The Behavior

1
CHAPTER 14

• The Behavior
• of
• Gases

2
Properties of Gases

• Recall from the last chapter that gases can
  expand to fill their containers, unlike a solid
  or liquid.
• Gases are also easily compressed, or squeezed
  into a smaller volume.
• Compressibility The measure of how much the
  volume of matter decreases under pressure.
• The Kinetic Theory explains why gases are
  compressed more easily because of the space
  between the particles in a gas.
• At room temperature, the distance between
  particles in an enclosed gas is about 10 times
  the diameter of a particle.

3
Properties of Gases

• Four variables are generally used to describe a
  gas
• Pressure (P) measured in kilopascals.
• Volume (V) measured in liters.
• Temperature (T) measured in Kelvins.
• Number of Moles (n).
• The amount of gas, volume, and temperature are
  factors that affect gas pressure.

4
Properties of Gases

• By adding gas to a closed system, you increase
  the number of particles, which increases the
  number of collisions, which then in turn,
  increases the pressure of a gas.
• Ex Doubling the number of particles doubles the
  pressure, tripling the number of particles
  triples the pressure, etc.
• If too much gas is added to a closed system, then
  it can cause the system to rupture.
• Ex A balloon, bike tire, etc.

5
Properties of Gases

• If the pressure in a closed system is lower than
  the outside air pressure, then air will rush into
  the container when it is opened.
• Ex Bags of chips.
• If the pressure in a closed system is higher than
  the outside air pressure, the gas will flow out
  of the container when it is opened.
• Ex Aerosol cans.
• High pressure always goes to low pressure.

6
Properties of Gases

• You can also raise the pressure of a contained
  gas by reducing its volume.
• The more it is compressed, the greater the
  pressure inside the container.
• Ex Sitting on a balloon.
• When the volume of a container is reduced by
  half, the pressure is doubled.
• This also has the opposite effect by increasing
  the volume of a container, the pressure of the
  container decreases.
• Ex Car engines (piston and cylinder).

7
Properties of Gases

• You can also raise the pressure inside of a
  container by increasing the temperature of the
  gas.
• As a gas is heated, the temperature increases and
  the average kinetic energy of the particles in
  the gas increases.
• Faster-moving particles impact the walls of the
  container with more energy.
• Doubling the Kelvin temperature doubles the
  pressure.
• Ex This is why you never want to throw an
  aerosol can into a fire (even if it is empty).
• The opposite is also true, decreasing the
  temperature of a gas in a container decreases the
  pressure.
• Halving the Kelvin temperature decreases the
  pressure by half.

8
The Gas Laws

• In 1962, Robert Boyle discovered that gas
  pressure and volume are related mathematically.
• These observations of Boyle and others led to the
  development of the gas laws.
• Gas Laws
• Simple mathematical relationships between the
  volume, temperature, pressure, and quantity of a
  gas.

9
The Gas Laws

• Boyles Law Pressure-Volume Relationship
• States that the volume of a fixed mass of gas
  varies inversely with the pressure at constant
  temperature.
• Mathematically, Boyles Law is expressed as
  follows
• PV k

10
The Gas Laws

• The value of k is constant for a given sample of
  gas and depends only on the mass of gas and the
  temperature.
• If the pressure of a given gas sample at constant
  temperature changes, the volume will change.
• However, the quantity PV will remain equal to the
  same value of k.

11
The Gas Laws

• Boyles Law can be used to compare changing
  conditions for a gas.
• Using the symbols P1 and V1 to stand for initial
  conditions and P2 and V2 to stand for the new
  conditions we can rewrite Boyles Law as
• P1V1 k P2V2 k
• OR
• P1V1 P2V2

12
The Gas Laws

• Example
• A sample of oxygen gas has a volume of 150 mL
  when its pressure is 0.947 atm. What will be the
  volume of the gas at a pressure of 0.987 atm if
  the temperature remains constant?

13
The Gas Laws

• Example
• A balloon filled with helium gas has a volume of
  500 mL at a pressure of 1 atm. The balloon is
  released and reaches an altitude 6.5 km, where
  pressure is 0.5 atm. Assuming that the
  temperature has remained the same, what volume
  does the gas occupy at this height?

