Law	Ideal Gas Equation	Combined Gas Law
equation	P V = n R T	P1 V1 = P2 V2 T1 T2
explanation	one gas at one set of conditions	one gas that is changing conditions
when to use it	when the problem gives 3 of these: P, V, n, T	more than one temperature, pressure, and/or volume in the problem
specific units req’d?	pressure = atm volume = liters quantity (n) = moles temperature = Kelvins	temperature = Kelvins pressure & volume can be any unit, but must be the same unit on both sides of the equation

Law	Boyle’s Law	Charles’ Law	Gay-Lussac’s Law
equation	P1 V1 = P2 V2	V1 = V2 T1 T2	P1 = P2 T1 T2
explanation	pressure & volume are inversely proportional; temperature is constant	volume & Kelvin temp of a gas are directly proportional; P is constant	pressure & Kelvin temp of a gas are directly proportional; V is constant
when to use it	given 2 difft pressures & 1 volume or given 2 difft volumes & 1 pressure	given 2 difft volumes & 1 temperature or given 2 difft temperatures & 1 volume	given 2 difft pressures & 1 temperature or given 2 difft temperatures & 1 pressure
specific units req’d?	any - but must be the same on both sides of equation	any unit for volume (same on both sides), Kelvin temperature	any unit for pressure (same on both sides), Kelvin temperature

Law	Dalton’s Law	Dalton’s Law	Graham’s Law
equation	Ptotal = Pgas1 + Pgas2 +...	Px = (moles gas X) . Ptotal (total moles)	rate A = √MM B rate B √MM A
explanation	the sum of the pressures of the individual gases in a mixture equals the total pressure exerted by the mixture	amount of a gas in mixture is proportionate to the amount of its partial pressure	rate of gas A compared to the rate of gas B is equal to the square root of the inverse of their molar masses
when to use it	mixture of gases; only pressures given	mixture of gases; moles & total pressure given	when any form of the word “effusion” or “diffusion” is in the problem
specific units req’d?	any - but all values must have same unit of pressure	any - but all values must have same unit of pressure	no

1. Convert the following temperatures.

(A) 104 ^oC to K (B) -3 ^oC to K (C) 67 K to ^oC (D) 1671 K to ^oC
377 K 270 K -206 ^oC 1398 ^oC

2. Convert the following pressures.

(A) 635 torr to atm (B) 104.2 kPa to mm Hg (C) 1.45 atm to Pa
0.836 atm 781.8 mm Hg 147,000 Pa (146885 before rounding)

3. A gas that effuses 1.19 times slower than nitrogen is added to light bulbs. What is the

molecular mass of this unknown gas?

Rate N₂ = √MM unknown 1.19 = √x x = 39.7 g/mole
rate unknown √MM N₂ 1 √28

4. (A) What is the molecular mass of a 0.2500 g sample of a gas at 99.8^oC and 0.9131 atm

in a 100.0 cm³ container? (B) What is the gas in the container?

MM = gRT (0.2500 g) (0.0821 L^.atm/mole^.K) (372.8 K) MM = 83.8 g/mole
PV (0.9131 atm) (0.1 L) Krypton

5. A small 2.00 L fire extinguisher has an internal pressure of 506.6 kPa at 25^oC. What

volume of methyl bromide, the fire extinguisher’s main ingredient, is needed to fill an

empty fire extinguisher at standard pressure if the temperature remains constant?
P₁V₁ = P₂V₂ (506.6 kPa) (2.00 L) = (101.3 kPa) V₂
V₂ = 10.0 L

6. If 45.0 g of propane gas burns completely in the following reaction:

C₃H_8(g) + 5 O_2(g) → 3 CO_2(g) + 4 H₂O_(g)

then how many liters of carbon dioxide gas will be released if the system is at STP?

45.0 g C₃H₈ | 1 mole = 1.023 moles C₃H₈ 1.023 moles C₃H₈ = x moles CO₂
| 44.0 g 1 3

X = 3.069 moles CO₂ | 22.4 L = 68.7 L
| 1 mole

7. Air in a closed cylinder is heated from 25°C to 36°C. If the initial pressure is 3.80 atm,

what is the final pressure?
P₁ = P₂ 3.80 atm = P₂ P₂ = 3.94 atm
T₁ T₂ 298 K 309 K

8. At what temperature Celsius will 19.4 g of molecular oxygen, O₂, exert a pressure of

1820 mm Hg in a 5.12 L cylinder?
PV = nRT 19.4 g O₂ | 1 mole = 0.60625 moles 1820 mm Hg | 1 atm = 2.395 atm
| 32 g | 760 mm Hg

(2.395 atm) (5.12 L) = (0.60625 moles) (0.0821 L^.atm/mole^.K) T
T = 246K --> -27 ^oC

9. To what temperature must 32.0 ft³ of a gas at 2.0 °C be heated for it to occupy

1.00 x 10² ft³ at the same pressure? (ft³ is a unit of volume)

V₁ = V₂ 32 ft³ = 100 ft³ T₂ = 859 K or 586 ^oC
T₁ T₂ 275 K T₂

10. Determine the molar mass of a gas that has a density of 2.18 g/L at 66°C and 720

mm Hg.
D = MM P 2.18 g/L = MM (0.947 atm) MM = 64 g/mole
RT (0.0821 L^.atm/mole^.K) (339 K)

11. A 3.10 mL bubble of methane gas forms at the bottom of a bog where the temp-

erature is 12^oC and the pressure is 8.5 atm. The bubble rises to the surface where the

temperature is 35^oC and the pressure is 1.18 atm. What is the new volume of the

methane bubble?

P₁V₁ = P₂V₂ (8.5 atm) (3.10 mL) = (1.18 atm) V₂ V₂ = 24 mL
T₁ T₂ 285 K 295 K

12. A mixture of 2.00 moles of H₂, 2.00 moles of NH₃, 4.00 moles of CO₂ and 5.00 moles

of N₂ exerts a total pressure of 800. torr.  What is the partial pressure of each gas?

P_x = moles x . P_total H₂ and NH₃ = 2.00 moles . 800 torr = 123 torr
total moles 13.00 moles

CO₂ = 4.00 moles . 800 torr = 246 torr N₂ = 5.00 moles . 800 torr = 308 torr
13.00 moles 13.00 moles

13. For the reaction 2 H_2(g) + O_2(g) → 2 H₂O_(g), how many liters of water can be made from

5.0 L of oxygen gas and an excess of hydrogen?
5.0 L O₂ = x L H₂O x = 10. L
1 2

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