1. Unit #9
Gases
and
The Gas Laws

2. Remember…
Solid
Liquid
Gas
Which has more
energy?
entropy?

3. Pressure -
The measure of force over a given area. It is caused by the collision of the gas molecules / atoms with the sides of the container.

4. Common units (All of the following are equal to each other):
1 atm (atmosphere)
760 mm/Hg (millimeters of Mercury)
KPa (Kilopascals)
14.7 psi or lb/in2

5. Volume -
The amount of space a gas is filling.

6. Temperature - A measure of the average velocity of the gas particles.
Standard temperature = 0oC

7. Mole -
1 mole of any gas at "STP" will always equal 22.4 liters.

8. STP - Standard Temperature and Pressure. Standard Temperature = 0 oC =
273 K
Standard Pressure =
1 atm

9. Universal Gas Constant -
An unchanging, numerical value, that "allows" the various units of the gas laws to be combined.
= L*atm/mol*K
= J/K*mol

10. Ideal Gas -
An imaginary gas whose behavior is described by the gas laws.

11. Observed Properties of Gases

12. Expansion -
Gases do not have a definite shape or volume. Their shape is determined by the container.

13. Pressure -
Directly proportional to temperature. As the temp goes up, so does the pressure.

14. Low Density -
Gases are approximately 1/1000 the density of their solid or liquid phase.
Example: 1.5 grams of "substance A" might have a volume of:
a) 1.0 mL when a solid
b) 1.3 mL when a liquid
c) 1050 mL when a gas

15. Diffusion -
The process of spreading out uniformly (without help), to occupy a space uniformly is a characteristic of all gases.

16. Kinetic Theory of a Gas (Description of a Gas)

17. Kinetic Theory of a Gas -
A gas consist of very small independent particles (atoms / molecules) that move at random in space; and experience elastic collisions.
[ This "imaginary gas" is called an Ideal Gas ].

18. Elastic Collision -
A collision that assumes there is no change in Kinetic energy, even after collisions with the inside of the container and each other.

19. 5 assumptions of The Kinetic Theory of a Gas:
1) The molecules are of an ideal mass.

20. 5 assumptions of The Kinetic Theory of a Gas:
2) The molecules are in constant random straight line motion.

21. 5 assumptions of The Kinetic Theory of a Gas:
3) The average Kinetic energy is proportional to the absolute temperature of the molecule.

22. 5 assumptions of The Kinetic Theory of a Gas:
4) All collisions are Elastic, (No change in Kinetic energy).

23. 5 assumptions of The Kinetic Theory of a Gas:
5) The molecules do not attract or repel each other.

24. There are intermolecular (van der Waal) attractive forces between gas molecules:
Condensation Temperature -
The lowest temperature a substance can exist as a gas at atmospheric pressure. At this temperature the Kinetic energy of the gas particle is not sufficient to overcome the forces of attraction between the particles.

25. Boyles Law -
At constant temperature, the volume is inversely proportional to the pressure applied.
a) P↑ V↓ and P↓ V↑
b) P1V1 = P2V2

26. Examples, (assume constant temperature):
A 14.5 liter sample of gas is under a pressure of KPa. What will the volume be if the pressure is decreased to 5.54 KPa ?
Answer: P1V1 = P2V2
(7.62 KPa) (14.5 L) = (5.54 KPa) (V2)
19.9 L = V2

27. Examples, (assume constant temperature):
A balloon contains 900 liters of "air" (assumed to be "Ideal") at 1.90 atm. What is the volume if the pressure is increased to 2.38 atm. ?
Answer: P1V1 = P2V2
(1.90 atm.)(900 L) = (2.38 atm.)(V2)
718 L = V2

28. Examples, (assume constant temperature):
A piston compresses the contents of a cylinder, which was at a pressure of 620 mm Hg (about 12 psi), from mL to 64.8mL. What is the new pressure inside the cylinder ?
Answer: P1V1 = P2V2
(620mmHg)(712.5mL) = (X mmHg)(64.8mL)
6817 mmHg = P2

29. Examples, (assume constant temperature):
A gas at 1 atmosphere of pressure, with a volume of 60 liters is allowed to expand to a volume of liters. What happens to the pressure ?
Answer: P1V1 = P2V2
(1 atm)(60L) = (X atm)(180L)
0.333 atm = P2

30. Charles' Law -
At constant pressure, the volume of a gas is directly proportional to its Kelvin temperature.
a) V↑ T↑ and V↓ T↓
b) T1/V1 = T2/V2 or T1V2 = T2V1
c) Temperature must be in Kelvin.
i) K = C
ii) C = K

31. Examples, (assume constant pressure):
A sample of CO2 has a volume of 3.50 liters at -10oC . What will its volume be at 100oC ?
Answer: First convert all temperatures to Kelvin.
K = C
K = C
K = -10oC
K = 100oC
K = K
K = K

32. Examples, (assume constant pressure):
A sample of CO2 has a volume of 3.50 liters at -10oC . What will its volume be at 100oC ?
Answer: Then solve using algebra.
T1V2 = T2V1
( K)(X L) = ( K)(3.50 L)
(X L) = L

