1. Chapter 11
Gas Laws

2. 11.1 and 11.2 Development of the Kinetic Theory of Gases
Gases are made up of molecules with lots of empty space between
Particles move quickly - pressure is caused by this motion
Collisions are completely elastic
There are no attractive or repulsive forces between molecules
KE = ½ mv2

3. Development of the Kinetic Theory of Gases
Properties of Gases resulting from the KTG
Expansion - no definite shape or definite volume
Fluidity - particles glide past each other ( gases and liquids are both fluids)
Low Density - gases are roughly 1/1000 the density of solids and liquids
Compressibility
Diffusion - spontaneous mixing of 2 substances due to random molecular motion
Effusion - a gas spreads through a small opening between containers

4. Development of the Kinetic Theory of Gases
A qualitative description of gases:
P = Pressure (mmHg, kPa, atm)
T = Temperature (K, Co)
V = Volume (mL, L)
n = moles

5. Combined Gas Law
Describes the relationship between Pressure, Temperature, and Volume.
Formula:
P1V1 = P2V2
T T2
STP = standard temperature and pressure:
Pressure units: kPa, 760 torr, 1 atm, 760 mmHg
Temperature units: 273 K, O C0 ( must use K with gas laws)
Volume: if one mole is present, then 22.4 L

6. Practice of Conversions
2.0 atm = ______ Kpa
560mmHg = ______ torr
35 oc = _____ K
298 K = _____ co
NOT IN PACKET – WRITE IT ON A SEPARATE SHEET OF PAPER

7. 11.3 Boyle’s Law
The volume of a gas varies inversely with pressure at constant temperature.
Formula: P1V1 = P2V2
T T2
P1V1 = P2V2
As the applied (outside pressure) increases, the volume decreases.
Graph: V P

8. Boyle’s Law
Ex1: If 150. ml of a sample of O2 at mm Hg has the pressure increased to mm Hg, what is the new volume?
x = 144 mL

9. Charles’ Law v t Formula: P1V1 = P2V2
The volume of a fixed mass of gas varies directly with temperature at constant pressure.
Formula: P1V1 = P2V2
T T2
V1 = V2
T1 T2
As the temperature increases, the volume increases. (hot air balloon)
When the graph is extrapolated to 0 K, the volume is 0. This is impossible as the gas would have volume of all the particles with no space between them. Of course, this is impossible to test since no gases exist at C0 (only solids and liquids). v t

10. Charles’ Law
If 753 ml of nitrogen at 25 C0 is heated to 50. C0, then what is the new volume?
820 mL

11. Gay-Lussac’s Law p t Formula: P1V1 = P2V2 T1 T2
The pressure of a fixed mass of gas varies directly with temperature at constant volume
Formula: P1V1 = P2V2
T T2
P1 = P2
T1 T2
As the temperature increases, the pressure increases. p t

12. Gay-Lussac’s Law
If a gas at 3.0 atm and 25 C0 is heated to 52 C0, what is the new pressure?
3.3 atm

13. Combine Gas Law
The relationship between pressure, volume, and temperature when the amount of gas is fixed
Formula
P1V1 = P2V2
T T2

14. Combine Gas Law
If a sample of gas at 22.0oc and 31 kPa occupies cm3, what space will it occupy at STP?

15. Combine Gas Law
A 350 mL air sample collected at 35oC has a pressure of 550 mmHg. What pressure will the air exert if it is allow to expand to 425 mL and 57oC?
NOT IN NOTES- WRITE IT DOWN

16. Dalton’s Law of Partial Pressures
The total pressure of a collection of gases in a mixture is equal to the sum of the pressures that each gas would exert by itself in the same volume.
Formula: PT = P P
Collecting gas over water:
Ptotal = Pwater Phydrogen
H2O(g) H2O(g)
H2O(g)
Zn(s) H2SO4(aq)  ZnSO4(aq) H2(g)

17. Dalton’s Law of Partial Pressures
A student collects oxygen gas over water at an atmospheric pressure of kPa and a temperature of 29.0 C0. What is the partial pressure of the oxygen?
At 29.0 C0 water has a pressure of 30.0 mmHg (or 4.00 kPa).
100.0 kPa = kPa + Poxygen
Poxygen = kPa

18. Graham’s Law of Diffusion
Graham noticed that gases with low densities diffuse faster than gases with higher densities.
Under the same conditions of temperature and pressure, gases diffuse at a rate inversely proportional to the square roots of their densities (or molecular mass).

19. Graham’s Law of Diffusion
Formulas:
rate of gas “A” = density of gas “B”
rate of gas “B” density of gas “A”
velocity of gas “A” = molecular weight of gas “B”
velocity of gas “B” molecular weight of gas “A”
This comes from KE = ½ mv2

20. Graham’s Law of Diffusion
If CO2 molecules travel at mph, how fast do H2 molecules go?
x = mph

21. Graham’s Law of Diffusion
If He atoms travel at mph, how fast do nitrogen molecules go?
x = mph

22. The Kinetic Theory and the Gas Law
In Boyle’s Law, Pressure = Force/Area. So….
In Charle’s Law, temperature is proportional to KE. So....
½ the volume means 2x the particles So, 2x the pressure
-doubling temperature = doubling KE
-doubling KE = doubling pressure (doubles the number of collisions)
-in order to keep pressure the same (constant), volume must double instead

23. The Kinetic Theory and the Gas Law
In Gay-Lussac’s Law, temperature is proportional to KE. So...
doubling temperature = doubling KE
doubling KE = doubling pressure (doubles the number of collisions)
volume is constant, so the pressure does change
In Dalton’s Law of Partial Pressures, if gas A exerts a pressure of 5 collisions/second and gas B exerts a pressure of 5 collisions/second, then the total # of collisions/second should = 10 (their sum).

24. Practice!!!!
To what temperature must a sample of nitrogen at 27oC and atm be heated so that its pressure becomes 855 mmHg at constant volume?
If the pressure exerted on a 240 mL sample of hydrogen gas at constant temperature is increased from 325 mmHg to 550 mmHg, what will be the final volume of the sample?

25. Practice!!!!
A sample of gas is collected over water at a temperature of 35.0o when the barometric pressure reading is 742 mmHg. What is the partial pressure of the dry gas?
A sample of air has a volume of 140 mL at 67oC. To what temperature must the gas be lowered to reduce its volume to 50 mL at constant pressure?

26. Practice!!!!
If CO atoms travel at mph, how fast do chlorine molecules go?
A gas measures of 1.75 L at -23oC and 150 kPa. At what temperature would the gas occupy 1.30 L at 210 kPa?

27. Ideal Gas Law