1. Chapter 10 Gases

2. 10.1 Characteristics of Gases

3. Characteristics of Gases
Unlike liquids and solids, gases
expand to fill their containers;
are highly compressible;
have extremely low densities.
P.395 GIST: What is the major reason that physical properties of gases do not differ much from one another?

4. 10.2 Pressure

5. Pressure F P = A Pressure is the amount of force applied to an area.
Atmospheric pressure is the weight of air per unit of area.

6. Units of Pressure
Pascals
1 Pa = 1 N/m2
Bar
1 bar = 105 Pa = 100 kPa

7. Units of Pressure mm Hg or torr
These units are literally the difference in the heights measured in mm (h) of two connected columns of mercury.
Atmosphere
1.00 atm = 760 torr

8. Manometer
This device is used to measure the difference in pressure between atmospheric pressure and that of a gas in a vessel.

9. Standard Pressure
Normal atmospheric pressure at sea level is referred to as standard pressure.
It is equal to
1.00 atm
760 torr (760 mm Hg)
kPa

10. Exercise 10.1 1) Convert 0.357 atm to torr
2) Convert 6.6 x 10-2 torr to atm
3) Convert kPa to torr
4) An English unit of pressure is pounds per square inch (lb/in2 or psi). 1 atm = 14.7 lb/in2. If a pressure is reported as 91.5 psi, express the measurement in atmospheres
5) What happens to the height of the mercury column in a barometer as you move to a higher altitude? Why?

11. Exercise 10.2
On a certain day, the laboratory barometer reads torr. A sample of gas is placed in a flask attached to an open-end mercury manometer. Using a meter stick, the level of mercury in the open-end has a height of mm, and the mercury in the arm that is in contact with the gas has a height of mm. What is the pressure of the gas in atm and in kPa?
Convert a pressure of atm into Pa and kPa.

12. 10.3 The Gas Laws

13. Boyle’s Law
The volume of a fixed quantity of gas at constant temperature is inversely proportional to the pressure.

14. As P and V are inversely proportional
A plot of V versus P results in a curve.
Since
V = k (1/P)
This means a plot of V versus 1/P will be a straight line.
PV = k

15. Charles’s Law
The volume of a fixed amount of gas at constant pressure is directly proportional to its absolute temperature.
i.e., V T
= k
A plot of V versus T will be a straight line.

16. Avogadro’s Law
The volume of a gas at constant temperature and pressure is directly proportional to the number of moles of the gas.
Mathematically, this means
V = kn

17. p.400 GIST
What happens to the volume of a gas if you double the pressure, say from 1 atm to 2 atm, while its temperature is held constant?
Does the volume of a fixed quantity of gas decrease to half its original value when the temperature is lowered from 100°C to 50°C?

18. Sample Exercise 10.3
1) Consider the following changes to a gas in a cylinder as shown on p Indicate how these changes will affect the average distance between molecules, the pressure of the gas, and the number of moles of gas present in the cylinder.
A) Heat the gas from 298 K to 360 K, while maintaining the position of the piston
B) Move the piston to reduce the volume of gas from 1 L to 0.5 L
C) Inject additional gas through the gas inlet valve

19. 10.3 Practice Exercise What happens to the density of a gas as
A) the gas is heated in a constant-volume container
B) the gas is compressed at constant temperature
C) additional gas is added to a constant-volume container

20. 10.4 The Ideal-Gas Equation

21. Ideal-Gas Equation V  nT P So far we’ve seen that
V  1/P (Boyle’s law)
V  T (Charles’s law)
V  n (Avogadro’s law)
Combining these, we get
V  nT P

22. Ideal-Gas Equation
The constant of proportionality is known as R, the gas constant.

23. Ideal-Gas Equation PV = nRT nT P V  nT P V = R or The relationship
then becomes or
PV = nRT

24. Molar Volume
If you have mol of an ideal gas at atm and 0.00 °C ( K), according to the ideal gas equation, the volume is L. This is the molar volume for standard temperature and pressure (STP).
p. 403 GIST: How many molecules are in L of an ideal gas at STP?

25. Exercise 10.4
1) CaCO3 decomposes upon heating to give CaO and CO2. A sample of CaCO3 is decomposed, and the CO2 is collected in a 250 mL flask. After decomposition, the gas has a pressure of 1.3 atm at a temperature of 31ºC. How many moles of CO2 gas were generated?
2) Tennis balls are usually filled with air or N2 gas to a pressure above atmospheric pressure to increase their bounce. If a particular tennis ball has a volume of 144 cm3 and contains 0.33 g N2 gas, what is the pressure inside the ball at 24ºC?

26. Exercise 10.5
3) The gas pressure in an aerosol can is 1.5 atm at 25ºC. What would the pressure be if the can were heated to 450ºC?
4) A large natural-gas storage tank is arranged so that the pressure is maintained at 2.20 atm. On a cold day when the temperature is -15ºC, the volume of gas in the tank is 28,500 ft3. What is the volume of the same quantity of gas on a warm July day when the temperature is 31ºC?

