1. Chapter 12 The Behavior of gases
12.3
The Gas Laws

4. All gases Are less dense when warmer
Are less dense when under less pressure
Are less dense when there are less particles in a volume
Obey laws, within limits, which allow us to predict their behavior under most conditions

5. Things you will learn Understand Boyle’s Law Understand Charles’s Law
Understand Gay-Lussac’s Law
Understand and be able to solve problems using the combined gas laws

6. Boyle’s Law The pressure-volume relationship of gases

7. Pressure and volume

8. Pressure and volume have an inverse relationship

9. Boyles Law essentials
The product of a pressure and volume of any two sets of conditions at a given temperature is constant:
P1 x V1 = P2 x V2
100 1 L = 50 2 L = L
The two conditions are inversely proportional
P~1/V

10. A high altitude balloon contains 30 L of He gas at 103 kPa
A high altitude balloon contains 30 L of He gas at 103 kPa. What is the volume when it gets to an altitude where the pressure is 25 kPa?

11. A high altitude balloon contains 30 L of He gas at 103 kPa
A high altitude balloon contains 30 L of He gas at 103 kPa. What is the volume when it gets to an altitude where the pressure is 25 kPa?
Knowns:
V1 = 30 L
P1 = 103 kPa
P2 = 25 kPa
Unknown: V2

12. Our equation is V1 x P1 = V2 x P2 30L x 103 kPa = v2 x 25 kPa
A high altitude balloon contains 30 L of He gas at 103 kPa. What is the volume when it gets to an altitude where the pressure is 25 kPa?
Our equation is V1 x P1 = V2 x P2
30L x 103 kPa = v2 x 25 kPa
30 L x 103 kPa
25 kPa
V2 = 124 L V2

13. Charles’s Law The temperature-volume relationship of gases

14. Charles’s Law esentials
An increase in the temperature of a gas yields an increase in the volume of a gas
V1/T1 = V2/T2
1 300K = 2 600k
The two conditions are directly proportional
V~T remember all temperature measurements are in kelvins

15. A balloon inflated in a room at temperature of 24°C has a volume of 4 L. The balloon is then heated to a temperature of 58°C. What is the new volume if the temperature remains constant?

16. Knowns: Unknown: V1 = 4 L T1 = 24°C T2 = 58°C V2
A baloon inflated in a room at temperature of 24°C has a volume of 4 L. The balloon is then heated to a temperature of 58°C. What is the new volume if the temperature remains constant?
Knowns:
V1 = 4 L
T1 = 24°C
T2 = 58°C
Unknown: V2

17. Our equation is V1/T1= V2 /T2 4L /24°C = xL/58°C 58C x 4L / 24°C = xL
A baloon inflated in a room at temperature of 24°C has a volume of 4 L. The balloon is then heated to a temperature of 58°C. What is the new volume if the temperature remains constant?
Our equation is V1/T1= V2 /T2
4L /24°C = xL/58°C
58C x 4L / 24°C = xL
wait, we haven’t converted to Kelvins!
331K x 4L = 4.46 L
297K

18. Gay-Lussac The temperature-volume relationship of gases

19. Gay-Lussac’s Law
The pressure of a gas is directly proportional to the temperature of a gas (in Kelvins) if the volume remains constant
Because these relations are directly related, they obey the formula:
P1/T1 = P2/T2

20. Sample problem The gas in an aerosol can may be 103 kPa, meaning it won’t squirt, at 25°C, but if thrown in a fire, the pressure could be quite dangerous. How high is the pressure if the fire is 928°C ?

21. Sample problem The pressure in a tire is 198 kPa at the start of a trip at 27°C. At the end of the trip, it is 225 kPa. What is the internal temperature of the tire

22. Combining the gas laws Boyles’ Law is Charles’s Law is
Gay-Lussac’s Law is

23. Combining the gas laws Boyles’ Law is P1 x V1 = P2 x V2
Charles’s Law is V1/T1 = V2/T2
Gay-Lussac’s Law is P1/T1 = P2/T2

24. The combined gas law P1 x V1 P2 x V2 T1 T2
If you hold the temperature constant, you have Boyle’s Law
If you hold volume constant, you have Gay-Lussac’s Law
If you hold the pressure constant, you have Charles’s Law

25. Sometimes you are not able to hold any of the variables constant
The volume of a gas filled balloon is 30L and 153 kPa. What volume will the balloon be at STP?

