Mixed Gas Question 2

Question

1. How many atm is the partial pressure of carbon dioxide in a container that holds 12.01 moles of CO₂, 30.12 moles of N₂ and 27.76 mole of H₂ and has a total pressure of 2.6 atm? Answer with correct significant figures and unit in abbreviation.
2. A gas takes up a volume of 52 liters, has a pressure of 14 atm, and a temperature of 48 K. If I change the temperature to 62 K and the pressure to 1.91 atm, what is the new volume of the gas in liters?  Answer with correct significant figures and unit in abbreviation.

Answer 1

Partial pressure = mol fraction X total pressure

P_gas = X_gas X P_total

First find mol fraction of CO₂:

Total moles of gas = 12.01 + 30.12 + 27.76 = 69.89 mols

mol fraction CO₂ = 12.01 / 69.89 = 0.1718

Next, find partial pressure of CO₂:

P_CO2 = X_CO2 x P_total

P_CO2 = 0.1718 X 2.6 atm = 0.45 atm (2 sig. figs.)

Use the combined gas law: P1V1/T1 = P2V2/T2

P1 = initial pressure = 14 atm

V1 = initial volume = 52 L

T1 = initial temperature in K = 48K

P2 = final pressure = 1.91 atm

V2 = final volume = ?

T2 = final temperature in K = 62K

(14)(52) / 48 = (1.91)(V2) / 62

Solve for V2:

V2 = 490 L (2 sig. figs.)