CHAPTER 12: GASES AND THEIR PROPERTIES

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CHAPTER 12 GASES AND THEIR PROPERTIES

• That this was not the case, I attributed to the
  force of prejudice, which, unknown to ourselves,
  biases not only our judgments, properly so
  called, but even the perceptions of our senses
  for we may take a maxim so strongly for granted,
  that the plainest evidence of sense will not
  entirely change, and often hardly modify, our
  persuasions, and the more ingenious a man is the
  more effectually he is entangled in his errors
  his ingenuity only helping him to deceive
  himself, by evading the force of truth.
• -Joseph Priestley (1790) recounting the
  discovery of oxygen/gases

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12.0 OBJECTIVES

• Describe the properties of gases (volume, amount,
  pressure, temperature), units of measurement, and
  instruments used to measure these quantities.
• Understand and use the ideal gas law to solve a
  variety of problems.
• Apply gas laws equations to stoichiometry
  problems.
• Understand the uses of Daltons Law and Grahams
  Law equations.
• Use the kinetic molecular theory to describe the
  behavior of gases at the molecular level.
• Compare the behavior of real gases to ideal gases.

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HOMEWORK

• HW1 11, 15, 17, 19, 21, 25, 65
• Conversions, Boyles, Charles, Combined
• HW2 27, 29, 31, 33, 37, 63, 75, 99
• Ideal Gas Law, Gas Density
• HW3 41, 45, 71, 85, 105
• Gas Stoichiometry
• HW4 47, 49, 97, 103
• Partial Pressures
• HW5 51, 55, 59, 61
• Kinetic-Molecular, Diffusion, Nonideal Gases

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12.1 PROPERTIES OF GASES

• 1. Study of gases as a separate unit in
  chemistry
• In the gas phase, all substances are remarkably
  similar and easily described by the kinetic
  molecular theory.
• Factors that affect gases are easy to describe
  and measure.
• Universal simple mathematical relationships apply
  to all gases.

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12.1 PROPERTIES OF GASES

• 2. Four inter-related variables associated with
  gases
• a. Volume V
• Gases take up a large volume
• Usually measured in L
• 1 mol 22.4 L _at_ STP
• b. Amount of gasn
• Measured in moles

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12.1 PROPERTIES OF GASES

• c. TemperatureT
• ENERGY! (avg. kinetic energy of particles)
• Impacts properties of gas
• Measured in K (Kelvin) KC273.15

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12.1 PROPERTIES OF GASES

• d. PressureP
• 1. Cause of pressure
• Atmosphere composed of gas molecules
• Mass of all of these cause pressure (Force/area)

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12.1 PROPERTIES OF GASES

• 2. Units of pressure
• Torr (mmHg), Atmosphere (atm), Pascal (Pa)
  N/m2, Bar, inHg
• 1 atm 760 torr 101.3 kPa 1.013 bar 29.92
  inHg
• STP
• Standard Temperature and Pressure
• 1 atm (760 torr) 273 K (0oC)

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12.1 PROPERTIES OF GASES

• 3. Measuring Pressure
• a. Manometer and Barometer
• Device used to measure pressure

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12.1 PROPERTIES OF GASES
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12.1 PROPERTIES OF GASES

• Manometer Problems
• Just follow along ?

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12.1 PROPERTIES OF GASES
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12.1 PROPERTIES OF GASES
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12.1 PROPERTIES OF GASES
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12.1 PROPERTIES OF GASES

• b. Altitude and barometric pressure
• What do YOU think the trend is?

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12.1 PROPERTIES OF GASES

• 4. Ex12.1 Express 753 mmHg in atm, kPa, and
  bars.

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12.2 GAS LAWS EXPERIMENTAL BASIS

• 1. Proportions
• a. Direct
• As one term increases, so does the other
• X 1
• Y
• b. Inverse
• As one term increases, the other decreases
• XY 1

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12.2 GAS LAWS EXPERIMENTAL BASIS

• 2. Volume and Pressure, T and n constant -
  Boyle's Law
• For a given amount of gas at constant
  temperature, the volume is inversely proportional
  to the Pressure
• P1V1 P2V2

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12.2 GAS LAWS EXPERIMENTAL BASIS

• Ex12.2 When an auto airbag inflates as a result
  of an accident, the gases inside are at a final
  volume of 25.0L and pressure of just over
  atmospheric pressure, 780mmHg. What is the
  pressure in the uninflated bag with a volume of
  1.00L?

