1. Gases
Chapter 5 Unit 3

2. The Properties of Gases
Only four quantities are needed to define the state of a gas
The quantity of gas, n (in moles)
The temperature of the gas, T (in Kelvins)
The volume of the gas, V (in liters)
The pressure of the gas, P (in atmospheres, torr, mm of Hg, or kPa)

3. 5.1 Pressure
pressure: the weight or force that is produced when something presses or pushes against something else (force/unit area)
Barometer: a device to measure atmospheric pressure, invented in by Evangelista Torricelli
The original barometer used the height of a column of mercury to measure gas pressure

5. Units of Pressure
760 mm Hg = 760 torr = 1.00 atm = kPa (the SI unit of measurement)
At sea level all of the above define standard pressure, but usually 1.00 atm is used to define standard pressure
Most AP questions use atm, but the conversion from mm Hg and torr is on the sheet of equations and constants

6. Manometer
Manometer: device for measuring the pressure of a gas in a container
The pressure of the gas is given by “h” (the difference in mercury levels)

7. Manometer

8. Pressure Conversions
The pressure of a gas is measured as 49 torr. Represent this pressure in both atmospheres and pascals
Answer: 6.4 x 10-2 atm, 6.5 x 103 Pa
Rank the following pressures in decreasing order of magnitude: 75 kPa, 300. torr, atm, and 350. mm Hg.
Answer:
75 kPa < 0.60 atm < 350. mm Hg < 300. torr

9. 5.2 Gas Laws
The gas laws are several mathematical laws that relate the properties of gases
The laws were derived from experiments that involved careful measurements of the properties so relationships could be discovered
AP exams can show these laws graphically

10. Boyle’s Law
The first quantitative experiments on gases were performed by Irish chemist Robert Boyle ( )
He studied the relationship between pressure and volume of a trapped gas
The AP “cheat sheet” gives us PV = nRT for gases
If nRT is held constant, then PV = k with “k” being a constant

11. The relationship discovered is inverse
Boyle’s law holds precisely only at very low pressures
We will assume that gases obey Boyle’s law unless otherwise stated
A more useful form of Boyle’s law lets us predict the new volume of a gas when the pressure is changed (at constant T)
P1V1 = P2V2

13. Example
Sulfur dioxide, a gas that plays a central role in the formation of acid rain, is found in the exhaust of automobiles and power plants. Consider a 1.53-L sample of gaseous SO2 at a pressure of 5.6 x 103 Pa. If the pressure is changed to 1.5 x 104 Pa at a constant temperature, what will be the new volume of the gas?
Answer: 0.57 L

14. Charles’ Law
If a given quantity of gas is held at a constant pressure, then its volume is directly proportional to the absolute temperature.
Must use Kelvin for the temperature scale
The useful form is : V1 = V2
T T2
Jacques Charles was a French physicist

16. Example
A sample of gas at 15.0°C and 1.00 atm has a volume of 2.58 L. What volume will this gas occupy at 38°C and 1.00 atm?
Remember to change °C to Kelvin
Answer: 2.79 L

17. Gay Lussac’s Law
Gay-Lussac’s law shows the relationship between pressure and temperature (must use Kelvin for temperature)
The relationship is direct
P = kT or P/T = k
Useful form: P1 = P2
T1 T2

19. Example
The gas in a container is at a pressure of atm at 25°C. Directions on the container warn the user not to keep it in a place where the temperature exceeds 52°C. What would the gas pressure in the container be at 52°C?
Answer: 3.27 atm

20. Avogadro’s Law
Avogadro’s law: for a gas at constant temperature and pressure, the volume is directly proportional to the number of moles of gas.
V = kn (“k” is sometimes shown as “a”)
“V” is volume, “k” is a proportionality constant, and “n” is the number of moles

22. Example
Suppose we have a 12.2-L sample containing 0.50 mol oxygen gas at a pressure of 1.0 atm and a temperature of 25°C. If all this O2 were converted to ozone (O3) at the same temperature and pressure, what would be the volume of the ozone?
Answer: 8.1 L

