 bar 1 atm 760 mmHg 1 x 105 Pa
  14.7 psi

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Barometer
4
Manometer
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Example 5.1

• A balloon with a volume of 2.06 L contains 0.368
  g of helium at 22 degrees Celsius and 1.08 atm.
  Express the volume of the balloon in m3, the
  temperature in K, and the pressure in mmHg.
• V 2.06 x 10-3 m3
• nHe 0.0919 mole
• T 22 273.15 295 K
• P 821 mmHg

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Gas Laws

• Boyles Law P1V1 P2V2
• Charles Law V1 V2
• T1 T2
• Gay-Lusaacs Law P1 P2
• T1 T2
• Combined Gas Law
• P1V1 P2V2
• T1 T2

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Example

• A tank is filled with a gas to a pressure of 977
  mmHg at 25C. When the tank is heated, the
  pressure increases to 1.50 atm. To what
  temperature was the gas heated?
• 75C

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5.2 The Ideal Gas Law 5.3 Gas Law Calculations

• The Ideal Gas Law Constant (R)
• 0.0821 L atm/mol K - ideal gas law problems
• 8.31 J/ mol K - equations involving energy
• 8.31 x 103 g m2/s2 mol k- molecular speed
  problems

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Molar Volume
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Initial Final State Problems

• Starting with a sample of gas at 25C and 1.00
  atm you might be asked to calculate the pressure
  developed when the sample is heated to 95C at a
  constant volume. Determine a two-point equation
  and solve for the final pressure.
• Initial State P1V nRT1
• Final State P2V nRT2
• Divide the 2 equations to derive a two-point
  equation
• P1 T1
• P2 T2
• Rearrange to solve for the variable you want P2
  P1 T2
• T1
• Ans 1.23 atm

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Example 5.2

• A 250.0 mL flask, open to the atmosphere,
  contains 0.0110 mol of air at 0 C. On heating,
  part of the air escapes how much remains in the
  flask at 100 C?
• 0.00805 mol of air

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Example 5.3

• If 2.50 g of sulfur hexafluoride is introduced
  into an evacuated 500.0 mL container at 83C,
  what pressure (atm) is developed?
• Ans 1.00 atm

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Density The Ideal Gas LawThe ideal gas law
offers a simple approach to the experimental
determination of the molar mass of a gas.

• Remember that m MM x n and n PV
  and d m
  RT V
• So you can substitute these equations into the
  ideal gas law to solve fro density (d) or molar
  mass (M)

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• Gas Density and Human Disasters Many gases that
  are denser than air have been involved in natural
  and human-caused disasters. The dense gases in
  smog that blanket urban centers, such as Mexico
  City (see photo), contribute greatly to
  respiratory illness. In World War I, poisonous
  phosgene gas (COCl2) was used against ground
  troops as they lay in trenches. In 1984, the
  unintentional release of methylisocyanate from a
  Union Carbide India Ltd. chemical plant in
  Bhopal, India, killed thousands of people as
  vapors spread from the outskirts into the city.
  In 1986 in Cameroon, CO2 released naturally from
  Lake Nyos suffocated thousands as it flowed down
  valleys into villages. Some paleontologists
  suggest that a similar process in volcanic lakes
  may have contributed to dinosaur kills.

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Example 5.4

• Acetone is widely used in nail polish remover. A
  sample of liquid acetone is placed in a 3.00 L
  flask and vaporized by heating to 95C at 1.02
  atm. The vapor filling the flask at this
  temperature and pressure weighs 5.87 g
• (a) What is the density of acetone vapor under
  these conditions?
• Ans 1.96 g/L
• (b) Calculate the molar mass of acetone.
• Ans 58.1 g/mol
• (c) Acetone contains three elements C, H, and
  O. When 1.00 g of acetone is burned 2.27 g of
  CO2 and 0.932 g of H2O are formed. What is the
  molecular formula of acetone?
• Ans C3H6O

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5.3 Stoichiometry of Gaseous Reactions

• A molar ratio from a balanced chemical reaction
  is also used in reactions involving gases
  however, the ideal gas law can now be applied.
• Example 5.5 A nickel smelter in Sudbury, Ontario
  produces 1 of the worlds supply of sulfur
  dioxide by the reaction of nickel II sulfide with
  oxygen another product of the reaction is nickel
  II oxide
• What volume of sulfur dioxide at 25C and a
  pressure of one bar is produced from a metric ton
  of nickel II sulfide?
• Ans 2.73 x 105 L

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Gas A to Gas B
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Example 5.6

• Octane, C8H18, is one of the hydrocarbons in
  gasoline. On combustion octane produces carbon
  dioxide and water. How many liters of oxygen,
  measured at 0.974 atm and 24C, are required to
  burn 1.00 g of octane?
• Ans 2.73 L

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Law of Combining Volumes

• The volume of any 2 gases in a reaction at
  constant temperature and pressure is the same as
  the reacting molar ratio
• 2 H2O (l) ? 2H2 (g) O2 (g)
• 4 L H2 x 1 L O2 2 L O2
• 2 L H2

