Suppose that Daniel has a 2.50 L bottle that contains a mixture of O2, N2, and CO2 under a total pressure of 5.80 atm. He knows that the mixture contains 0.290 mol N2 and that the partial pressure of CO2 is 0.250 atm. If the temperature is 273 K, what is the partial pressure of O2?

The partial pressure of O₂ = 2.95 atm

Explanation:

Given: Total volume: V = 2.5 L, Total Pressure: P = 5.80 atm, Temperature: T=273K

Number of moles of N₂: n₁ = 0.290 mol, Partial pressure of CO₂: p₂ = 0.250 atm

To find the total number of moles of gas (n), we use the ideal gas equation: P·V = n·R·T

Here, R is the gas constant = 0.08206 L·atm / (mol·K)

⇒ Total number of moles: n = (P·V) : (R·T) = (5.8 atm * 2.5 L) : (0.08206 L·atm / (mol·K) * 273 K) = 0.647 mole

To find the number of moles of CO₂ in the gas mixture:

p₂·V = n₂·R·T

Here p is the partial pressure of CO₂

⇒ number of moles of CO₂: n₂ = (p₂·V) : (R·T) = (0.250 atm * 2.5 L) : (0.08206 L·atm / (mol·K) * 273 K) = 0.028 mole

As the total number of moles of gas in the mixture (n) = Number of moles of N₂ + Number of moles of CO₂ + Number of moles of O₂

⇒ n = n₁ + n₂ + n₃

⇒ number of moles of O₂: n₃ = n - (n₁ + n₂) = 0.647 - (0.290 + 0.028) = 0.329 mole

The mole fraction of O₂ = number of moles of O₂ : total number of moles = 0.329 : 0.647 = 0.508

Therefore the partial pressure of O₂: p₃ = mole fraction * total pressure (P) = 0.508 * 5.80 atm = 2.95 atm