26. The volume of a gas filled balloon is 30L and 153 kPa
The volume of a gas filled balloon is 30L and 153 kPa. What volume will the balloon be at STP?
Knowns:
V1=30 L
T1=40C
T2= 273K (standard temp)
P1= 153 kPa
P2=101.3 kPa (standard pressure

27. The volume of a gas filled balloon is 30L and 153 kPa
The volume of a gas filled balloon is 30L and 153 kPa. What volume will the balloon be at STP?
Knowns:
V1=30 L
T1=40C
T2= 273K (standard temp)
P1= 153 kPa
P2=101.3 kPa (standard pressure
Change all temps to Kelvins
Isolate V2 and solve

28. Practice problems
A gas at 155 kPa and 25C occupies a container with an initial volume of 1 L. By changing the volume, the pressure of the gas increases to 605 kPa as the temperature is raised to 125C. What is the new volume?

29. Practice problems
A 5 L air sample at a temperature of -50C has a pressure of 107 kPa. What will be the new pressure if the temperature is raised to 102C and the volume expands to 7 L?

30. Ideal gas law
Up to this point, we have left out another thing that can change pressure, volume and temperature

31. We have used the combined gas law to find changes in a system when we change conditions such as temperature, pressure or volume.
P1 x V1 T1
P2 x V2 T2

32. But the amount of gas- the number of moles- can change the pressure and volume also
It makes sense that the volume and pressure in a container must be proportional to the number of moles
We can add the term for moles (n) to the combined gas laws that we just looked at :
so P1V1/T1 becomes P1V1 / T1n1

33. This shows that the term P x V/ T x n is a constant
This will allow us to find unknowns in a system where we are not changing conditions
P1 x V1
T1 x n1
P2 x V2
T2 x n2

34. P1V1 = T1n1 This is called the Ideal Gas Law
We need to evaluate this in order to come up with a constant which will make the equation work
We do this at STP
What is STP

35. We use STP as a starting point
P= kPa (one ATM)
V= 22.4 Liters (volume of 1 mole at STP)
N= 1 mole
T= 273K (melting point of ice in K)
The constant, R, = (P x V) / (T x n)
or 8.31 (L x kPa) / (K x mol)

36. The ideal gas law becomes:
PV=nRT
Pressure x volume = # moles x temp x constant
This will allow us to figure any one of the variables in any system if we know the other three

38. Sample problem
You fill a rigid steel cylinder that has a volume of 20.0 L with nitrogen gas to a final pressure of 2 x 104 kPa at 28C. How many moles of gas are in the cylinder?

39. You fill a rigid steel cylinder that has a volume of 20
You fill a rigid steel cylinder that has a volume of 20.0 L with nitrogen gas to a final pressure of 2 x 104 kPa at 28C. How many moles of gas are in the cylinder?
Knowns:
P = 2x104 kPa
V = 20 L
T = 28C
Unknown:
N = ?

40. You fill a rigid steel cylinder that has a volume of 20
You fill a rigid steel cylinder that has a volume of 20.0 L with nitrogen gas to a final pressure of 2 x 104 kPa at 28C. How many moles of gas are in the cylinder?
Convert 28C to K K
Isolate n (number of moles)
n = P x V
R x T

41. n = 2x104kPa x 20L 8.31 L x kPa x 301K K x mol
You fill a rigid steel cylinder that has a volume of 20.0 L with nitrogen gas to a final pressure of 2 x 104 kPa at 28C. How many moles of gas are in the cylinder?
n = x104kPa x 20L
8.31 L x kPa x 301K
K x mol

42. n = 2x104kPa x 20L 8.31 L x kPa x 301K K x mol
You fill a rigid steel cylinder that has a volume of 20.0 L with nitrogen gas to a final pressure of 2 x 104 kPa at 28C. How many moles of gas are in the cylinder?
n = x104kPa x 20L
8.31 L x kPa x 301K
K x mol

43. You fill a rigid steel cylinder that has a volume of 20
You fill a rigid steel cylinder that has a volume of 20.0 L with nitrogen gas to a final pressure of 2 x 104 kPa at 28C. How many moles of gas are in the cylinder?
n = x 102 mol N2

44. When the pressure of a rigid hollow sphere containing 685 L of helium gas is held at 621K, the pressure of the gas is 1.89 x 103 kPa. How many moles of helium does the sphere contain?

45. What pressure will be exerted by
What pressure will be exerted by .450 mol of a gas at 25C if it is contained in a .650 L vessel?

46. A deep underground cavern contains 2
A deep underground cavern contains 2.24 x 106 L of methane (CH4) at a pressure of 1.50 x 103 kPa and a temperature of 42C. How many kilograms of CH4 does this deposit contain?

