1. CHAPTER 14
Gases
14.2 The Gas Laws

2. Gases consist of widely separated atoms or molecules in constant, random motion
Mostly empty space
No interaction between gas atoms or molecules except in collisions
Straight trajectories until collision occurs

3. Gases consist of widely separated atoms or molecules in constant, random motion
Mostly empty space
No interaction between gas atoms or molecules except in collisions
Straight trajectories until collision occurs
Because gases can expand and contract they behave differently from solid and liquids.

4. Gas pressure is increased by
more frequent and/or harder collisions

5. You can affect the gas pressure by changing:
1. the density
More molecules means more impacts and a higher pressure.

6. You can affect the gas pressure by changing:
1. the density
More molecules means more impacts and a higher pressure.
2. the volume of the container
With less space to move around, there are more collisions and a higher pressure.

7. You can affect the gas pressure by changing:
1. the density
More molecules means more impacts and a higher pressure.
2. the volume of the container
With less space to move around, there are more collisions and a higher pressure.
3. the temperature
With more kinetic energy, the molecules move faster. The collisions are harder and more frequent.

8. Boyle’s law: V versus P Robert Boyle’s experiment:
Mercury (Hg) was poured down a tube shaped like the letter “J.”
- The tube was closed on the lower end.
The gas inside the tube took up space (volume).
The temperature and number of gas molecules inside the tube stayed constant.
- Boyle observed the change in pressure in mmHg as a function of volume. He then graphed the relationship between pressure and volume.

9. Boyle’s law: V versus P Pressure versus volume Temperature
Number of moles
constant

10. Boyle’s law: V versus P Pressure versus volume Temperature
Number of moles
constant

11. Boyle’s law: V versus P
At higher altitudes, the pressure outside the balloon is lower, so the volume of the balloon increases.
With a rubber balloon, the pressure inside is slightly greater than the pressure outside, to compensate for the tension of the rubber.
The pressure inside the balloon is equal to the pressure outside

12. Boyle’s law: V versus P

13. Boyle’s law: V versus P
If a weather balloon is released on the ground with a volume of 3.0 m3 and a pressure of 1.00 atm, how large will it get when it reaches an altitude of 100,000 ft, where the pressure is atm?

14. Boyle’s law: V versus P
If a weather balloon is released on the ground with a volume of 3.0 m3 and a pressure of 1.00 atm, how large will it get when it reaches an altitude of 100,000 ft, where the pressure is atm?
Asked: Volume of the balloon when it reaches 100,000 ft
Given:
Relationships:

15. Boyle’s law: V versus P
If a weather balloon is released on the ground with a volume of 3.0 m3 and a pressure of 1.00 atm, how large will it get when it reaches an altitude of 100,000 ft, where the pressure is atm?
Asked: Volume of the balloon when it reaches 100,000 ft
Given:
Relationships:
Solve:
Answer: The balloon will have a volume of 300 m3.

16. Gases can only push
Three states of inhalation

17. Gases can only push Three states of inhalation
When you inhale, you create a lower pressure in your lungs, and the air outside pushes in

18. There is no such thing as suction
Gases can only push
Three states of inhalation
There is no such thing as suction

19. Charles’s law: V versus T
The volume decreases as the temperature decreases

20. Charles’s law: V versus T
The volume increases as the temperature increases

21. Charles’s law: V versus T
Volume versus temperature
Pressure
Number of moles
constant

22. Charles’s law: V versus T
Doubling the Kelvin temperature will double the volume of a gas
Kelvin temperatures simplify the V versus T relationship

23. Charles’s law: V versus T

24. Charles’s law: V vs. T
If you inflate a balloon to a size of 8.0 L inside where the temperature is 23oC, what will be the new size of the balloon when you go outside where it is 3oC?

25. Charles’s law: V vs. T
If you inflate a balloon to a size of 8.0 L inside where the temperature is 23oC, what will be the new size of the balloon when you go outside where it is 3oC?
Asked: Volume of the balloon when the temperature drops to 3oC
Given:
Relationships:

26. Charles’s law: V vs. T
If you inflate a balloon to a size of 8.0 L inside where the temperature is 23oC, what will be the new size of the balloon when you go outside where it is 3oC?
Asked: Volume of the balloon when the temperature drops to 3oC
Given:
Relationships:
Solve:

27. Charles’s law: V vs. T
If you inflate a balloon to a size of 8.0 L inside where the temperature is 23oC, what will be the new size of the balloon when you go outside where it is 3oC?
Asked: Volume of the balloon when the temperature drops to 3oC
Given:
Relationships:
Solve:

28. Combined gas law

29. Imagine you were to hitch a ride on a high-altitude research balloon that reaches and altitude of 100,000 ft. At sea level, where the pressure is atm and the temperature is 20oC, you’ll need 18 m3 of helium to fill the balloon. What will be the new volume of the gas when you reach altitude, where the pressure is atm and the temperature is –50oC?