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12.2 GAS LAWS EXPERIMENTAL BASIS

• Volume and Temperature, n and P constant -
  Charles Law
• The volume of a gas is directly proportional to
  the temperature (in Kelvin) at constant pressure
  and amount of gas
• V1 V2
• T1 T2

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12.2 GAS LAWS EXPERIMENTAL BASIS

• Volume and moles, T and P constant Gay-Lussacs
  Law
• Volume is directly proportional to of moles
• of molecules ? ? Volume ?
• So, coefficients in a balanced equation involving
  gases are also the volume ratio

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12.2 GAS LAWS EXPERIMENTAL BASIS

• 6. Temperature and Pressure, n and V constant
  Amontons Law
• The temperature is directly proportional to the
  pressure
• P1 P2
• T1 T2

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12.2 GAS LAWS EXPERIMENTAL BASIS

• 7. Combined Gas Law
• _P1V1_ _P2V2_
• n1T1 n2T2

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12.2 GAS LAWS EXPERIMENTAL BASIS

• Ex12.3 A gas occupies a volume of 7.50L at
  300.mmHg and 200.0oC. What is its volume if the
  same sample of gas is at a pressure of 1.50atm
  and at a temperature of 22.0oC?

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12.2 GAS LAWS EXPERIMENTAL BASIS

• 9. Avogadro's Hypothesis
• Equal volumes of gases at the same Temp. and
  Pressure have the same number of molecules

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12.2 GAS LAWS EXPERIMENTAL BASIS

• 10. Derivation of Volume-moles relationship
• Compared masses of equal volumes of different
  gases and determined weight ratios? atomic
  weights.
• Avogadro molded together Daltons atomic theory
  with Gay-Lussacs law of combining volumes
• Avogadro threatened Daltons ideas about
  atom/molar masses? work was ignored for 50 years!

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12.2 GAS LAWS EXPERIMENTAL BASIS

• Ex12.4 Given the Haber reaction below a. What
  volume of hydrogen is required to form 12.0L of
  ammonia? b. What volume of nitrogen gas is
  necessary to react completely with 1.41 Liters of
  hydrogen gas? Assume constant T and P.
• 3H2(g) N2(g) ? 2NH3(g)

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12.3 IDEAL GAS LAW

• 1. Derivation of Ideal Gas Law
• Combination of Boyles, Charles, and Avogadros
  Laws
• PV nRT

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12.3 IDEAL GAS LAW

• 2. Value of the gas law constant, R
• R .0821 Latm R 8.314 J
• molK molK

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12.3 IDEAL GAS LAW

• 3. Ex12.5 Will it be safe to store 2500g of
  oxygen gas in a 10.0L container at 20.0oC if the
  container is built to a tolerance of 200atm?

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12.3 IDEAL GAS LAW

• 4. Ex12.6 Calculate the number of moles of
  ammonia present in a sample with a volume of
  12.0L, at 22.0oC and 715mmHg.

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12.3 IDEAL GAS LAW

• 5. Density of gas
• PV mass RT mass P(M.M.) D
• M.M. V RT

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12.3 IDEAL GAS LAW

• 6. Ex12.7 What is the density of oxygen gas at
  1.00 atm and 27.0oC?

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12.3 IDEAL GAS LAW

• 7. Calculating molar mass
• PV mass RT
• M.M.

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12.3 IDEAL GAS LAW

• 8. Ex12.8 What is the molar mass of a gas whose
  density is 5.00g/L at 25.0oC and 1.00atm?

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12.4 GAS LAWS AND CHEMICAL REACTIONS

• 1. Ex12.9 Hydrogen peroxide decomposes in the
  presence of sunlight to produce oxygen gas and
  water. Calculate the amount, in grams, of
  hydrogen peroxide needed to produce 2.50L of
  oxygen, measured at STP.

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12.4 GAS LAWS AND CHEMICAL REACTIONS

• 2. Ex12.10 How many liters of oxygen gas at
  1.00atm and 27.0oC are needed to burn 1.00g of
  octane (C8H18)?

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12.4 GAS LAWS AND CHEMICAL REACTIONS

• 3. Ex12.11 What mass in grams of potassium
  chlorate must be used to produce 1.75L of oxygen
  gas, measured at 18.0oC and 0.950atm according to
  the following equation?
• 2KClO3(s) ? 3O2(g) 2KCl(s)

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12.5 GAS MIXTURES AND PARTIAL PRESSURES

• 1. Statement of Dalton's Law of Partial
  Pressures
• Total pressure of a mixture of gases is equal to
  sum of the partial pressures of each component
• Ptotal Pgas 1 Pgas 2 Pgas 3

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12.5 GAS MIXTURES AND PARTIAL PRESSURES

• 2. Ex12.12 A gas mixture has a total pressure
  of 1.50atm. If the mixture consists of 0.150mol
  of methane and an unknown amount of ethane in an
  8.50L vessel at 298K, what is the partial
  pressure due to ethane?