27. Exercise 10.6
5) An inflated balloon has a volume of 6.0 L at sea level (1.0 atm) and is allowed to ascend in altitude until the pressure is 0.45 atm. The temperature falls from 22ºC to -21ºC. Calculate the new volume of the balloon.
6) A 0.50 mol sample of oxygen gas is confined at 0ºC in a cylinder with a movable piston. The gas has an initial pressure of 1.0 atm. The gas is then compressed by the piston so that its final volume is half the initial volume. The final pressure of the gas is 2.2 atm. What is the final temperature of the gas in degrees Celsius?

28. 10.5 Further Applications of the Ideal-Gas Equation

29. Densities of Gases n P V = RT
If we divide both sides of the ideal-gas equation by V and by RT, we get n V P RT =

30. Densities of Gases n   = m P RT m V = We know that
moles  molecular mass = mass
n   = m
So multiplying both sides by the molecular mass ( ) gives P RT m V =

31. Densities of Gases P RT m V = d =
Mass  volume = density
So, P RT m V =
d =
Note: One only needs to know the molecular mass, the pressure, and the temperature to calculate the density of a gas.

32. Molecular Mass P d = RT dRT P  =
We can manipulate the density equation to enable us to find the molecular mass of a gas: P RT
d =
Becomes
dRT P
 =

33. Exercise 10.7
1) What is the density of carbon tetrachloride vapor at 714 torr and 125ºC?
2) The mean molar mass of the atmosphere at the surface of Titan, Saturn’s largest moon, is 28.6 g/mol. The surface temperature is 95 K, and the pressure is 1.6 atm. Calculate the density of Titan’s atmosphere.
3) Is water vapor more or less dense than N2 under the same conditions of temperature and pressure?

34. Exercise 10.8
3) A large flask is evacuated and found to weigh g. It is then filled with gas to a pressure of 735 torr at 31ºC and reweighed; its mass is now g. Finally, the flask is filled with water at 31ºC and found to weigh g. The density of water at this temperature is g/mL. Calculate the molar mass of the unknown gas.
4) Calculate the average molar mass of dry air if it has a density of 1.17 g/L at 21ºC and 740 torr.

35. Exercise 10.9
5) The air bags in automobiles are inflated by nitrogen gas produced from rapid decomposition of sodium azide, NaN3.
2NaN3(s) → 2Na(s) + 3N2(g)
If an air bag has a volume of 36 L and is filled with nitrogen gas at a pressure of 1.15 atm at a temperature of 26.0ºC, how many grams of NaN3 must be decomposed.

36. Practice
6) In the first step in the industrial process for making nitric acid, ammonia reacts with oxygen in the presence of a suitable catalyst to form nitric oxide and water vapor:
4 NH3(g) + 5 O2(g) → 4 NO(g) + 6 H2O(g)
How many liters of ammonia at 850ºC and 5.00 atm are required to react with 1.00 mol of O2 in this reaction?

37. 10.6 Gas Mixtures and Partial Pressures

38. Dalton’s Law of Partial Pressures
The total pressure of a mixture of gases equals the sum of the pressures that each would exert if it were present alone.
In other words,
Ptotal = P1 + P2 + P3 + …

39. Exercise 10.10
1) A gaseous mixture made from 6.00 g O2 and 9.00 g CH4 is placed in a 15.0 L vessel at 0ºC. What is the partial pressure of each gas, and what is the total pressure in the vessel?
2) What is the total pressure exerted by a mixture of 2.00 g of H2 and 8.00 g of N2 at 273 K in 10.0 L vessel?

40. Sample Exercise 10.11
3) A synthetic plant gas atmosphere is 1.5 mol percent CO2, 18.0 mol percent O2, and 80.5 mol percent Ar.
A) Calculate the partial pressure of O2 in the mixture if the total pressure of the atmosphere is 745 torr.
B) If this atmosphere is held in a 120 L space at 295 K, how many moles of O2 are needed?

41. Practice
4) From data gathered by Voyager 1, scientists have estimated the composition of the atmosphere of Titan, Saturn’s largest moon. The total pressure on the surface of Titan is 1220 torr. The atmosphere consists of 82 mol percent N2, 12 mol percent Ar, and 6.0 mol percent CH4. Calculate the pressure of each of these gases in Titan’s atmosphere.

42. Partial Pressures
When one collects a gas over water, there is water vapor mixed in with the gas.
To find only the pressure of the desired gas, one must subtract the vapor pressure of water from the total pressure.

43. Sample Exercise 10.12
1) A sample of KClO3 is partially decomposed producing O2 gas that is collected over water. The volume of the gas collected is L at 26ºC and 765 torr total pressure.
A) How many moles of O2 are collected?
B) How many grams of KClO3 were decomposed?

