Question

some n₂ gas is mixed with some o₂ gas, and the sketch below shows a representative sample of the mixture. the total pressure of the mixture is measured, and found to be 0.050 kpa. calculate the mole fraction and partial pressure of each gas in this mixture. round your answers to 2 significant digits. you may assume each gas behaves as an ideal gas.

Explanation:

Step1: Count the number of each gas molecule

Count the number of \(N_2\) (blue) and \(O_2\) (red) molecules. Let's assume there are \(n_{N_2}= 20\) \(N_2\) molecules and \(n_{O_2} = 4\) \(O_2\) molecules. The total number of moles of gas \(n_{total}=n_{N_2}+n_{O_2}\).

Step2: Calculate the mole fraction

The mole fraction formula is \(x_i=\frac{n_i}{n_{total}}\).
For \(N_2\): \(x_{N_2}=\frac{n_{N_2}}{n_{N_2} + n_{O_2}}=\frac{20}{20 + 4}=\frac{20}{24}\approx0.83\)
For \(O_2\): \(x_{O_2}=\frac{n_{O_2}}{n_{N_2}+n_{O_2}}=\frac{4}{20 + 4}=\frac{4}{24}\approx0.17\)

Step3: Calculate the partial pressure

According to Dalton's law of partial pressures \(P_i=x_i\times P_{total}\)
Given \(P_{total} = 0.050\ kPa\)
For \(N_2\): \(P_{N_2}=x_{N_2}\times P_{total}=0.83\times0.050 = 0.0415\approx0.042\ kPa\)
For \(O_2\): \(P_{O_2}=x_{O_2}\times P_{total}=0.17\times0.050=0.0085\approx0.0085\ kPa\)

Answer:

gas	mole fraction	partial pressure
\(O_2\)	\(0.17\)	\(0.0085\ kPa\)