1. Gas Laws

2. Physical Properties of Gases
Have mass
Easily compressed
Fill containers completely
Different gases move through each other rapidly – diffusion
Exert pressure
Pressure depends on temperature

3. The Kinetic-Molecular Theory
Small particles with mass
Separated by large distances
In constant rapid motion
Exert pressure by colliding with walls of container
Elastic: collisions lose no energy of motion

4. The Kinetic-Molecular Theory
Pressure = force per unit area
More gas = more collisions = more pressure
Increase temp causes increase pressure
Temperature is a measure of kinetic energy
KE = mv2/2
Increase velocity causes increased force on container

5. Measuring Gases Amount (n) in moles = mass/molar mass
Volume (v) : 1L = 1000cm3
Temperature (T) – use K
T(K) = T(c) + 273
Pressure (P)

6. Atmospheric Pressure and the Barometer
Atmosphere exerts pressure
Pump air out of can and see it crush
Air has mass – attracted by earths gravity
Force exerted on a unit area of earths surface = atmospheric pressure
SI units: force = newton pressure = pascal (Pa)
1Pa = 1 newton of force per square meter
Atmosphere (atm) = another unit of pressure
1 atm is close to average pressure at sea level
1 atm = 101,325 Pa or kPa

7. Atmospheric Pressure and the Barometer
Pressure varies with altitude: lower altitude = longer and heavier column of air
Altimeter converts pressure to altitude
Water vapor is lighter than nitrogen and oxygen
So high water vapor = low pressure = rain storm likely.

8. Barometer
Glass tube sealed at end, filled with mercury inverted in a reservoir of mercury.
Hg in tube seeks a height so pressure exerted on surface of Hg in reservoir is balanced by pressure of Hg in column.
1 atm = 760mm up column at sea level.

9. Units of Pressure 1 atmosphere (atm) = 101,325 Pa
1 atm = 760 mm Hg = 760 torr
1 atm = lb/in2
1 bar = 100,000 Pa = atm

10. Sample Problem
The column of mercury in a barometer is 745 mm above the mercury reservoir at the bottom. What is the atmospheric pressure in pascals?
Ans = 99,300 Pa

11. Practice Problems
The air pressure inside the cabin of an airplane is 8.3 lb/in2. What is this pressure in atmosphere units?
Ans = 0.56 atm

12. Practice Problems
Pressure is considered the most accurate measure of storm strength, with lower pressure indicating a stronger storm. One of the lowest recorded pressures in the Western Hemisphere is kPa. How high a column of mercury would be balanced by this atmospheric pressure?
Ans = mm Hg

13. Enclosed Gases Pressure of open container = pressure of atmosphere.
Manometer: measures pressure in closed container.

14. Sample Problem
You have a closed container attached to a U-tube. The mercury in the open-ended side of the tube is higher, and the difference between the heights of the mercury columns is 27 mm. Atmospheric pressure is 755 mm Hg. What is the pressure of the gas in the container in atmospheres?
Ans = pressure in container is mm Hg = 782 mm Hg. Convert this to atm = 1.03 atm

15. Practice Problems
A balloon is attached to an open-ended manometer. The mercury level in the manometer is 13 mm lower on the side attached to the balloon than on the side open to the atmosphere. The pressure of the atmosphere is measured to be 755 mm Hg in a separate measurement. What is the gas pressure in the balloon?
Ans = 768 mm Hg

16. Practice Problem
Suppose you have a gas container fitted with a manometer. You measure the height of the mercury on the side of the manometer open to the atmosphere. Then the atmospheric pressure drops and you measure the height of the mercury on the open side again. Will the level of the mercury on the open side have moved, and if so, in which direction?
Ans = it will have moved upward

17. The Gas Laws

18. Reminder of STP Standard temperature and pressure = 0oC or 273 K
1 atm = 760 mm Hg = 101,325 Pa

19. Boyle’s Law: The Pressure – Volume Relationship
Robert Boyle
Trapped fixed amount of air, changing its pressure, and measuring its volume.
Temperature was held constant.

20. Boyle’s Law: The Pressure – Volume Relationship
Boyle found volume decrease as pressure increased.
Boyle’s Law: If temp is constant, the product of pressure x volume has a constant value. PV=k1
So P1V1=P2V2 for a given amount at constant temp.