23. Combined Gas Law
A gas sample frequently undergoes changes in temperature, pressure, and volume all at the same time.
The amount of gas remains constant
Combined gas law: expresses the relationship between pressure, volume, and temperature of a fixed amount of gas

24. Example
A sample of diborane gas (B2H6), a substance that bursts into flame when exposed to air, has a pressure of 345 torr at a temperature of 15°C and a volume of L. If conditions are changed so that the temperature is 36°C and the pressure is 468 torr, what will be the volume of the sample?
3.07 L

25. 5.3 Ideal Gas Law If you consider all the laws together, you get:
PV = nRT
where P is pressure, V is volume, n is number of moles, R is a proportionality constant called the universal gas constant, and T is temperature
Useful only at low P and high T and you can assume these are the conditions unless told otherwise

26. Universal Gas Constant
You should always use liters for volume and Kelvin for temperature
The gas constant changes depending on the units used for pressure
On the “cheat sheet” you are given the gas constant for atm, torr (also mm Hg) and the one you use when dealing with energy

27. Example
A sample of hydrogen gas (H2) has a volume of 8.56 L at a temperature of 0°C and a pressure of 1.5 atm. Calculate the moles of H2 molecules present in this gas sample.
Answer: 0.57 mol H2

28. More Practice with Gas Laws
Suppose we have a sample of ammonia gas with a volume of 3.5 L at a pressure of 1.68 atm. The gas is compressed to a volume of 1.35 L at a constant temperature. Calculate the final pressure.
Answer: 4.4 atm

29. More
A sample of methane gas that has a volume of 3.8 L at 5°C is heated to 86°C at constant pressure. Calculate its new volume. Answer: 4.9 L
A sample containing 0.35 mol argon gas at a temperature of 13°C and a pressure of 568 torr is heated to 56°C and a pressure of 897 torr. Calculate the change in volume that occurs.
Answer: 3 L decrease

30. 5.4 Gas Stoichiometry Solve for the volume of one mol of gas at STP:
V = nRT V = (1) ( ) (273) = P
22. 4 L
This is the molar volume of a gas at STP

32. Examples
A sample of nitrogen gas has a volume of L at STP. How many mol of N2 are present?
Answer: 7.81 x 10-2 mol N2

33. More
Quicklime (CaO) is produced by the thermal decomposition of CaCO3. Calculate the volume of CO2 at STP produced from the decomposition of g CaCO3 by the reaction:
CaCO3(s)  CaO(s) + CO2(g)
Answer: 34.0 L CO2

34. One More
A sample of methane gas having a volume of 2.80 L at 25°C and 1.65 atm was mixed with a sample of oxygen gas having a volume of 35.0 L at 31°C and atm. The mixture was then ignited to form carbon dioxide and water. Calculate the volume of CO2 formed at a pressure of 2.50 atm and a temperature of 125°C.
Answer: 2.47 L CO2

35. Molar Mass of a Gas
The densities of gases are reported in g/L not g/mL
Since n = m/M and substituting m/V as gas density (d) into the ideal gas law equation gives you:
Molar mass (M) = dRT P
“Molar mass kitty cat”

36. Gas Density/ Molar Mass
The density of a gas was measured at atm and 27°C and found to be g/L. Calculate the molar mass of the gas.
Answer: 32.0 g/mol

37. 5.5 Dalton’s Law of Partial Pressures
For a mixture of gases in a container, the total pressure exerted is the sum of the pressures that each gas would exert if it were alone
Ptotal = P1 + P2 + P3 + …
The symbols P1, P2 and P3 refer the partial pressure of each individual gas

38. Moles of Gas
For a mixture of ideal gases, it is the total number of moles of particles that is important, not the identity of the gases

