1. University of Nebraska-Lincoln
Chemistry
Second Edition
Julia Burdge
Lecture Powerpoints
Jason A. Kautz
University of Nebraska-Lincoln 11
Gases
Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

2. 11 Gases 11.1 Properties of Gases Characteristics of Gases
Gas Pressure: Definition and Units
Calculation of Pressure
Measurement of Pressure
11.2 The Gas Laws
Boyle’s Law: The Pressure-Volume Relationship
Charles’s and Gay-Lussac’s Law: The Temperature-Volume Relationship
Avogadro’s Law: The Amount-Volume Relationship
11.3 The Ideal Gas Equation
Deriving the Ideal Gas Equation from the Empirical Gas Laws
Applications of the Ideal Gas Equation
11.4 Reactions with Gaseous Reactants and Products
Calculating the Required Volume of a Gaseous Reactant
Determining the Amount of Reactant Consumed Using Change in Pressure
Predicting the Volume of a Gaseous Product

3. 11 Gases 11.5 Gas Mixtures Dalton’s Law of Partial Pressures
Mole Fractions
Using Partial Pressures to Solve Problems
11.6 The Kinetic Molecular Theory of Gases
Application of the Gas Laws
Molecular Speed
Diffusion and Effusion
11.7 Deviation from Ideal Behavior
Factors That Cause Deviation from Ideal Behavior
The van der Waals Equation

4. Properties of Gases
11.1
Gases differ from solids and liquids in the following ways:
A sample of gas assumes both the shape and volume of the container.
Gases are compressible.
The densities of gases are much smaller than those of liquids and solids and are highly variable depending on temperature and pressure.
Gases form homogeneous mixtures (solutions) with one another in any proportion.

5. Properties of Gases
Pressure is defined as the force applied per unit area:
The SI unit of force is the newton (N), where
The SI unit of pressure is the pascal (Pa), defined as 1 newton per square meter.
1 N = 1 kg•m/s2
1 Pa = 1 N/m2

6. Properties of Gases

7. Properties of Gases
A barometer is an instrument that is used to measure atmospheric pressure.
Standard atmospheric pressure (1 atm) was originally defined as the pressure that would support a column of mercury exactly 760 mm high.
h = height in m
d = is the density in kg/m3
g = is the gravitational constant ( m/s2)

8. Properties of Gases
A barometer is an instrument that is used to measure atmospheric pressure.
1 atm* = 101,325 Pa
= 760 mmHg*
= 760 torr*
= bar
= 14.7 psi
* Represents an exact number

9. Properties of Gases
A manometer is a device used to measure pressures other than atmospheric pressure.

10. at constant temperature
The Gas Laws
11.2
(a)
(b)
(c)
P (mmHg)
760
1520
2280
V (mL)
100 50 33
Boyle’s law states that the pressure of a fixed amount of gas at a constant temperature is inversely proportional to the volume of the gas.
P1V1 = P2V2
at constant temperature

11. The Gas Laws
Calculate the volume of a sample of gas at 5.75 atm if it occupies 5.14 L at 2.49 atm. (Assume constant temperature.)
Solution:
Step 1: Use the relationship below to solve for V2:
P1V1 = P2V2

12. The Gas Laws
Charles’s and Gay-Lussac’s law, (or simply Charles’s Law) states that the volume of a gas maintained at constant pressure is directly proportional to the absolute temperature of the gas.
Higher temperature
Lower temperature

13. The Gas Laws
Charles’s and Gay-Lussac’s law, (or simply Charles’s Law) states that the volume of a gas maintained at constant pressure is directly proportional to the absolute temperature of the gas.
at constant pressure

14. The Gas Laws
A sample of gas originally occupies 29.1 L at 0.0°C. What is its new volume when it is heated to 15.0°C? (Assume constant pressure.)
Solution:
Step 1: Use the relationship below to solve for V2: (Remember that temperatures must be expressed in kelvin.