14
The Gas Laws

• Example
• A gas has a pressure of 1.26 atm and occupies a
  volume of 7.40 L. If the gas is compressed to a
  volume of 2.93 L, what will its pressure be,
  assuming constant temperature?

15
The Gas Laws

• Example
• Divers know that the pressure exerted by the
  water increases about 100 kPa with every 10.2 m
  of depth. This means that at 10.2 m below the
  surface, the pressure is 201 kPa at 20.4 m, the
  pressure is 301 kPa and so forth. Given that the
  volume of a balloon is 3.5 L at STP and that the
  temperature of the water remains the same, what
  is the volume 51 m below the waters surface?

16
The Gas Laws

• Charless Law
• States that the volume of a fixed mass of gas at
  constant pressure varies directly with the Kelvin
  temperature.
• Charless Law may be expressed as follows
• V kT OR k V/T

17
The Gas Laws

• The value of T is the Kelvin temperature, and k
  is a constant.
• The value of k depends only on the quantity of
  gas and the pressure.
• The form of Charless Law that can be applied
  directly to most volume-temperature problems
  involving gases is as follows
• V1/T1 V2/T2

18
The Gas Laws

• Example
• A sample of neon gas occupies a volume of 752 mL
  at 25C. What volume will the gas occupy at 50C
  if the pressure remains constant?

19
The Gas Laws

• Example
• A helium-filled balloon has a volume of 2.75 L at
  20C. The volume of the balloon decreases to 2.46
  L after it is placed outside on a cold day. What
  is the outside temperature?

20
The Gas Laws

• Example
• A gas at 65C occupies 4.22 L. At what Celsius
  temperature will the volume be 3.87 L, assuming
  the same pressure?

21
The Gas Laws

• Gay-Lussacs Law Pressure-Temperature
• The pressure of a fixed mass of gas at constant
  volume varies directly with the Kelvin
  temperature.
• Mathematically, Gay-Lussacs law is expressed as
  follows
• P kT OR k P/T

22
The Gas Laws

• The value of T is the temperature in kelvins, and
  k is a constant.
• k depends on the quantity of gas and the volume.
• Unknown values can be found using this form of
  Gay-Lussacs law
• P1/T1 P2/T2

23
The Gas Laws

• Example
• The gas in an aerosol can is at a pressure of
  3.00 atm at 25C. Directions on the can warn the
  user not to keep the can in a place where the
  temperature exceeds 52C. What would the gas
  pressure in the can be at 52C?

24
The Gas Laws

• Example
• Before a trip from New York to Boston, the
  pressure in an automobile tire is 1.8 atm at
  20C. At the end of the trip, the pressure gauge
  reads 1.9 atm. What is the new Celsius
  temperature of the air inside the tire? (Assume
  tires with constant volume.)

25
The Gas Laws

• Example
• At 120C, the pressure of a sample of nitrogen is
  1.07 atm. What will the pressure be at 205C,
  assuming constant volume?

26
The Gas Laws

• Example
• A sample of helium gas has a pressure of 1.20 atm
  at 22C. At what Celsius temperature will the
  helium reach a pressure of 2.00 atm?

27
The Gas Laws

• The Combined Gas Law
• Expresses the relationship between pressure,
  volume, and temperature of a fixed amount of gas.
• Can be expressed as
• PV/T k

28
The Gas Laws

• In the equation, k is a constant and depends on
  the amount of gas.
• The combined gas law can also be written as
• P1V1/T1 P2V2/T2

29
The Gas Laws

• Example
• A helium filled balloon has a volume of 50.0 L at
  25C and 1.08 atm. What volume will it have at
  0.855 atm and 10C?

30
The Gas Laws

• Example
• The volume of a gas is 27.5 mL at 22C and 0.974
  atm. What will the volume be at 15C and 0.993
  atm?

31
The Gas Laws

• Example
• A 700 mL gas sample at STP is compressed to a
  volume of 200 mL, and the temperature is
  increased to 30C. What is the new pressure of
  the gas in Pa?

