Summary of the Gas Laws

1. AVOGADRO’S LAW: the volume is directly proportional to the number of moles of gas, for a gas at constant temperature and pressure

V a n as n, V and as n¯, V¯ V₁/n₁ = V₂/n₂ @ constant T and P

2. BOYLE’S LAW: the volume is inversely proportional to the pressure of gas, when n & T are constant

V a 1/P as P, V¯ and as P¯, V P₁V₁ = P₂V₂ @ constant n and T

3. CHARLES’S LAW: the volume is directly proportional to the Kelvin temperature of gas, when n & P are constant

V a T T, V and as T¯, V¯ V₁/T₁ = V₂ /T₂ @ constant n and P

4. DALTON’S LAW: the total pressure of a gas is equal to the sum of it’s partial pressures

P_T = P₁ + P₂ + P₃ + …etc.

5. THE COMBINED GAS LAW: Sometimes several variables are changing at the same time and the missing variable can be solved for given all the others. Note: Terms that are constant are dropped.

PV/nT = R Therefore, P₁V₁/n₁T₁ = P₂V₂/n₂T₂

6. THE IDEAL GAS LAW: The following is true for an ideal gas, PV = nRT where P is in atmospheres, V is in liters, n is in moles, T is in Kelvins and R = 0.08206 L·atm/(mol·K).

Real gases behave “ideally” at ______ pressures and ________ temperatures because under those conditions, the gas particles are less likely to ______________ each other and they take up a ______________ % of the space when they occupy larger volumes.

7. GRAHAM'S LAW: A mathematical equation that relates the rates of effusion (or diffusion) of two gases to the masses of the molecules (or atoms) of the two gases.

effusion A = molecular mass of B

effusion B √ molecular mass of A

Bottom Line: Heavier gases move ____________ and lighter gases move ____________.

Things To Memorize In This Chapter:

The Universal Gas Constant will be provided so there is no need to memorize it. Commit the ideal gas law and the combined gas law to memory. Pay attention to units of temperature, they must always be converted to ______________. Just add __________ to the Celsius temperature to convert to the absolute zero scale.

STP: Standard temperature and pressure. The standard temperature is __°C and the standard pressure is ______ mmHg or ______ torr or __ atm.

An ideal gas occupies ________ L/mol at STP. Do Not overuse this fact.

Example #1:

An automobile tire is filled with air at a pressure of 30 lb/in² @ 25°C. When a cold front moves in, the temperature drops to 5°C. Assuming that the volume of the tire is constant, what is the new air pressure in the tire. Express your answer in lb/in².

Estimate: The volume and number of moles of gas is constant, but the temperature decreases, therefore the pressure must also decrease.

Solution: Rearrange PV = nRT so the variables are on the L.H.S. and the constants are on the R.H.S.

P₁/T₁ = nR/V, P₂/T₂= nR/V and P₁/T₁ = P₂/T₂

now substitute in values of each variable

P₂/278.15K = 30 lb/in² /298.15K, solve for P₂. P₂ = 28 lb/in².

This agrees with our estimate.

Example #2:

How many moles of hydrogen gas occupy 200.00mL at 25°C and 760 torr?

Estimate: Here the temperature is higher than 0°C, therefore the answer must be even less than 0.20000L/(22.41L/mol) = 0.008925 moles

Solution: Use PV = nRT, and solve for n. Convert mL to L, °C to K, and Torr to atm.

n = PV/RT = (760/760 atm) (0.20000 L)/[ 0.08206 L·atm/(mol·K) x (298.15K)]

= 0.00817 moles of H_2.

This agrees with our estimate.

Example #3:

When a valve between a 5-L tank containing a gas at 9 atm and a 10-L tank containing a gas at 6 atm is opened, what are the new pressures of each gas? What is the new total pressure?

Solution: Using Boyle’s and Dalton’s Laws P₁V₁ = P₂V₂ @ constant n and T

(9atm)(5-L) = P₂ (15-L) and (6atm)(10-L) = P₂ (15-L)

P₂ = (9atm)(5-L)/(15-L) = 3 atm P₂ = (6atm)(10-L)/(15-L) = 4 atm

Therefore, P_total = 3 atm + 4 atm = 7 atm.

Example #4: