Question

What are the mole fractions and partial pressures of each gas in a 2.50-L container into which 100.00g of nitrogen and 200.00 g of carbon dioxide are added at 25 degrees C? What is the total pressure?

Thanks!

Answer 1

first calulate no. of mole of each gas

molar mass of N₂ = 28.0134 gm/mole then 100 gm of N₂ = 100 / 28.0134 = 3.57 mole

molar mass of CO₂ = 44.01 gm/mole then 200 gm CO₂ = 4.54 mole

total mole of gas = 3.57 + 4.54 = 8.11 mole

now calculate total pressure of gas by using ideal gas equation

PV = nRT             where, P = atm pressure= ?

V = volume in Liter = 2.50 L

n = number of mole = 8.11 mol

R = 0.08205L atm mol^-1 K^-1 =Proportionality constant = gas constant,

T = Temperature in K = 25⁰C = 273.15+ 25 = 298.15 K

We can write ideal gas equation

P = nRT/V

Substitute value in above equation

P = 8.11X 0.08205X 298.15 / 2.50 = 79.36 atm

total pressure of gas = 79.36 atm

mole fraction = no. of mole of indivisual gas / total mole

mole fraction of N₂ = 3.57 / 8.11 = 0.44

mole fraction of CO₂ = 4.54 / 8.11 = 0.56

partial pressure = mole fraction X total pressure

partial pressure of N₂ = 0.44 X 79.36 = 34.92 atm

partial pressure of CO₂ = 0.56 X 79.36 = 44.44 atm