47. What volume will 12 g of oxygen gas (O2) occupy at 25C and a pressure of 52.7 kPa?

48. Ideal gas??
The ideal gas law assumes that gas particles occupy no volume and that there are no attractions between particles. This is never true.
Gases under high pressure and low temperatures turn to liquids. Gases do occupy volume (obviously), and there are attractions (intermolecular forces) as we learned in chapter 10.
Boyle’s law implies that gases are infinitely compressible, but this is not the case

51. Partial pressures (Dalton’s Law)
The pressure exerted by a mixture of gases (our atmosphere, for example) equals the sum of the pressures of each individual gas in the mixture
Ptotal = Pa + Pb + Pc

53. Partial pressures Ptotal =ntotalRT / V
Each gas in a mixture acts independently of each other
The total pressure exerted by the gases in a mixture is directly related to the number of moles in the mixture Ptotal ~ ntotal
Ptotal =ntotalRT / V

54. The total pressure of a mixture of hydrogen, argon and nitrogen is 120 kPa. The partial pressure of hydrogen is 32 kPa and the partial pressure of argon is 58 kPa. What is the partial pressure of the nitrogen?

55. The total pressure of a mixture of hydrogen, argon and nitrogen is 120 kPa. The partial pressure of hydrogen is 32 kPa and the partial pressure of argon is 58 kPa. What is the partial pressure of the nitrogen?
Using Ptotal = Pa + Pb + Pc
120 kPa = 32 kPa + 58 kPa + Pnitrogen
Pnitrogen = 30 kPa

56. A mixture of .25 mole CO2 and .30 mole of O2 is in a 10 L container at 298K. What is the total pressure of the mixture? What is the partial pressure of the CO2? What is the partial pressure of the O2?

57. The total pressure depends on the total number of moles (.55)
A mixture of .25 mole CO2 and .30 mole of O2 is in a 10 L container at 298K. What is the total pressure of the mixture? What is the partial pressure of the CO2? What is the partial pressure of the O2?
The total pressure depends on the total number of moles (.55)
Ptotal =ntotalRT / V

58. The total pressure depends on the total number of moles (.55)
A mixture of .25 mole CO2 and .30 mole of O2 is in a 10 L container at 298K. What is the total pressure of the mixture? What is the partial pressure of the CO2? What is the partial pressure of the O2?
The total pressure depends on the total number of moles (.55)
Ptotal =ntotalRT / V
Ptotal = .55 mole x 8.3 x 298K / 10L
= 136kPa

59. A mixture of .25 mole CO2 and .30 mole of O2 is in a 10 L container at 298K. What is the total pressure of the mixture? What is the partial pressure of the CO2? What is the partial pressure of the O2?

60. A mixture of .25 mole CO2 and .30 mole of O2 is in a 10 L container at 298K. What is the total pressure of the mixture? What is the partial pressure of the CO2? What is the partial pressure of the O2?
The partial pressure of each gas depends on the number of moles of each gas (.25 mole CO2)
PCO2 =nCO2RT / V

61. A mixture of .25 mole CO2 and .30 mole of O2 is in a 10 L container at 298K. What is the total pressure of the mixture? What is the partial pressure of the CO2? What is the partial pressure of the O2?
The partial pressure of each gas depends on the number of moles of each gas (.25 mole CO2)
PCO2 =nCO2RT / V
PCO2 =.25 mol x 8.3 x 298 / 10
= 62 kPa

62. A mixture of .25 mole CO2 and .30 mole of O2 is in a 10 L container at 298K. What is the total pressure of the mixture? What is the partial pressure of the CO2? What is the partial pressure of the O2?

63. A mixture of .25 mole CO2 and .30 mole of O2 is in a 10 L container at 298K. What is the total pressure of the mixture? What is the partial pressure of the CO2? What is the partial pressure of the O2?
Ptotal = Pa + Pb + Pc

64. Ptotal = Pa + Pb + Pc 136 kPa = 62 kPa + PO2 PO2 = 74 kPa
A mixture of .25 mole CO2 and .30 mole of O2 is in a 10 L container at 298K. What is the total pressure of the mixture? What is the partial pressure of the CO2? What is the partial pressure of the O2?
Ptotal = Pa + Pb + Pc
136 kPa = 62 kPa + PO2
PO2 = 74 kPa

65. The gas laws Boyle’s Law Charle’s Law Gay-Lussac’s Law
Combined gas law
Ideal gas law
Dalton’s Law

67. Boyle’s Law P1V1 = P2V2 Pressure and volume change
Temperature is held constant

68. Charle’s Law V1/T1 = V2/T2 Volume and temperature change
Pressure remains constant

69. Gay-Lussac’s Law P1/T1 = P2/T2 Pressure and temperature change
Volume remains constant

70. Combined gas law P1V1/T1 = P2V2/T2
Pressure, volume and temperature change
# moles remains constant

71. Ideal gas law
PV = nRT
Used for finding conditions where nothing is changing.
One variable can be missing
Units must be:
P (kPa)
V (L)
N (moles)
T (Kelvins)
R (8.3)

72. Dalton’s Law Ptotal = Pa + Pb + Pc
The total pressure of a mixture of gases is the sum of the pressures of each different gas (partial pressures)