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12.5 GAS MIXTURES AND PARTIAL PRESSURES

• 3. Gases collected by bubbling through water and
  water vapor pressure
• Collection over water? Ptotal Pgas PH2O
• When level of gas level of water, pressures are
  equal
• See. Pg. 13 in Reference Booklet

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12.5 GAS MIXTURES AND PARTIAL PRESSURES

• 4. Ex12.13 30.0mL of hydrogen gas is collected
  over water at a total pressure of 744mmHg and at
  20.0oC. Calculate the pressure due to hydrogen
  gas and the number of moles of hydrogen gas.

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12.5 GAS MIXTURES AND PARTIAL PRESSURES

• 5. Mole fractions
• The ratio of the moles of a gas over the total
  moles of a gas in a mixture of ideal gases
• Xa na
• ntotal

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12.5 GAS MIXTURES AND PARTIAL PRESSURES

• 6. Relationship between partial pressure, mole
  fraction, and total pressure
• Pa Xa
• Ptotal

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12.5 GAS MIXTURES AND PARTIAL PRESSURES

• 7. Ex12.14 Calculate the mole fractions of
  hydrogen and water vapor in the previous problem.

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12.6 KINETIC MOLECULAR THEORY OF GASES

• 1. Basic statements of Kinetic Molecular Theory
• a. Gases consist of particles whose separation
  is much greater than the size of the particles,
  themselves.
• b. The particles of a gas are in constant,
  random, and rapid motion.
• c. Gas particles constantly collide with one
  another and with the walls of their container,
  but they do so without loss of energy.
• d. The average kinetic energy of a sample of gas
  particles is proportional to the absolute
  temperature of the gas. Therefore, all molecules
  of gas, regardless of their mass, have the same
  average kinetic energy at the same temperature.

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12.6 KINETIC MOLECULAR THEORY OF GASES

• 2. The kinetic energy of a single molecule
• KE ½ mu2
• u speed
• Different molecules can have different speeds, so
  only applies to a single molecule
• 3. The average kinetic energy of a sample of gas
  molecules depends on
• Kelvin Temperature only

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12.6 KINETIC MOLECULAR THEORY OF GASES

• 4. The average kinetic energy of the molecules
  in a gas sample is related to average u2
• KE ½ mu2
• 5. The relationship between mass, average speed,
  and temperature is
• ?u2 3RT (Maxwells Eqn)
• M.M.

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12.6 KINETIC MOLECULAR THEORY OF GASES

• 6. Maxwell-Boltzmann Distribution
• Distribution of speeds (KE) of molecules
• Areas under curves are the same

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12.6 KINETIC MOLECULAR THEORY OF GASES

• 7. Ex12.15 Calculate the average velocity (rms
  speed) of an oxygen molecule at 25.0oC.

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12.6 KINETIC MOLECULAR THEORY OF GASES

• 8. Ex12.16 A professional tennis player can
  serve a tennis ball at 45m/sec. At what
  temperature will an oxygen molecule have the same
  average speed?

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12.7 DIFFUSION AND EFFUSION

• 1. Diffusion and Effusion
• Diffusion mixing of gases due to molecular
  motion
• Ex. Spread of aroma of a baking pie
• Effusion movement of gas through a tiny opening
  in a container to another container of lower P
• Ex. Punching a hole in a He balloon

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12.7 DIFFUSION AND EFFUSION

• 2. Graham's Law relating molar mass, rate of
  speed, and time
• Rate of effusion of gas 1 M.M.-gas 2
• Rate of effusion of gas 2 ?M.M.-gas 1
• Rate of effusion of gas 1 rms for gas 1
  ? 3RT/(MM-gas 1)
• Rate of effusion of gas 2 rms for gas 2
  ? 3RT/(MM-gas 2)

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12.7 DIFFUSION AND EFFUSION

• 3. Ex12.17 It takes 40sec for a sample of
  oxygen to effuse through a small opening into a
  vacuum. Another gas takes only 10sec to effuse
  under the same conditions. What is the molar
  mass of the second gas?

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12.7 DIFFUSION AND EFFUSION

• 4. Ex12.18 The ratio of the average rate of
  effusion of SO2(g) to CH4(g) at 300K is

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12.8 NON-IDEAL BEHAVIOR REAL GASES

• 1. Equations used to describe ideal gases are
  based on assumptions of kinetic molecular theory.
• Gases actually have a volume
• 1L container does not mean gas molecules have 1L
  to move about
• Elastic Collisions are not always observed
• When we approach the condensation point?
  molecules MUST have some attraction

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12.8 NON-IDEAL BEHAVIOR REAL GASES

• 2. Real gases deviate from ideal behavior under
  two main conditions
• Low Temperature (approaching condensation)
• High Pressure (molecular volume becomes
  significant)

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12.8 NON-IDEAL BEHAVIOR REAL GASES

• 3. van der Waal's Equation - a better predictor
  of gas behavior under extreme conditions
• Corrects for intermolecular forces and molecular
  volume