32
Ideal Gases

• In the early 1800s, French chemist Joseph
  Gay-Lussac studied gas volume relationships
  involving a chemical reaction between hydrogen
  and oxygen.
• He observed that 2 L of hydrogen react exactly
  with 1 L of oxygen to form 2 L of water vapor,
  assuming the same temperature and pressure.
• Hydrogen gas Oxygen gas ? Water vapor
• 2 L H2 1 L O2 ? 2 L H2O
• 2 Volumes 1 Volume ? 2 Volumes
• Gay-Lussacs Law of Combining Volumes of Gases
  At constant temperature and pressure, the volumes
  of gaseous reactants and products can be
  expressed as ratios of small whole numbers.

33
Ideal Gases

• In our study of the gas laws, we have looked at
  changes in properties for a specified amount (n)
  of gas.
• Now we will consider how the properties of a gas
  change when there is a change in the number of
  moles or grams.
• Example
• When you blow up a balloon, its volume increases
  because you add more air molecules.
• If a basketball gets a hole in it, and some of
  the air leaks out, its volume decreases.

34
Ideal Gases

• In 1811, Amedeo Avogadro stated that the volume
  of a gas is directly related to the number of
  moles of a gas when the temperature and pressure
  are not changed.
• Avogadros Law Equal volumes of gases at the
  same temperature and pressure contain equal
  number of molecules.
• If the number of moles of a gas are doubled, then
  the volume will doubles as long as we do not
  change the pressure or temperature.
• Avogadros Law
• V1/n1 V2/n2

35
Ideal Gases

• Example
• A balloon with a volume of 220 mL is filled with
  2.0 moles of helium. To what volume will the
  balloon expand if 3.0 moles of helium are added,
  to give a total of 5.0 moles of helium?
• 220 mL/2.0 moles V2/5.0 moles
• V2 550 mL

36
Ideal Gases

• Example
• At a certain temperature and pressure, 8.00 grams
  of oxygen has a volume of 5.00 L. What is the
  volume after 4.00 grams of oxygen is added to the
  balloon?
• 5.00 L/(8.00 g/32.00 g) V2/(12.00 g/32.00 g)
• V2 7.50 L

37
Ideal Gases

• Using Avogadros Law, we can say that any two
  gases will have equal volumes if they contain the
  same number of moles of gas at the same
  temperature and pressure.
• To help us make comparisons between different
  gases, arbitrary conditions called Standard
  Temperature and Pressure (STP) were selected
• Standard Temperature 0C (273 K)
• Standard Pressure 1 atm (760 mm Hg)

38
Ideal Gases

• At STP, 1 mole of any gas occupies a volume of
  22.4 L.
• This value is known as the molar volume of a gas.
• As long as a gas is at STP conditions (0C and 1
  atm), its molar volume can be used as a
  conversion factor to convert between the number
  of moles of gas and its volume.
• 1 mole gas (STP)/22.4 L and 22.4 L/1 mole gas
  (STP)

39
Ideal Gases
40
Ideal Gases

• Example
• A chemical reaction produces 0.0680 moles of
  oxygen gas. What volume in liters is occupied by
  this gas sample at STP?
• 0.0680 mol O2 (22.4 L O2/1 mol O2) 1.52 L O2

41
Ideal Gases

• Example
• At STP, what is the volume of 7.08 moles of
  nitrogen gas?
• 7.08 moles N2 (22.4 L N2/1 mole N2) 159 L N2

42
Ideal Gases

• Example
• A sample of hydrogen gas occupies 14.1 L at STP.
  How many moles of the gas are present?
• 14.1 L H2 (1 mole H2/22.4 L H2) 0.629 moles H2

43
Ideal Gases

• Example
• At STP, a sample of neon gas occupies 550.0 cm3.
  How many moles of neon does this represent?
• 550.0 cm3 Ne (1 L Ne/1000 cm3 Ne) (1 mole Ne/22.4
  L Ne)
• 0.02455 moles Ne