44. Practice
2) Ammonium nitrite, NH4NO2, decomposes upon heating to form N2 gas:
NH4NO2(s) → N2(g) + 2H2O(l)
When a sample of NH4NO2 is decomposed in a test tube, 511 mL of nitrogen gas is collected over water at 26ºC and 745 torr total pressure. How many grams of NH4NO2 were decomposed?

45. 10.7 Kinetic-Molecular Theory

46. Kinetic-Molecular Theory
This is a model that aids in our understanding of what happens to gas particles as environmental conditions change.

47. Main Tenets of Kinetic-Molecular Theory
Gases consist of large numbers of molecules that are in continuous, random motion.

48. Main Tenets of Kinetic-Molecular Theory
The combined volume of all the molecules of the gas is negligible relative to the total volume in which the gas is contained.

49. Main Tenets of Kinetic-Molecular Theory
Attractive and repulsive forces between gas molecules are negligible.

50. Main Tenets of Kinetic-Molecular Theory
Energy can be transferred between molecules during collisions, but the average kinetic energy of the molecules does not change with time, as long as the temperature of the gas remains constant.

51. Main Tenets of Kinetic-Molecular Theory
The average kinetic energy of the molecules is proportional to the absolute temperature.

52. p GIST
Consider three samples of gas: HCl at 298 K, H2 at 298 K, and O2 at 350 K. Compare the average kinetic energies of the molecules in the three samples.
Consider three samples of gas all at 298 K: HCl, H2, and O2. List the molecules in order of increasing average speed.

53. Sample Exercise 10.13
1) A sample of O2 gas at STP is compressed to a smaller volume at constant temperature. What effect does this change have on:
A) The average kinetic energy of O2 molecules
B) The average speed of O2 molecules
C) The total number of collisions of O2 molecules with the container walls in a unit time
D) The number of collisions of O2 molecules with a unit area of container wall per unit time?

54. Practice 2) How is the rms speed of N2 molecules in a gas changed by:
A) An increase in temperature
B) An increase in volume
C) Mixing with a sample of Ar at the same temperature?

55. 10.8 Molecular Effusion and Diffusion

56. rms speed
Particles of a lighter gas have a higher rms speed, u, than the particles in a heavier gas.

57. Exercise 10.14
1) Calculate the rms speed, u, of an N2 molecule at 25ºC.
2) What is the rms speed of an He atom at 25ºC?

58. Effusion
Effusion is the escape of gas molecules through a tiny hole into an evacuated space.

59. Effusion
The difference in the rates of effusion for helium and nitrogen, for example, explains a helium balloon would deflate faster.

60. Diffusion
Diffusion is the spread of one substance throughout a space or throughout a second substance.

61. Graham's Law KE1 KE2 = 1/2 m1v12 1/2 m2v22 = = m1 m2 v22 v12

62. Exercise 10.15
1) An unknown gas composed of homonuclear diatomic molecules effuses at a rate that is only times that of O2 at the same temperature. Calculate the molar mass of the unknown and identify it.
2) Calculate the ratio of effusion rates of N2 and O2.
3) Will the following changes increase, decrease, or have no effect on the mean free path of the gas molecules:
A) increasing pressure
B) increasing temperature

63. 10.9 Real Gases: Deviations from Ideal Behavior

64. Real Gases
In the real world, the behavior of gases only conforms to the ideal-gas equation at relatively high temperature and low pressure.

65. Real Gases
Even the same gas will show wildly different behavior under high pressure at different temperatures.

66. Deviations from Ideal Behavior
The assumptions made in the kinetic-molecular model (negligible volume of gas molecules themselves, no attractive forces between gas molecules, etc.) break down at high pressure and/or low temperature.

67. Corrections for Nonideal Behavior
The ideal-gas equation can be adjusted to take these deviations from ideal behavior into account.
The corrected ideal-gas equation is known as the van der Waals equation.

68. The van der Waals Equation
) (V − nb) = nRT
n2a V2
(P +

69. p GISt
Would you expect helium gas to deviate from ideal behavior more at (a) 100 K and 1 atm, (b) 100 K and 5 atm, or (c) 300 K and 2 atm?
List two reasons why gases deviate from ideal behavior.

70. Exercise 10.16
1) If mol of an ideal gas were confined to L at 0.0ºC, it would exert a pressure of atm. Use the Van der Waals equation and the constants in table 10.3 to estimate the pressure exerted by mol of Cl2 in L at 0.0ºC
2) Consider a mol sample of CO2 confined to a volume of L at 0.0ºC. Calculate the pressure of the gas using the ideal gas equation and also the Van der Waals equation.

71. Integrative Exercise
Cyanogen, a highly toxic gas, is composed of 46.2% C and 53.8% N by mass. At 25ºC and 751 torr, 1.05 g of cyanogen occupies L.
A) What is the molecular formula?
B) Predict its molecular structure.
C) Predict the polarity of the compound.