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Question

A container holds a mixture of 3.01 x 10^23 molecules of H22 gas, 1.20 x 10^24 molecules of CO22 gas, and 1.50 x 10^24 molecules O22. If the total pressure of the container is 1.00atm, what is the partial pressure of oxygen gas in atmospheres

Answer 1

The partial pressure of each gas will be the mole fraction of that gas times the total pressure. So, first we need to find moles of each gas, then find the mole fraction of O₂ gas and then the partial pressure of O₂.

moles H₂ = 3.01x1023 molecules x 1 mol / 6.02x1023 molecules = 0.500 moles H₂

moles CO₂ = 1.20x1024 molecules x 1 mol / 6.02x1023 molecules = 1.99 moles CO₂

moles O₂ = 1.50x1024 molecules x 1 mol / 6.02x1023 molecules = 2.49 moles O₂

Total moles of gas = 0.500 + 1.99 + 2.49 = 4.98 moles

Mole fraction of O₂ = 2.49 mols / 4.98 mols = 0.5

Partial pressure of O₂ = 0.5 x 1.00 atm = 0.500 atm

Answer 2

I'll convert to moles so we don't have such large numbers:

H₂ = (3.01 x 10²³)/(6.022 x 10²³) = 0,4998 moles

CO₂ = (1.20 x 10²⁴)/(6.022 x 10²³) = 1.9926 moles

O₂ = (1.50 x 10²⁴)/(6.022 x 10²³) = 2.4908 moles

Total number of moles of all gasses: 0,4998 + 1.9926 + 2.4908 = 4.9833

Partial pressure of H₂ = (mole fraction)(total pressure) = (0,4998/4.9833)(1.00) = 0.100 atm

Partial pressure of CO₂ = (mole fraction)(total pressure) = (1.9926/4.9833)(1.00) = 0.400 atm

Partial pressure of O₂ = (mole fraction)(total pressure) = (2.4908/4.9833)(1.00) = 0.500 atm