21. Practice Problems
A gas at a pressure of 608 mm Hg is held in a container with a volume of 545 cm3. The volume of the container is then increased to 1065 cm3 without a change in temperature. Calculate the new pressure of the gas.
Ans = 311 mm Hg

22. Sample Problem
You need to fill 300 helium balloons for a party. A store that will rent a 25-L tank filled with helium gas at a pressure of 30.0 atm. Each balloon holds 2.5 L of helium at a pressure of 1.04 atm. Will one tank be enough to fill all of the balloons? Assume unchanged temperature.
Ans = 290 balloons can be filled

23. Practice Problems
A partially inflated helium weather balloon contains 150 L of gas. The balloon’s internal gas pressure is 1.0 atm when it is released. The research team wants to place a payload of measurement instruments at an altitude of 41 km, where the atmospheric pressure (and therefore the pressure inside the balloon is only 0.4 atm. How large must the balloon be to accommodate the gas volume at 41 km, assuming the gas temperature does not change and the balloon does not leak.
Ans = 375L

24. Gay-Lussac Law P1/T1=P2/T2
Before a trip from New York to Boston, the pressure in an automobile tire was 1.8 atm at 20o C. At the end of the trip, the tire pressure gauge reads 1.9 atm. What is the new Celsius temperature in the tire? (Assume tires with constant volume.)
Ans: 36 oC

25. Gay-Lussac Law
At 120o C, the pressure of a sample of nitrogen is 1.07 atm. what will the pressure be at 205o C, assuming constant volume?
Ans: 1.30 atm

26. Charles’s Law: The Temperature – Volume Relationship
Used a cylinder with a movable piston.
Immersed in water baths of different temperatures.
Pressure and amount held constant.

27. Charles’s Law: The Temperature – Volume Relationship
Calculated the lower limit for temperature to be –273.15oC
Absolute zero
K = oC + 273
Charles’s Law:
V = k2T or k2 = V/T
So V1/T1 = V2/T2

28. Sample Problem
On a cool morning (10.0oC) a group of hot-air balloonists start filling their balloon with air, using a large fan. After the balloon’s envelope is three-fourths filled, they turn on the propane burner to heat the air. At what Celsius temperature will the air completely fill the envelope to its maximum capacity of m3. (assume constant pressure)
Ans = 104oC

29. Practice Problems
What will be the volume of a gas sample at 355 K if its volume at 273 K is 8.57 L? Assume constant pressure.
Ans = 11.1 L

30. Practice Problems
A gas can be used as a thermometer. If it is known that a sample of gas has a volume of 1.00 L at 255 K, what is the temperature if the volume of the same gas sample is changed to 0.45 L at constant pressure?
Ans = 110 K

31. Combined Gas Law
P1V1 = P2V2
T1 T2

32. Avogadro’s Law: The Amount – Volume Relationship
Equal volumes of gases at the same temperature and pressure contain an equal number of particles.
V = k3n

33. Dalton’s Law of Partial Pressures
Dalton looked at mixtures of gases.
Sum of partial pressures of all components in gas mixture = total pressure of mixture.
PT = pa + pb + pc …

34. Sample Problem
What is the atmospheric pressure if the partial pressures of nitrogen, oxygen, and argon are mm Hg, mm Hg, and 0.5 mm Hg, respectively?
Ans = mm Hg

35. Practice Problems
Oxygen gas from the decomposition of potassium chlorate was collected by water displacement. The barometric pressure and the temperature during the experiment were torr and 20.0oC, respectively. What was the partial pressure of the oxygen collected.
Table A-8 gives partial pressure of water vapor
Answer: torr

36. Practice Problems
The gases carbon dioxide, oxygen, nitrogen, neon, and krypton are mixed in a container. All gases have the same partial pressure and the total pressure in the container is 33,500 Pa. What is the partial pressure of nitrogen?
Ans = 6700 Pa

37. The Ideal Gas Law PV = nRT
Applies most of the time accept at low temperatures or high pressure.
R = gas constant
if units are atm-L/mol-K
if units are Pa-m3/mol-K
if units are J/mol-K

38. The Ideal Gas Law PV = nRT As n increases P increases
As T increases P increases
As V decreases P increases

39. Sample Problems
How many moles of a gas at 100.oC does it take to fill a 1.00 L flask to a pressure of 1.50 atm?
Ans = mol

40. Practice Problems
What is the volume occupied by 9.45 g of C2H2 at STP?
Ans = 8.15 L

41. Practice Problems
A camping stove uses a 5.0 L propane tank that holds 3.0 kg of liquid C3H8. How large a container would be needed to hold the same amount of propane as a gas at 25oC and a pressure of 3.0 atm?
Ans = 560 L

42. Gas Stoichiometry

43. Practice Problem
An airbag inflates in less than 50 msec by the reaction of NaN3 to produce Na and nitrogen gas at 25C.
NaN3  Na + N2
The volume of the airbag is about 30 liters, and it is filled to a pressure of 1.4 atm. How much NaN3 must be used for each air bag?
Ans: 74.5 grams

44. Practice Problem
Calculate the volume of methane (CH4) produced by the bacterial breakdown of 2.32 kg of sugar (C6H12O6) at 321 K and 707 torr
C6H12O6  3 CH4 + 3 CO2
Ans 1095 L