15. at constant temperature and pressure
The Gas Laws
Avogadro’s law states that the volume of a sample of gas is directly proportional to the number of moles in the sample at constant temperature and pressure.
at constant temperature and pressure

16. The Gas Laws
What volume in liters of water vapor will be produced when 34 L of H2 and 17 L of O2 react according to the equation below:
2H2(g) + O2(g) → 2H2O(g)
Assume constant pressure and temperature.
Solution:
Step 1: Because volume is proportional to the number of moles, the balanced equation determines in what volume ratio the reactants combine and the ratio of product volume to reactant volume. The amounts of reactants given are stoichiometeric amounts.
34 L of H2O will form.

17. The Gas Laws
The combined gas law can be used to solve problems where any or all of the variables changes.

18. The Gas Laws
The volume of a bubble starts at the bottom of a lake at 4.55°C increases by a factor of 10 as it rises to the surface where the temperature is 18.45°C and the air pressure is atm. Assume the density of the lake water is 1.00 g/mL. Determine the depth of the lake.
Solution:
Step 1: Use the combined gas law to find the pressure at the bottom of the lake; assume constant moles of gas.

19. The Gas Laws
The volume of a bubble starts at the bottom of a lake at 4.55°C increases by a factor of 10 as it rises to the surface where the temperature is 18.45°C and the air pressure is atm. Assume the density of the lake water is 1.00 g/mL. Determine the depth of the lake.
Solution:
Step 2: Use the equation P = hdg to determine the depth of the lake The pressure represents the difference in pressure from the surface to the bottom of the lake.
Pressure exerted by the lake = Pbottom of lake – Pair
P = 9.19 atm – atm = atm

20. The Gas Laws
The volume of a bubble starts at the bottom of a lake at 4.55°C increases by a factor of 10 as it rises to the surface where the temperature is 18.45°C and the air pressure is atm. Assume the density of the lake water is 1.00 g/mL. Determine the depth of the lake.
Solution:
Step 2 (Cont): Convert pressure to pascals and density to kg/m3.
P = hdg
833,398 Pa = h(1000 kg/m3)(9.81 m/s2)
h = 85.0 m

21. The Ideal Gas Equation
11.3
The gas laws can be combined into a general equation that describes the physical behavior of all gases.
Boyle’s law
Charles’s law
Avogadro’s law
PV = nRT
rearrangement
R is the proportionality constant, called the gas constant.

22. The Ideal Gas Equation
The ideal gas equation (below) describes the relationship among the four variables P, V, n, and T.
PV = nRT
An ideal gas is a hypothetical sample of gas whose pressure-volume-temperature behavior is predicted accurately by the ideal gas equation.

23. The Ideal Gas Equation
The gas constant (R) is the proportionality constant and its value and units depend on the units in which P and V are expressed.
PV = nRT

24. The Ideal Gas Equation
Standard Temperature and Pressure (STP) are a special set of conditions where:
Pressure is 1 atm
Temperature is 0°C ( K)
The volume occupied by one mole of an ideal gas is then L:
PV = nRT

25. The Ideal Gas Equation
Using algebraic manipulation, it is possible to solve for variables other than those that appear explicitly in the ideal gas equation.
PV = nRT
d is the density (in g/L)
M is the molar mass (in g/mol)

26. The Ideal Gas Equation
What pressure would be required for helium at 25°C to have the same density as carbon dioxide at 25°C and 1.00 atm?
Solution:
Step 1: Use the equation below to calculate the density of CO2 at 25°C and 1 atm.

27. The Ideal Gas Equation
What pressure would be required for helium at 25°C to have the same density as carbon dioxide at 25°C and 1 atm?
Solution:
Step 2: Use the density of CO2 found in step 1 to calculate the pressure
for He at 25°C.
P = 11.0 atm

28. Reactions with Gaseous Reactants and Products
11.4
What mass (in grams) of Na2O2 is necessary to consume 1.00 L of CO2 at STP?
2Na2O2(s) + 2CO2(g) → 2Na2CO3(s) + O2(g)
Solution:
Step 1: Convert 1.00 L of CO2 at STP to moles using the ideal gas equation.
PV = nRT
(1 atm)(1.00 L) = n( Latm/mol K)( K)
n = moles CO2

29. Reactions with Gaseous Reactants and Products
What mass (in grams) of Na2O2 is necessary to consume 1.00 L of CO2 at STP?
2Na2O2(s) + 2CO2(g) → 2Na2CO3(s) + O2(g)
Solution:
Step 2: Determine the stoichiometric amount of Na2O2.

