1. THE PROPERTIES OF GASES
A gas uniformly fills any container, is easily compressed and mixes completely with any other gas.
Only four quantities define the state of a gas:
a. the quantity of the gas, n (in moles)
b. the temperature of the gas, T (in KELVINS)
c. the volume of the gas, V (in liters)
d. the pressure of the gas, P (in atmospheres)

2. PRESSURE A measure of the force that a gas exerts on its container.
Force is the physical quantity that interferes with inertia.
Gravity is the force responsible for weight.
Newton’s 2nd Law: Force = m × a
The units of force follow: N = kg × m/s2
Pressure - Force ÷ unit area; N/m2

3. PRESSURE Standard Pressure
mm Hg
torr
1.00 atm
kPa ≈ 105 Pa
The SI unit of pressure is the Pascal; 1 Pa = 1 N/m2

4. PRESSURE Pressure is measured in a variety of units.
ABBREVIATION
COMPARE TO 1 ATM
Kilopascal
kPa
101.3 kPa
Millimeters of mercury
mmHg
760.0 mmHg
Torr
torr
760.0 torr
Atmosphere
atm
1.0 atm
Pounds per square inch*
psi
14.7 psi
*We will use all of these but psi.

5. PRESSURE
Barometer - measures gas pressure (especially atmospheric). 1 mm of Hg = 1 torr
Manometer—a 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] in units of torr (equivalent to mm Hg).

6. PRESSURE

7. PRACTICE ONE
The pressure of a gas is measured as 49 torr. Represent this pressure in both atmospheres and pascals.

8. PRACTICE TWO
Rank the following pressures in decreasing order of magnitude (largest first, smallest last): 75 kPa, 300. torr, 0.60 atm, and mm Hg.

9. THE GAS LAWS Boyle’s Law: V and P;
inversely proportional.
Charles’ Law: T and V; directly proportional.
Gay-Lussac’s Law: P and T; directly proportional.
Avogadro’ Principle: moles and P or V; directly proportional.

10. BOYLE’S LAW

11. BOYLE’S LAW
THE LAW: the volume of a confined gas is inversely proportional to the pressure exerted on the gas: P1V1 = P2V2
P ∝ 1/V plot = straight line

12. GOOD HABITS EVERY TIME you do a gas laws problem:
Write what you know and what you are trying to find
Write the formula
Plug in the numbers with units and solve with the correct number of sig figs.

13. PRACTICE THREE
Consider a 1.53L sample of gaseous SO2 at a pressure of 5.6 × 1O3 Pa. If the pressure is changed to 1.5 × 104 Pa at a constant temperature, what will be the new volume of the gas ?

14. PRACTICE FOUR
Using the results listed below, calculate the Boyle’s law constant for NH3 at the various pressures.
Experiment Pressure (atm) Volume (L)

15. PV vs. P
What is the y- intercept? How about the 3rd graph on page two?
Molar Volume of a gas: L

16. CHARLES’ LAW

17. CHARLES LAW
THE LAW: If a given quantity of gas is held at a constant pressure, then its volume is directly proportional to the absolute temperature.
V1T2 = V2T1
You must use the Kelvin!
 K = °C

18. CHARLES’ LAW Where do all the gases cross the x- intercept?
If the volume is zero, what is the temperature?
ºC or 0K

19. PRACTICE FIVE
A sample of gas at 15ºC and 1 atm has a volume of 2.58 L. What volume will this gas occupy at 38ºC and 1 atm ?

20. GAY-LUSSAC’S LAW

21. GAY-LUSSAC’S LAW
THE LAW: An increase in temperature increases the frequency of collisions between gas particles. In a given volume, raising the KELVIN temperature also raises the pressure.
P1 T2 = P2T1
 You must use Kelvin!