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Example 5.7

• Consider the reaction for the formation of water
  from its elemental units.
• (a) What volume of hydrogen gas at room
  temperature and 1.00 atm is required to react
  with 1.00 L of oxygen at the same temperature and
  pressure?
• Ans 2.00 L hydrogen gas
• (b) What volume of water at 25C and 1.00 atm
  (d0.997 /mL) is formed from the reaction in (a)?
• Ans 1.48 mL of water
• (c) What mass of water is formed from the
  reaction assuming a yield of 85.2?
• Ans 1.26 g of water

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Limiting Reactant Problems

• The alkali metals react with the halogens to
  form ionic metal halides. What mass of potassium
  chloride forms when 5.25 L of chlorine gas at
  0.950 atm and 293 K reacts with 17.0 g of
  potassium?
• Ans 30.9 g KCl

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5.5 Daltons Law of Partial Pressures

• The total pressure of a gas mixture is the sum of
  the partial pressures of the components of the
  mixture.
• Ptot PA PB ..
• PH2 2.46 atm PHe 3.69 atm then Ptot
  6.15 atm

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Wet Gases

• When a gas is collected by bubbling through water
  then it picks up water vapor. Then the total
  pressure is the sum of the pressure of the water
  vapor and the gas collected. So Daltons Law can
  be applied by
• Ptot PH2O PA
• The partial pressure of water is equal to the
  vapor pressure of water. This has a fixed value
  at a given temperature (PH2O _at_ 25C 23.76 mmHg)

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Gas collection by water displacement.
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Example 5.8

• A student prepares a sample of hydrogen gas by
  electrolyzing water at 25C. She collects 152 mL
  of hydrogen gas at a total pressure of 758 mmHg.
  Calculate
• (a) the partial pressure of hydrogen gas.
• Ans 734 mmHg
• (b) the number of moles of hydrogen gas
  collected.
• Ans 0.00600 mol of hydrogen gas

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Partial Pressures Mole Fraction

• The partial pressure of a gas (PA) divided by the
  total pressure (Ptot) is equal to the number of
  moles of that gas divided by the total moles of
  gases
• PA nA
• Ptot ntot
• Mole fraction XA nA
• ntot
• Partial Pressures PA XA Ptot

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Example 5.9

• Methane burns in air. When one mole of methane
  and four moles of oxygen are heated
• (a) What are the mole fractions of oxygen,
  carbon dioxide, and water vapor in the resulting
  mixture (assume all the methane is converted)?
• XCH4 0, XCO2 0.200, XH2O 0.400, XO2
  0.400
• (b) If the total pressure of the mixture is 1.26
  atm, what are the partial pressures of each gas?
• PCO2 0.252 atm, PH2O 0.504 atm, PO2 0.504
  atm

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5.6 Kinetic Theory of Gases

• The Molecular Model of Gases (pg 115)
• Gases are mostly empty space (assumes that gases
  do not have their own volume).
• Gas molecules are in constant and chaotic motion.
  Their velocities are constantly changing because
  of this.
• Collisions of gases are elastic (assumes no
  attractive forces).
• Gas pressure is caused by collisions of molecules
  with the walls of the container. As a result,
  pressure increases with the energy and frequency
  of these collisions.

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Average Speed

• The equation below is derived from the average
  translational kinetic energy of a gas molecule
• It follows that at a given temperature, molecules
  of different gases have the same average kinetic
  energy of translational motion
• and
• the average translational kinetic energy of a gas
  molecule is directly proportional to the Kelvin
  temperature so that
• u (3RT) ½
• (MM)
• An R value of 8.31 x 103 g m2/(s2 mol K) is
  used for average speed calculations.

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Grahams Law of Effusion

• The average speed is inversely proportional to
  the square root of the molar mass (MM). So for
  two different gases A and B at the same
  temperature then we can write
• rate of effusion B (MMA) 1/2
• rate of effusion A (MMB)

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Example Using Grahams Law

• A mixture of helium (He) and methane (CH4) is
  placed in an effusion apparatus. Calculate the
  ratio of their effusion rates
• Ans He effuses 2.002 times faster than
  methane

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Example 5.11
In an effusion experiment, argon gas is allowed
to expand through a tiny opening into an
evacuated flask of volume 120.0 mL for 32.0 s,
at which point the pressure in the flask is
found to be 12.5 mmHg. This experiment is
repeated with a gas X of unknown molar mass at
the same T and P. It is found that the pressure
in the flask builds up to 12.5 mmHg after 48.0 s.
Calculate the molar mass of X. Ans 89.9 g/mol
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Real Gases

• The ideal gas law has been used with the
  assumption that it applies exactly. However, all
  real gases deviate at least slightly from the
  ideal gas law.
• These deviations arise because the ideal gas law
  neglects two factors
• 1. attractive forces between gas particles
• 2. the finite volume of gas particles
• In general, the closer a gas is to the liquid
  state, the more it will deviate from the ideal
  gas law.

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Correction for Real Gas Behavior