39. Total Pressure P1 = n1RT, P2 = n2RT, P3 = n3RT V V V
Ptotal = n1RT, + n2RT, n3RT
V V V
Ptotal = (ntotal) RT V

40. Example
Mixtures of helium and oxygen can be used in scuba diving tanks to help prevent “the bends”. For a particular dive, 46 L He at 25°C and 1.0 atm and 12 L O2 at 25°C and 1.0 atm were pumped into a tank with a volume of 5.0 L. Calculate the partial pressure of each gas and the total pressure in the tank at 25°C.
Answers: PHe = 9.3 atm, PO2 = 2.4 atm, PT = 11.7 atm

41. Mole Fraction
The ratio of the number of moles of a given component in a mixture to the total number of moles in the mixture (no units)
X = moles A
total moles
PA = Ptotal x XA and XA = PA
Ptotal

42. Examples
The partial pressure of oxygen was observed to be 156 torr in air with a total atmospheric pressure of 743 torr. Calculate the mole fraction of O2 present.
Answer: 0.210
The mole fraction of nitrogen in the air is Calculate the partial pressure of N2 in air when the atmospheric pressure is 760. torr.
Answer: 593 torr

43. Water Displacement
It is common to collect a gas by water displacement.
This means some of the pressure is due to water vapor collected as the gas is passing through.
You correct for this by looking up the partial pressure due to water vapor by knowing the temperature

45. Example
A sample of KClO3 (potassium chlorate) was heated in a test tube and decomposed by the reaction:
2KClO3(s)  2KCl(s) + 3O2(g)

46. Continued
The O2 produced was collected by water displacement at 22°C at a total pressure of 754 torr. The volume of gas collected was L, and vapor pressure of water at 22°C is 21 torr. Calculate the partial pressure of O2 in the gas collected and the mass of KClO3 in the sample that was decomposed.
Answers: PO2 = 733 torr, 2.12 g KClO3

47. 5.6 Kinetic Molecular Theory of Gases
Assumptions of the model:
All particles are in constant, random motion
All collisions between particles are perfectly elastic
The volume of the particles in a gas is negligible
The average kinetic energy of the molecules is directly proportional to its Kelvin temperature

48. Explanations
Boyle’s law: If the volume is decreased that means that the gas particles will hit the wall more often, thus increasing pressure
Charles’ law: when a gas is heated, the speed of its particles increase and thus hit the walls more often and with more force, so the volume must increase

49. More
Gay-Lussac’s law: when the temperature of a gas increases, the speeds of its particles increase, the particles are hitting the wall with greater force and greater frequency. Since the volume remains the same, this would result in increased gas pressure.

50. More
Avogadro’s law: an increase in the number of particles at the same temperature would cause the pressure to increase if the volume were held constant. The only way to keep constant P is to vary the V.

51. One More
Dalton’s law: the P exerted by a mixture of gases is the sum of the partial pressures since gas particles are acting independent of each other and the volumes of the individual particles do not matter.

52. Maxwell-Boltzmann Distribution Curve
The distribution shows how the speeds of molecules are distributed at different temperatures for an ideal gas.
The Maxwell-Boltzmann distribution is often represented with the following graph.
It is frequently used to show the energy distribution at different temperatures
Temperature is NOT on any axis

55. 5.7 Graham’s Law of Diffusion and Effusion
Diffusion: the term used to describe the mixing of gases
The rate of diffusion is the rate of mixing
Matter will move from an area of high concentration to an area of low concentration

56. Diffusion in Cells

57. Effusion
Effusion: the passage of a gas through a tiny orifice into an evacuated chamber
The rate of effusion measures the speed at which the gas is transferred into the chamber
rate of effusion of gas 1 = √M2
rate of effusion of gas √M1

59. Example
Calculate the ratio of the effusion rates of hydrogen gas (H2) and uranium hexafluoride (UF6), a gas used in the enrichment process to produce fuel for nuclear reactors.
Answer: 13.2

60. 5.8 Real Gas vs. Ideal Gas
Most gases behave ideally until you reach high pressure and low temperature
A gas acts close to ideally when:
The pressure is low
The temperature is high
The gas is nonpolar