44
Ideal Gases

• Example
• A chemical reaction produced 98.0 mL of sulfur
  dioxide gas, SO2, at STP. What was the mass (in
  grams) of the gas produced?
• 98.0 mL SO2 (1 L SO2/1000 mL SO2) (1 mole
  SO2/22.4 L SO2) (64.07 g SO2/1 mole SO2)
• 0.280 grams SO2

45
Ideal Gases

• Example
• What is the mass of 1.33 104 mL of oxygen at
  STP?
• 1.33 104 mL O2 (1 L O2/1000 mL O2) (1 mole
  O2/22.4 L O2) (31.99 g O2/1 mole O2)
• 19.0 grams O2

46
Ideal Gases

• Example
• What is the volume of 77.0 grams of nitrogen
  dioxide gas at STP?
• 77.0 g NO2 (1 mole NO2/45.995 g NO2) (22.4 L
  NO2/1 mole NO2)
• 37.5 L NO2

47
Ideal Gases

• Example
• At STP, 3 L of chlorine is produced during a
  chemical reaction. What is the mass of this gas?
• 3 L Cl2 (1 mole Cl2/22.4 L Cl2) (70.901 g Cl2/1
  mole Cl2)
• 10 g Cl2

48
Ideal Gases

• The four properties used in the measurement of a
  gas pressure (P), volume (V), temperatue (T),
  and amount of a gas (n) can be combined to give
  a single expression called the Ideal Gas Law
• PV nRT
• The value for R, the universal gas constant, is
  0.0821 Latm/moleK 62.4 Lmm Hg/moleK.
• The ideal gas law is a useful expression when you
  are given the measurements for any three of the
  four properties of a gas.
• In working problems using the ideal gas law, the
  units of each variable must match the units in
  the R you select.

49
Ideal Gases

• Example
• What is the pressure in atmospheres exerted by a
  0.500 mole sample of nitrogen gas in a 10.0 L
  container at 298 K?
• P ((0.500 mol)(0.0821 Latm/molK)(298 K))/10.0
  L
• P 1.22 atm

50
Ideal Gases

• Example
• What pressure, in atmospheres, is exerted by
  0.325 moles of hydrogen gas in a 4.08 L container
  at 35C?
• P ((0.325 mol)(0.0821 Latm/molK)(308 K))/4.08
  L
• P 2.01 atm

51
Ideal Gases

• Example
• What is the volume, in liters, of 0.250 mol of
  oxygen gas at 20.0C and 0.974 atm pressure?
• V ((0.250 mol)(0.0821 Latm/molK)(293
  K))/0.974 atm
• V 6.17 L

52
Ideal Gases

• Example
• What mass of chlorine gas is contained in a 10.0
  L tank at 27C and 3.50 atm of pressure?
• n ((3.50 atm)(10.0 L))/((0.0821
  Latm/molK)(300 K))
• n 1.42 mol
• Mass 1.42 mol (70.90 g/1 mol)
• Mass 101 g

53
Ideal Gases

• Example
• An oxygen gas container has a volume of 20.0 L.
  How many grams of oxygen are in the container if
  the gas has a pressure of 845 mm Hg at 22C?
• n ((845 mm Hg)(20.0 L))/((62.4 Lmm
  Hg/molK)(295 K))
• n 0.918 mol
• Mass 0.918 mol (32.00 g/1 mol)
• Mass 29.4 g

54
Ideal Gases

• An equation showing the relationship between
  density, pressure, temperature, and molar mass
  can be derived from the ideal gas law.
• D MP/RT
• M Molar Mass

55
Ideal Gases

• Example
• What is the density of a sample of ammonia gas,
  NH3, if the pressure is 0.928 atm and the
  temperature is 63.0C?
• D ((17.04 g)(0.928 atm))/((0.0821
  Latm/molK)(336 K))
• D 0.573 g/L

56
Ideal Gases

• Example
• What is the density of argon gas at a pressure of
  551 torr and a temperature of 25C?
• D ((39.95 g)(551 mm Hg))/((62.4 Lmm
  Hg/molK)(298))
• D 1.18 g/L

57
Ideal Gases

• You can apply the discoveries of Gay-Lussac and
  Avogadro to calculate the stoichiometry of
  reactions involving gases.
• For gaseous reactants or products, the
  coefficients in chemical equations not only
  indicate molar amounts and mole ratios but also
  reveal volume ratios.
• Example
• 2CO(g) O2(g) ? 2CO2(g)
• 2 molecules 1 molecule ? 2 molecules
• 2 mol 1 mole ? 2 mol
• 2 volumes 1 volume ? 2 volumes
• Volumes can be compared in this way only if all
  are measured at the same temperature and pressure.