30. Imagine you were to hitch a ride on a high-altitude research balloon that reaches and altitude of 100,000 ft. At sea level, where the pressure is atm and the temperature is 20oC, you’ll need 18 m3 of helium to fill the balloon. What will be the new volume of the gas when you reach altitude, where the pressure is atm and the temperature is –50oC?
Asked: Volume of the balloon when it reaches 100,000 ft
Given:
Relationships:

31. Imagine you were to hitch a ride on a high-altitude research balloon that reaches and altitude of 100,000 ft. At sea level, where the pressure is atm and the temperature is 20oC, you’ll need 18 m3 of helium to fill the balloon. What will be the new volume of the gas when you reach altitude, where the pressure is atm and the temperature is –50oC?
Asked: Volume of the balloon when it reaches 100,000 ft
Given:
Relationships:
Solve:

32. Avogadro’s law: V versus moles
Two equal volumes of hydrogen react with one volume of oxygen to produce two volumes of water vapor.
Gas volumes act like moles because the same size container has the same number of molecules (at the same temperature and pressure).

33. Avogadro’s law: V versus moles
Moles versus volume
Temperature
Pressure
constant

34. Avogadro’s law: V versus moles
Moles versus volume
Temperature
Pressure
constant

35. Avogadro’s law: V versus moles
Moles versus volume
Temperature
Pressure
constant
Twice the volume, twice the number of molecules assuming the temperature and pressure are constant

36. Avogadro’s law: V versus moles
Moles versus volume
Temperature
Pressure
constant
Liquid volumes result from the number of molecules, whereas gas volumes result from the size of the container

37. Avogadro’s law: V versus moles
Moles versus volume
Temperature
Pressure
constant
Each molecule here has the same kinetic energy.
In gases with the same temperature, lighter molecules move faster, so the force from the impact is the same as for the slower molecules that have more mass.
14.2 The Gas Laws

38. Restrictions

39. The ideal gas law
Combining the previous gas laws, we obtain the ideal gas law
In reality, the ideal gas law is an approximation which is accurate for many gases over a wide range of conditions.
The ideal gas law is not accurate at very high density or at very low temperature.

40. The ideal gas law
R is the only constant
The universal gas constant

41. The ideal gas law
Calculating the universal gas constant using various units
Watch out for the units!

42. The ideal gas law Limitations of the ideal gas law
In an ideal gas, we assume that:
1. individual gas molecules take up no space
For very small volumes, the size of gas atoms or molecules becomes significant

43. The ideal gas law Limitations of the ideal gas law
In an ideal gas, we assume that:
1. individual gas molecules take up no space
2. gas molecules do not interact with each other
For very small volumes or very low temperatures, gas atoms and molecules are very close together, and van der Waals attractions are no longer negligible

44. PV = nRT

45. PV = nRT
What would be the pressure inside of a 50.0 L tank containing 1,252 g of helium at 20oC?

46. PV = nRT
What would be the pressure inside of a 50.0 L tank containing 1,252 g of helium at 20oC?
Asked: Tank pressure
Given:
Relationships:

47. PV = nRT
What would be the pressure inside of a 50.0 L tank containing 1,252 g of helium at 20oC?
Asked: Tank pressure
Given:
Relationships:
Solve:

48. PV = nRT
What would be the pressure inside of a 50.0 L tank containing 1,252 g of helium at 20oC?
Asked: Tank pressure
Given:
Relationships:
Solve:

49. If T1 = T2

50. What would be the new volume of a bubble in a bread dough once it goes from a room temperature (20oC) volume of cm3 to a 191oC oven?

51. What would be the new volume of a bubble in a bread dough once it goes from a room temperature (20oC) volume of cm3 to a 191oC oven?
Asked: Find the volume of a bubble under changing temperature conditions
Given:
Relationships:

52. What would be the new volume of a bubble in a bread dough once it goes from a room temperature (20oC) volume of cm3 to a 191oC oven?
Asked: Find the volume of a bubble under changing temperature conditions
Given:
Relationships:
Solve: Pressure and moles stay constant, so they cancel out.

53. What would be the new volume of a bubble in a bread dough once it goes from a room temperature (20oC) volume of cm3 to a 191oC oven?
Asked: Find the volume of a bubble under changing temperature conditions
Given:
Relationships:
Solve: Pressure and moles stay constant, so they cancel out.

54. What would be the new volume of a bubble in a bread dough once it goes from a room temperature (20oC) volume of cm3 to a 191oC oven?
Asked: Find the volume of a bubble under changing temperature conditions
Given:
Relationships:
Solve: Pressure and moles stay constant, so they cancel out.

55. Boyle’s law
Charles’s law
Avogadro’s law

56. Boyle’s law
Charles’s law
Avogadro’s law
Combined gas law

57. Boyle’s law Combined gas law Charles’s law Avogadro’s law
Ideal gas law
R = universal gas law