Question

a molecular - level representation of a mixture of two gases (a and b) is shown below. the total pressure in the container is 145 kpa.
what is the mole fraction of gas a?
what is the mole fraction of gas b?
what is the partial pressure of gas a? kpa
what is the partial pressure of gas b? kpa

Explanation:

Step1: Count the number of moles

Count the number of gas A molecules (blue) and gas B molecules (brown). There are 8 gas A molecules and 5 gas B molecules. The total number of moles \(n_{total}=n_A + n_B=8 + 5=13\).

Step2: Calculate mole fractions

The mole fraction formula is \(x_i=\frac{n_i}{n_{total}}\).
For gas A: \(x_A=\frac{n_A}{n_{total}}=\frac{8}{13}\approx0.615\).
For gas B: \(x_B=\frac{n_B}{n_{total}}=\frac{5}{13}\approx0.385\).

Step3: Calculate partial pressures

The partial - pressure formula is \(P_i=x_i\times P_{total}\).
Given \(P_{total} = 145\ kPa\).
For gas A: \(P_A=x_A\times P_{total}=\frac{8}{13}\times145\ kPa=\frac{1160}{13}\ kPa\approx89.2\ kPa\).
For gas B: \(P_B=x_B\times P_{total}=\frac{5}{13}\times145\ kPa=\frac{725}{13}\ kPa\approx55.8\ kPa\).

Answer:

Mole fraction of gas A: \(0.615\)
Mole fraction of gas B: \(0.385\)
Partial pressure of gas A: \(89.2\ kPa\)
Partial pressure of gas B: \(55.8\ kPa\)