58
Ideal Gases

• Volume to Volume Calculations
• Given Volume A (Volume Ratio of B/A) Wanted
  Volume B
• Example
• Propane, C3H8, is a gas that is sometimes used
  for cooking and heating. The complete combustion
  of propane occurs according to the following
  equation
• C3H8(g) 5O2(g) ? 3CO2(g) 4H2O(g)
• What will be the volume, in liters, of oxygen
  required for the complete combustion of 0.350 L
  of propane?
• What will be the volume of carbon dioxide
  produced in the reaction?

59
Ideal Gases

• 0.350 L C3H8 (5 L O2/1 L C3H8) 1.75 L O2
• 0.350 L C3H8 (3 L CO2/1 L C3H8) 1.05 L CO2

60
Ideal Gases

• Example
• Assuming all volume measurements are made at the
  same temperature and pressure, what volume of
  hydrogen gas is needed to react completely with
  4.55 L of oxygen gas to produce water vapor?
• 2H2(g) O2(g) ? 2H2O(g)
• 4.55 L O2 (2 mol H2/1 mol O2) 9.10 mol H2

61
Ideal Gases

• Volume to Mass Calculations
• Gas Volume A ? Moles A? Moles B ? Mass B
• Example
• Calcium carbonate, CaCO3, also known as
  limestone, can be heated to produce calcium oxide
  (lime), an industrial chemical with a wide
  variety of uses. The balanced equations for the
  reaction follows
• CaCO3(s) ??? CaO(s) CO2(g)
• How many grams of calcium carbonate must be
  decomposed to produce 5.00 L of carbon dioxide
  gas at STP?

62
Ideal Gases

• n ((1 atm)(5.00 L))/((0.0821 Latm/molK)(273
  K))
• n 0.223 mol CO2
• 0.223 mol CO2 (1 mol CaCO3/1 mol CO2)(100.09 g
  CaCO3/1 mol CaCO3)
• 22.3 g CaCO3

63
Ideal Gases

• Mass to Volume Calculations
• Mass A ? Moles A ? Moles B ? Gas Volume B
• Example
• Tungsten, W, a metal is used in light-bulb
  filaments, is produced industrially by the
  reaction of tungsten oxide with hydrogen.
• WO3(s) 3H2(g) ? W(s) 3H2O(L)
• How many liters of hydrogen gas at 35C and 0.980
  atm are needed to react completely with 875 grams
  of tungsten oxide?

64
Ideal Gases

• 875 g WO3 (1 mol WO3/231.84 g WO3)(3 mol H2/1 mol
  WO3)
• 11.3 mol H2
• ((11.3 mol H2)(0.0821 Latm/molK)(308 K))/0.980
  atm
• 292 L H2

65
Gases Mixtures and Movements

• Daltons Law of Partial Pressures
• States that the total pressure of a mixture of
  gases is equal to the sum of the partial
  pressures of the component gases.
• The law is true regardless of the number of
  different gases that are present.
• May be expressed as
• PT P1 P2 P3 ...

66
Gases Mixtures and Movements

• PT is the total pressure of the mixture.
• P1, P2, P3,.. are the partial pressures of the
  component gases.

67
Gases Mixtures and Movements

• Gases Collected by Water Displacement
• Gases produced in the laboratory are often
  collected over water.
• The gas produced by a reaction displaces the
  water, which is more dense, in the collecting
  bottle.
• You can apply Daltons law of partial pressures
  in calculating the pressures of gases collected
  in this way.

68
Gases Mixtures and Movements

• A gas collected by water displacement is not pure
  but is always mixed with water vapor.
• This happens because the water molecules at the
  surface evaporate and mix with the other gas
  molecules.
• Water vapor, like other gases, exerts a pressure,
  known as water-vapor pressure.