33. Examples, (assume constant pressure):
A 600mL (20 oz.) cylinder is full of CO2 at 20oC. What will the temperature be in Celsius, if the volume is dropped to 150mL?
Answer: First convert all temperatures to Kelvin.
K = C
K = 20oC
K = K

34. Examples, (assume constant pressure):
A 600mL (20 oz.) cylinder is full of CO2 at 20oC. What will the temperature be in Celsius, if the volume is dropped to 150mL?
Answer: Then solve using algebra.
T1V2 = T2V1
( K)(150 mL) = (X K)(600 mL)
(73.28 K) = (X K)

35. DO WE ALL AGREE WITH THIS ANSWER?
A 600mL (20 oz.) cylinder is full of CO2 at 20oC. What will the temperature be in Celsius, if the volume is dropped to 150mL?
This question wants the answer in Celsius.
Answer:
(73.28 K) = (X K)
C = K
C =
C = oC

36. Ideal Gas Law -
The equation: PV = nRT, which relates the: # of moles, volume, temperature, and pressure; of an ideal gas.

37. PV = nRT P = pressure in atmospheres V = volume in Liters
n = # of moles of the gas
R = the universal gas constant = L * atm / mol * K
T = temperature in Kelvin

38. Ideal Gas -
Remember:
An imaginary gas whose behavior is described by the gas laws and Kinetic Theory of a gas.

39. Examples:
What is the pressure of liters of a Nitrous oxide that is stored at 32oF ?
Answer:
PV = nRT
P =
X atm
V =
22.4 L
n =
1 mole (use DIMO to convert liters to moles)
R =
L*atm / mol*K
T =
32oF =
0oC =
= K

40. Substituting in the appropriate values we get:
PV = nRT
(X atm.)(22.4 L) = (1 mol)( L*atm / mol*K)( K)
(X atm) = atm.

41. What is the temperature of 1 mole of Oxygen stored at 14
What is the temperature of 1 mole of Oxygen stored at 14.7 psi inside a 22.4 L cylinder?
PV = nRT
(1 atm) (22.4 L) = (1 mol) ( L*atm/mol*K) (T)
K = T

42. What is the volume of 6.02*1023 molecules of H2S (Hydrogen sulfide) if it is under STP conditions?
PV = nRT
(1 atm) (V L) = (1 mol) ( L*atm/mol*K) ( K)
V = 22.4 L

43. How many moles of Chlorine would fill a balloon if its internal pressure was 760 mmHg while at a temperature of 32oF and holding 22.4 liters of the gas?
PV = nRT
(1 atm) (22.4 L) = (X mol) ( L*atm/mol*K) ( K)
= X mol

44. Practical Applications of the Ideal Gas Law
If an aerosol can with a volume of 750 mL has a pressure of 80 psi is heated from 20oC (68oF) to 60oC (140oF). First, how many moles of the gas are in the can ? Secondly, what is the new pressure in the can ?

45. I suggest making a chart (using the data given in the "problem") like the one that follows for all of these types of problems.

46. Initial Final Pressure Volume # of moles R 80 psi Y 750 mL 750 mL X X
Temperature
80 psi Y
750 mL
750 mL X X
L*atm/mol*K
20 oC
60 oC

47. At this point you should be able to see that you first have to solve for "x" in the original problem.
You will first have to convert the information into the correct units.

48. Pi =
Vi =
n =
R =
Ti =
5.44 atm
0.75 liters
X mol
l * atm / mol * K K
Therefore using PV = nRT
n = moles

49. Initial Final Pressure Volume # of moles 0.1695 mol R 80 psi Y 750 mL
Temperature
80 psi Y
750 mL
750 mL
L*atm/mol*K
20 oC
60 oC

50. Pf = y
Vf = 0.75 liters
n = moles (calculated above)
R = l * atm / mol * K
Tf = K
Solving for Pf =
6.18 atm =
90.846 X
psi

51. Dalton’s Law of Partial Pressure
At constant volume and temperature, the total pressure exerted by a mixture of gases is equal to the sum of the partial pressures of the component gases.
Ptotal = P1 + P2 + P3 + P4…

52. Partial Pressure
The contribution each gas in a mixture makes to the total pressure.
Represented by: PX (the name of the gas)
Like any pressure, Partial Pressure depends on:
# of moles
Volume
Average kinetic energy
(Temperature)

53. Mole fraction
The fraction of moles of a component gas in the total moles of a mixture of gases.

54. Example #1: Air contains Oxygen, Nitrogen, Carbon dioxide, and some other gases. What is the partial pressure of Oxygen (PO2) at 760 mmHg if PN2 = mmHg, PCO2 = 0.3 mmHg and POthers = 7.05 mmHg?

55. PTotal = PO2 + PN2 + PCO2 + POthers

56. A 10. 0 liter flask contains 1. 031 g. of O2 and 0. 572 g
A 10.0 liter flask contains g. of O2 and g. of CO2 at 18˚C. What are the partial pressures of the O2 and CO2? What is the pressure inside the flask? What is the mole fraction of the O2 in the mixture?