22. AVOGADRO’S LAW Volume: 22.42L 22.42L 22.42L Mass: 39.95g 32.00g 28.02g
Quantity: 1 mol 1 mol 1 mol
Pressure: 1 atm 1 atm 1 atm
Temperature: K K K

23. AVOGADROS’S LAW
The volume of a gas, at a given temperature and pressure, is directly proportional to the quantity of gas.
Equal volumes of gases under the same conditions of temperature and pressure contain equal numbers of molecules.
In gas law problems, moles is designated by an “n”.
One mole of a gas has a volume of L (dm3) at STP. It also has 6.02 x 1023 particles of that gas.

24. PRACTIVE SIX
Suppose we have a 12.2-L sample containing mol oxygen gas (O2) at a pressure of 1 atm and a temperature of 25ºC. If all this O2 were converted to ozone (O3) at the same temperature and pressure, what would be the volume of the ozone ?

25. HINT
PTV

26. HINT
PVT
Put the scientists' names in alphabetical order. Boyle’s uses the first 2 variables, Charles’ the second 2 variables and Gay- Lussac’s the remaining combination of variables.

27. From the Boyle’s, Charles’, and Gay-Lussac’s laws, we can derive the
COMBINED GAS LAW
From the Boyle’s, Charles’, and Gay-Lussac’s laws, we can derive the
Combined Gas Law:
P1V1 T2 = P2V2 T1
Mnemonic: Potato and Vegetable on top of the Table for P1V1 = P2V2
T1 T2

28. STANDARDS T = 0°C = 273 K V = 22.4 L (at STP) P = 1.00 atm = 101.3 kPa
= mm Hg = torr
Remember only kPa has limited sigfigs.

29. PUTTING IT ALL TOGETHER
Simulation on gas laws: Structure and Properties of Matter

30. PV = nRT IDEAL GAS LAW Ideal Gas Equation:
“R” is the universal gas constant.
V ∝ (nT)/P
replace ∝ with constant, R

31. UNIVERSAL GAS CONSTANTS
R = L• atm mol • K R = L•mmHg R = L • torr R = L • kPa
Why are there four constants?

32. IDEAL GAS LAW Remember:
Always change the temperature to KELVINS and convert volume to LITERS
Check the units of pressure to make sure they are consistent with the “R” constant given or convert the pressure to the gas constant (“R”) you want to use.

33. PRACTICE SEVEN
A sample of hydrogen gas (H2) has a volume of L at a temperature of 0ºC and a pressure of 1.5 atm. Calculate the moles of H2 molecules present in this gas sample.

34. PRACTICE EIGHT
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 temp. Use the ideal gas law to calculate the final pressure.

35. PRACTICE NINE
A sample of methane gas that has a volume of 3.8 L at 5ºC is heated to 86ºC at constant pressure. Calculate its new volume.

36. PRACTICE TEN
A sample of diborane gas (B2H6) has a pressure of 345 torr at a temp. of -15ºC and a volume of L. If conditions are changed so that the temp. is 36ºC and the pressure is 468 torr, what will be the volume of the sample?

37. PRACTICE ELEVEN
A sample containing 0.35 mol argon gas at a temp. of 13ºC and a pressure of 568 torr is heated to 56ºC and a pressure of 897 torr. Calculate the change in volume that occurs.

38. Use the ideal gas law to convert quantities that are NOT at STP.
GAS STOICHIOMETRY
VOLUME mol STP
1 mole mole
PARTICLES MOLE MASS
6.02 x molar mass
Use the ideal gas law to convert quantities that are NOT at STP.

39. HINT
You must have a balanced equation to do a stoichiometry problem.

40. PRACTICE TWELVE
Use PV = nRT to solve for the volume of one mole of gas at STP.

41. PRACTICE THIRTEEN
A sample of nitrogen gas has a volume of L at STP. How many moles of N2 are present?

42. PRACTICE FOURTEEN
Calculate the volume of CO2 at STP made from the decomposition of 152 g CaCO3 by the reaction CaCO3(s) → CaO(s) + CO2(g).