69
Gases Mixtures and Movements

• According to Daltons law of partial pressures,
  the following is true
• Patm Pgas PH2O
• You will need to look up the value of PH2O at the
  temperature of the experiment in a standard
  reference table like that in Table A-8 of your
  book.

70
Gases Mixtures and Movements

• Example
• Oxygen gas from the decomposition of potassium
  chlorate, KClO3, was collected by water
  displacement. The barometric pressure and the
  temperature during the experiment were 731.0 torr
  and 20C, respectively. What was the partial
  pressure of the oxygen collected?

71
Gases Mixtures and Movements

• Example
• Some hydrogen gas is collected over water at
  20C. The levels of water inside and outside the
  gas-collection bottle are the same. The partial
  pressure of hydrogen is determined to be 742.5
  torr. What is the barometric pressure at the time
  the gas is collected?

72
Gases Mixtures and Movements

• Example
• Helium gas is collected over water at 25C. What
  is the partial pressure of the helium, given that
  the barometric pressure is 750 mm Hg?

73
Gases Mixtures and Movements

• The constant motion of gas molecules causes them
  to spread out to fill any container in which they
  are placed.
• The mixing of two gases due to their spontaneous,
  random motion is known as diffusion.
• Effusion is the process whereby the molecules of
  a gas confined in a container randomly pass
  through a tiny opening in the container.
• The rates of effusion and diffusion depend on the
  relative velocities of gas molecules.
• The velocity of a gas varies inversely with its
  mass.
• Lighter molecules move faster than heavier
  molecules at the same temperature.

74
Gases Mixtures and Movements

• In the mid-1800s the Scottish chemist Thomas
  Graham studied the effusion and diffusion of
  gases.
• Grahams Law of Effusion The rates of effusion
  of gases at the same temperature and pressure are
  inversely proportional to the square roots of
  their molar masses.
• Rate of Effusion of A/Rate of Effusion of B
  vMB/vMA

75
Gases Mixtures and Movements

• Grahams experiments dealt with the densities of
  gases.
• The density of a gas varies directly with its
  molar mass.
• Therefore, the square roots of the molar masses
  can be replaced by the square roots of the gas
  densities.
• Rate of Effusion of A/Rate of Effusion of B
  vDensityB/vDensityA

76
Gases Mixtures and Movements

• Grahams law also provides a method for
  determining molar masses (at the same temperature
  and pressure).
• Example
• The separation of the isotopes of Uranium (23892U
  and 23592U).
• The uranium was converted to a gas and passed
  through porous membranes, where the isotopes
  diffused at different rates due to their
  different densities and were thereby separated.

77
Gases Mixtures and Movements

• Example
• Compare the rate of effusion of hydrogen and
  oxygen at the same temperature and pressure.
• Rate of Effusion of H2/Rate of Effusion of O2
  v32 g O2/v2 g H2
• 4/1
• Hydrogen effuses 4 times faster than oxygen.

78
Gases Mixtures and Movements

• Example
• A sample of hydrogen effuses through a porous
  container about 9 times faster than an unknown
  gas. Estimate the molar mass of the unknown gas.
• 92 81 2 g/mol H2 160 g/mol

79
Gases Mixtures and Movements

• Example
• Compare the rate of effusion of carbon dioxide
  with that of hydrogen chloride at the same
  temperature and pressure.
• Rate of Effusion of CO2/Rate of Effusion of HCl
  v36.46/v44.01
• 6.04/6.63 0.9110
• CO2 will effuse about 0.9110 times as fast as HCl

80
Gases Mixtures and Movements

• Example
• If neon gas travels at 400 m/s at a given
  temperature, estimate the rate of diffusion of
  butane gas, C4H10, at the same temperature.
• Rate of Effusion of Ne/Rate of Effusion of C4H10
  v58.14/v20.18
• 7.62/4.49 1.70
• Ne diffuses 1.70 times faster than butane
• Butane diffuses at a speed of 400/1.70 235 m/s