30. Reactions with Gaseous Reactants and Products
Although there are no empirical gas laws that focus on the relationship between n and P, it is possible to rearrange the ideal gas equation to find the relationship.
PV = nRT
rearrangement
The change in pressure in a reaction vessel can be used to determine how many moles of gaseous reactant are consumed:

31. Ptotal = PN2 + PO2 = 4.48 atm + 4.48 atm = 8.96 atm
Gas Mixtures
11.5
When two or more gases are placed in a container, each gas behaves as though it occupies the container alone.
1.00 mole of N2 in a 5.00 L container at 0°C exerts a pressure of 4.48 atm.
Addition of 1.00 mole of O2 in the same container exerts an additional 4.48 atm of pressure.
The total pressure of the mixture is the sum of the partial pressures (Pi):
Ptotal = PN2 + PO2 = 4.48 atm atm = 8.96 atm

32. Gas Mixtures
Dalton’s law of partial pressure states that the total pressure exerted by a gas mixture is the sum of the partial pressures exerted by each component of the mixture:

33. Gas Mixtures
Determine the partial pressures and the total pressure in a 2.50-L vessel containing the following mixture of gases at 15.8°C: mol He, mol H2, and mol Ne.
Solution:
Step 1: Since each gas behaves independently, calculate the partial pressure of each using the ideal gas equation:

34. Gas Mixtures
Determine the partial pressures and the total pressure in a 2.50-L vessel containing the following mixture of gases at 15.8°C: mol He, mol H2, and mol Ne.
Solution:
Step 2: Use the equation below to calculate total pressure.
Ptotal = atm atm atm = 2.17 atm

35. Gas Mixtures
The relative amounts of the components in a gas mixture can be specified using mole fractions.
There are three things to remember about mole fractions:
The mole fraction of a mixture component is always less than 1.
The sum of mole fractions for all components of a mixture is always 1.
Mole fractions are dimensionless.
Χi is the mole fraction.
ni is the moles of a certain component
ntotal is the total number of moles.

36. Ptotal = Pcollected gas + PH2O
Gas Mixtures
The volume of gas produced by a chemical reaction can be measured using an apparatus like the one shown below.
When gas is collected over water in this manner, the total pressure is the sum of two partial pressures:
Ptotal = Pcollected gas + PH2O

37. Gas Mixtures
The vapor pressure of water is known at various temperatures.

38. Gas Mixtures
Calculate the mass of O2 produced by the decomposition of KClO3 when 821 mL of O2 is collected over water at 30.0°C and atm.
Solution:
Step 1: Use Table 11.5 to determine the vapor pressure of water at 30.0°C.

39. Gas Mixtures
Calculate the mass of O2 produced by the decomposition of KClO3 when 821 mL of O2 is collected over water at 30.0°C and atm.
Solution:
Step 2: Convert the vapor pressure of water at 30.0°C to atm and then use Dalton’s law to calculate the partial pressure of O2.
Ptotal = PO2 + PH2O
PO2 = Ptotal – PH2O
PO2 = atm – atm = atm

40. Gas Mixtures
Calculate the mass of O2 produced by the decomposition of KClO3 when 821 mL of O2 is collected over water at 30.0°C and atm.
Solution:
Step 3: Convert to moles of O2 using the ideal gas equation and then find mass.
PV = nRT

41. The Kinetic Molecular Theory
11.6
The kinetic molecular theory explains how the molecular nature of gases gives rise to their macroscopic properties.
The basic assumptions of the kinetic molecular theory are as follows:
A gas is composed of particles that are separated by large distances. The volume occupied by individual molecules is negligible.
Gas molecules are constantly in random motion, moving in straight paths, colliding with perfectly elastic collisions.
Gas molecules do not exert attractive or repulsive forces on one another.
The average kinetic energy of a gas molecules in a sample is proportional to the absolute temperature:

42. The Kinetic Molecular Theory
Gases are compressible because molecules in the gas phase are separated by large distances (assumption 1).
Pressure is the result of the collisions of gas molecules with the walls of their container (assumption 2).
Decreasing volume increases the frequency of collisions.
Pressure increases as collision frequency increases.

