Question

1. a mixture of gases contains 5.00 grams of ne, 5.00 grams of o₂, and 5.00 grams of co₂. what is the mole fraction of each gas?

Explanation:

Step1: Calculate moles of Ne

Molar mass of Ne = 20.18 g/mol. Moles = mass/molar mass:
$n_{\text{Ne}} = \frac{5.00}{20.18} \approx 0.2478$ mol

Step2: Calculate moles of O₂

Molar mass of O₂ = 32.00 g/mol:
$n_{\text{O}_2} = \frac{5.00}{32.00} = 0.15625$ mol

Step3: Calculate moles of CO₂

Molar mass of CO₂ = 44.01 g/mol:
$n_{\text{CO}_2} = \frac{5.00}{44.01} \approx 0.1136$ mol

Step4: Total moles of mixture

Sum the moles:
$n_{\text{total}} = 0.2478 + 0.15625 + 0.1136 \approx 0.51765$ mol

Step5: Mole fraction of Ne

$\chi_{\text{Ne}} = \frac{n_{\text{Ne}}}{n_{\text{total}}} \approx \frac{0.2478}{0.51765} \approx 0.479$

Step6: Mole fraction of O₂

$\chi_{\text{O}_2} = \frac{n_{\text{O}_2}}{n_{\text{total}}} \approx \frac{0.15625}{0.51765} \approx 0.302$

Step7: Mole fraction of CO₂

$\chi_{\text{CO}_2} = \frac{n_{\text{CO}_2}}{n_{\text{total}}} \approx \frac{0.1136}{0.51765} \approx 0.219$

Answer:

Mole fraction of Ne ≈ 0.479; Mole fraction of O₂ ≈ 0.302; Mole fraction of CO₂ ≈ 0.219