43. PRACTICE FIFTEEN
A sample of methane gas having a volume of L at 25ºC and 1.65 atm was mixed with a sample of oxygen gas having a volume of 35.0 L at 31ºC and 1.25 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 125ºC.

44. DETERMINING DENSITY
This modified version of the ideal gas equation can also be used to solve for the density of a gas.
PV = nRT bcomes D = PM RT

45. DETERMINING DENSITY D = m = PMM or D = PMM V RT RT
The density of gases is g/L NOT g/mL.
Mnemonic given in notes.

46. PRACTICE SIXTEEN What is the approximate molar mass of air?
What is the approximate density of air?
List 3 gases that float in air.
List 3 gases that sink in air.

47. PRACTICE SEVENTEEN
The density of a gas was measured at atm and 27ºC and found to be 1.95 g/L. Calculate the molar mass of the gas.

48. DALTON’S LAW OF PARTIAL PRESSURES
THE LAW: The pressure of a mixture of gases is the sum of the pressures of the different components of the mixture:
Ptotal = P1 + P2 + P Pn

49. DALTON’S LAW OF PARTIAL PRESSURES
Also uses the concept of mole fraction, χ
χ A = moles of A
moles A + moles B + moles C
so now, PA = χ A / Ptotal
The partial pressure of each gas in a mixture of gases in a container depends on the number of moles of that gas. The total pressure is the SUM of the partial pressures and depends on the total moles of gas particles present, no matter what they are.

50. DALTON’S LAW OF PARTIAL PRESSURES

51. PRACTICE SEVENTEEN
For a particular dive, 46 L He at 25ºC and 1.0 atm and 12 L O2 at 25ºC 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 25ºC.

52. PRACTICE EIGHTEEN
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.

53. PRACTICE NINETEEN
The mole fraction of nitrogen in the air is Calculate the partial pressure of N2 in air when the atmospheric pressure is 760. torr.

54. WATER DISPLACEMENT
 It is common to collect a gas by water displacement which means some of the pressure is due to water vapor collected as the gas was passing through the water.
You must correct for this.
You look up the partial pressure due to water vapor in a table by knowing the temperature.

55. DALTON’S LAW OF PARTIAL PRESSURES

56. PRACTICE TWENTY
A sample of solid potassium chlorate (KClO3) was heated in a test tube (see the figure above) and decomposed by the following reaction: 2 KClO3(s) → 2 KCl(s) + 3 O2(g) The oxygen produced was collected by displacement of water at 22ºC at a total pressure of 754torr. The volume of the gas collected was L, and the vapor pressure of water at 22ºC is 21torr. Calculate the partial pressure of O2 in the gas collected and the mass of KClO3 in the sample that was decomposed.

57. KINETIC MOLECULAR THEORY
Assumptions of the KMT 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 its Kelvin temperature.

58. KINETIC MOLECULAR THEORY
This neglects any intermolecular forces as well.
Gases expand to fill their container, solids/liquids do not.
Gases are compressible; solids/liquids are not appreciably compressible.

59. KINETIC MOLECULAR THEORY
Boyle’s Law: If the volume is decreased, the gas particles will hit the wall more often, thus increasing pressure.

60. KINETIC MOLECULAR THEORY
Charles’ Law: When a gas is heated, the speed of its particles increase and thus hit the walls more often and with more force. The only way to keep the P constant is to increase the volume of the container.

61. KINETIC MOLECULAR THEORY
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.

62. KINETIC MOLECULAR THEORY
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.

63. DISTRIBUTION OF MOLECULAR SPEED
Although the molecules in a sample of gas have an average KE (and therefore an average speed), the individual molecules move at various speeds and they stop and change direction according to the law of density measurements and isolation → they exhibit a distribution of speeds.
Some move fast, others relatively slowly.
Collisions change individual molecular speeds but the distribution of speeds remains the same.

64. DISTRIBUTION OF MOLECULAR SPEED
Maxwell’s equation:
Urms means root mean square velocity which is the measure of the average velocity of particles in a gas.
Use the “energy R” or molar gas constant, J/K• mol for this equation since kinetic energy is involved.