43. The Kinetic Molecular Theory
Heating a sample of gas increases its average kinetic energy (assumption 4).
Gas molecules must move faster.
Faster molecules collide more frequently and at a greater speed.
Pressure increases as collision frequency increases.

44. The Kinetic Molecular Theory
Cooling at constant volume:
Pressure decreases
Heating at constant volume: pressure increases

45. The Kinetic Molecular Theory
Cooling at constant pressure:
volume decreases
Heating at constant pressure: volume increases

46. The Kinetic Molecular Theory
The presence of additional molecules causes an increase in pressure.

47. The Kinetic Molecular Theory
Each component of a gas mixture exerts a pressure independent of the other components. The total pressure is the sum of the partial pressures.

48. The Kinetic Molecular Theory
The total kinetic energy of a mole of gas is equal to:
The average kinetic energy of one molecule is:
For one mole of gas:
m is the mass
is the mean square speed
rearrange and
Take the square root
(m x NA = M)

49. The Kinetic Molecular Theory
The root-mean-square (rms) speed (urms) is the speed of a molecule with the average kinetic energy in a gas sample.
urms is directly proportional to temperature

50. The Kinetic Molecular Theory
The root-mean-square (rms) speed (urms) is the speed of a molecule with the average kinetic energy in a gas sample.
urms is inversely proportional to the square root of M.

51. The Kinetic Molecular Theory
When two gases are at the same temperature, it is possible to compare the the urms values of the different gases.

52. The Kinetic Molecular Theory
Diffusion is the mixing of gases as the result of random motion and frequent collisions.
Effusion is the escape of gas molecules from a container to a region of vacuum.

53. The Kinetic Molecular Theory
Graham’s law states that the rate of diffusion or effusion of a gas is inversely proportional to the square root of its molar mass.

54. The Kinetic Molecular Theory
Determine the molar mass and identity of a diatomic gas that moves 4.67 times as fast as CO2.
Solution:
Step 1: Use the equation below to determine the molar mass of the unknown gas:
urms(unknown gas) = 4.67 x urms(CO2)
The gas must be H2.

55. Deviation from Ideal Behavior
11.7
The van der Waals equation is useful for gases that do not behave ideally.
Experimentally measured pressure
Container volume
corrected
pressure term
corrected
volume term

56. Deviation from Ideal Behavior
The van der Waals equation is useful for gases that do not behave ideally.

57. Deviation from Ideal Behavior
Calculate the pressure exerted by 0.35 mole of oxygen gas in a volume of 6.50 L at 32°C using (a) the ideal gas equation and(b) the van der Waals equation.
Solution:
Step 1: Use the ideal gas equation to calculate the pressure of O2.
PV = nRT

58. Deviation from Ideal Behavior
Calculate the pressure exerted by 0.35 mole of oxygen gas in a volume of 6.50 L at 32°C using (a) the ideal gas equation and(b) the van der Waals equation.
Solution:
Step 2: Use table 11.6 to find the values of a and b for O2.

59. Deviation from Ideal Behavior
Calculate the pressure exerted by 0.35 mole of oxygen gas in a volume of 6.50 L at 32°C using (a) the ideal gas equation and (b) the van der Waals equation.
Solution
Step 2: Use the van der Waals equation to calculate P.
P = 1.3 atm

60. Chapter Summary: Key Points11
Characteristics of Gases
Gas Pressure: Definition and Units
Calculation of Pressure
Measurement of Pressure
Boyle’s Law: The Pressure-Volume Relationship
Charles’s and Gay-Lussac’s Law: The Temperature-Volume Relationship
Avogadro’s Law: The Amount-Volume Relationship
Deriving the Ideal Gas Equation from the Empirical Gas Laws
Applications of the Ideal Gas Equation
Calculating the Required Volume of a Gaseous Reactant
Determining the Amount of Reactant Consumed Using Change in Pressure
Predicting the Volume of a Gaseous Product
Dalton’s Law of Partial Pressures
Mole Fractions
Using Partial Pressures to Solve Problems
Application of the Gas Laws
Molecular Speed
Diffusion and Effusion
Factors That Cause Deviation from Ideal Behavior
The van der Waals Equation