1. Gas Laws
Chapter 14

2. Three Variables Pressure – P Volume – V Temperature – T
atm, mmHg, torr
Volume – V
liters, milliliters
Temperature – T
Celcius, Kelvin (Use Kelvin for gas laws!)
For gas law problems, make sure units match!!!

3. STP STP = standard temperature and pressure
Standard Temp.  0oC or 273oK
Standard Press.  1atm (760 torr, 760 mmHg, KPa)

4. Boyle’s Law
Boyle’s Law – At constant temperature, the volume of a gas varies inversely with the pressure.
If pressure , volume
P1V1 = P2V2

5. Boyle’s Law Problems
A sample of gas occupies 500 mL at 1.0 atm of pressure at constant temperature. If the pressure decreases to 0.50 atm, what will the final volume be?
P1V1 = P2V2
P1  1.0atm V1  500mL P2  0.50 atm
V2 = P1V V2 = (1.0atm)(500mL)
P atm
V2 = 1000 mL

6. Charles’s Law
Charles’s Law – At constant pressure, the temp. of a gas varies directly with the volume.
If temp , volume
Remember to use KELVIN!
V V2
T T2 =

7. Charles’s Law Problem
At constant pressure, 2.75 L of a gas is at 20.0oC. If the temperature changes so that the gas occupies 1.87 L, what is the final temperature?
V1  2.75L T1  = 293K
V2  L T2  ?
V1 = V2
T T2
2.75 L = L
293 K T2
T2 = K

8. Gay-Lussac’s Law
Gay-Lussac’s Law – At constant volume, the pressure of a gas varies directly with the temperature.
If temp , pressure
Remember to use KELVIN!
P P2
T T2 =

9. Gay-Lussac’s Law Problem
A gas at 1.8 atm and 23.0oC expands to 2.5 atm. Assuming the volume does not change, what is the new temperature?
P1  1.8 atm T1  23.0oC = 296K
P2  2.5 atm T2  ? =
P P2
T T2
1.8 atm atm
296 K T2 =
T2 = K

10. Combined Gas Law
P1V1 = P2V2
T T2
A gas at atm and 25.0oC occupies a volume of 27.5 mL. What volume will the gas occupy at STP conditions?
P1 = atm P2 = 1.0 atm
V1 = 27.5 mL V2 = ?
T1 = 298K T2 = 273K
(0.974 atm)(27.5 mL) = (1.0 atm)(V2)
298 K K
V2 = 23.9 mL

11. Avogadro’s Law
Avogadro’s Law – At constant temperature and pressure, equal volumes of gases contain the same number of molecules.
If volume , number of moles
n = number of moles
V1 = V2
n n2

12. Avogadro’s Law Problem
If you have 2 moles of a gas in a 4-liter container, how many moles would you end up with if it fills a 3-liter container and retain the same pressure and temperature.
n1 = 2 moles V1 = 4 L n2 = ? V2 = 3 L
4 L L
2 moles n n2 = 1.5 moles

13. Ideal Gas Law
PV = nRT P = pressure (units depend on R) V = volume (L) n = moles R = ideal gas law constant (in ref. pack) T = temperature (K)

14. Ideal Gas Law Problem
If mol of a gas occupies 9.25 L at 15.0oC, what is its pressure in atm?
P = ? V = 9.25 L n = mol
R = (L*atm)/(mol*K) T = 15.0oC  288K
P(9.25 L) = (0.622 mol)(0.0821)(288K)
P = 1.59 atm

15. Ideal Gas Law Problem 2
What is the volume of 12 grams of carbon dioxide, if it is at STP?

16. Ideal Gas Law Problem 2
What is the volume of 12 grams of carbon dioxide, if it is at STP?
P = 1.0 atm T = 273 K mass = 12 grams
Because you know the molar mass of CO2, you can use it to solve for the moles:
12 g CO mole = 0.27 moles CO2
44 g CO2
PV = nRT (1.0 atm)(V) = (0.27mol)(0.0821)(273 K)
V = 6.05 L

17. Dalton’s Law of Partial Pressures
Dalton’s Law of Partial Pressures – The total pressure of a mixture of gas is equal to the sum of the partial pressures of each component gas.
Ptotal = P1 + P2 + P3 + … Pn
Partial Pressure of a Gas: the portion of the total pressure contributed by a single gas.

18. Collecting a Gas Over Water
Ptotal = Pgas + Pwater vapor
Ptotal  the atmospheric pressure
Pwater vapor  - based on the temp of the
water
- will be given to you.

19. Example: Collecting a Gas Over Water
Example: Hydrogen gas is collected over water at 25oC. The atmospheric pressure is 765 mmHg. The water vapor pressure at 25oC is 23.8 mmHg. What is the pressure of the hydrogen gas?
765 mmHg = (Pgas) + (23.8 mmHg)
Pgas = mmHg