65. DISTRIBUTION OF MOLECULAR SPEED
By taking the root of the square of the average velocities, you can acquire the average speed of gaseous particles.
The root-mean-square velocity takes into account both molecular mass and temperature, two factors that directly affect the KE of a material.
What happens if we change to a gas that has a higher MM?
What happens if we lower the temperature?

66. PRACTICE TWENTY-ONE
Calculate the root mean square velocity for the atoms in a sample of helium gas at 25ºC.

67. DISTRIBUTION OF MOLECULAR SPEED
If we could monitor the path of a single molecule it would be very erratic.
Mean free path—the average distance a particle travels between collisions. It’s on the order of a tenth of a micrometer - very small.
Examine the effect of temperature on the numbers of molecules with a given velocity as it relates to temperature. They heat up, they speed up.

68. DISTRIBUTION OF MOLECULAR SPEED
Drop a vertical line from the peak of each of the three bell shaped curves — that point on the x- axis represents the AVERAGE velocity of the sample at that temperature.
Note how the bells are “smashed” as the temperature increases.
the Maxwell-Boltzmann Distribution which describes particle speeds of gases.

69. GRAHAM’S LAW OF EFFUSION AND DIFFUSION
Effusion is closely related to diffusion.
Diffusion is the term used to describe the mixing of gases. The rate of diffusion is the rate of the mixing.
Effusion (pictured at left) is the term used to describe the passage of a gas through a tiny orifice into an evacuated chamber as shown on the right.
The rate of effusion measures the speed at which the gas is transferred into the chamber.

70. GRAHAM’S LAW OF EFFUSION AND DIFFUSION
Graham's Law of Effusion: The rates of effusion of two gases are inversely proportional to the square roots of their molar masses at the same temperature and pressure.
If two bodies of different masses have the same kinetic energy, the lighter body moves faster.

71. CALCULATIONS KE = ½mv2 ½ mava2 = ½ mcvc2 ½ mava2 = ½ vc2 mc
½ ma = ½ vc2
mc va2
ma = vc2
mc va2

72. GRAHAM’S LAW OF EFFUSION AND DIFFUSION
REMEMBER rate is a change in a quantity over time, NOT just the time!
If they give you time, divide the time into 1 to get the rate.

73. PRACTICE TWENTY-TWO
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.

74. PRACTICE TWENTY-THREE
A pure sample of methane is found to effuse through a porous barrier in 1.50 minutes. Under the same conditions, an equal number of molecules of an unknown gas effuses through the barrier in minutes. What is the molar mass of the unknown gas?

75. DIFFUSION
450 m/s
660 m/s

76. REAL vs. IDEAL GASES
Most gases behave ideally until you reach high pressure and low temperature. (Remember, either of these can cause a gas to liquefy)
Under very high pressure, real gases have trouble compressing completely. The ideal gas law fails. Ideal gases have no volume, but real gases do.

77. van der Waals EQUATION
corrects for negligible volume of molecules and accounts for inelastic collisions leading to intermolecular forces.
Pressure is increased (IMFs lower real pressure, you’re correcting for this)
Volume is decreased (corrects the container to a smaller “free” volume).
a and b are van der Waals constants.

78. INTERPRETATION When PV / nRT = 1.0, the gas is ideal.
All of these are at 200K.
Note the pressures where the curves cross the dashed line [ideality].

79. INTERPRETATION This graph is just for nitrogen gas.
Note that although non-ideal behavior is evident at each temperature, the deviations are smaller at the higher temperature.

80. THE AP EXAM
Don’t underestimate the power of understanding these graphs.
AP loves to ask questions comparing the behavior of ideal and real gases - not an entire free-response gas problem on the real exam.
Gas Laws are tested extensively in the multiple choice since it is easy to write questions involving them! You will most likely see PV = nRT as one part of a problem in the free response, just not a whole problem!