Question

what is the mole fraction and partial pressure of co₂ in a sample of gas that contains 1.25 g of co₂, 1.49 g of ch₄, and 3.31 g of he, in which the total pressure is 5.78 atm?
x = select
p_{co₂} = select atm

Explanation:

Step1: Calculate moles of each gas

Molar mass of \( \text{CO}_2 \) is \( 44.01 \, \text{g/mol} \), \( \text{CH}_4 \) is \( 16.04 \, \text{g/mol} \), \( \text{He} \) is \( 4.00 \, \text{g/mol} \).
Moles of \( \text{CO}_2 \): \( n_{\text{CO}_2} = \frac{1.25 \, \text{g}}{44.01 \, \text{g/mol}} \approx 0.0284 \, \text{mol} \)
Moles of \( \text{CH}_4 \): \( n_{\text{CH}_4} = \frac{1.49 \, \text{g}}{16.04 \, \text{g/mol}} \approx 0.0929 \, \text{mol} \)
Moles of \( \text{He} \): \( n_{\text{He}} = \frac{3.31 \, \text{g}}{4.00 \, \text{g/mol}} \approx 0.8275 \, \text{mol} \)

Step2: Calculate total moles

\( n_{\text{total}} = 0.0284 + 0.0929 + 0.8275 \approx 0.9488 \, \text{mol} \)

Step3: Calculate mole fraction of \( \text{CO}_2 \)

Mole fraction \( x_{\text{CO}_2} = \frac{n_{\text{CO}_2}}{n_{\text{total}}} = \frac{0.0284}{0.9488} \approx 0.030 \)

Step4: Calculate partial pressure of \( \text{CO}_2 \)

Using \( p_i = x_i \cdot P_{\text{total}} \), where \( P_{\text{total}} = 5.78 \, \text{atm} \)
\( p_{\text{CO}_2} = 0.030 \cdot 5.78 \approx 0.173 \, \text{atm} \) (or more precisely, \( 0.0284/0.9488 \cdot 5.78 \approx 0.172 \, \text{atm} \))

Answer:

Mole fraction (\( x \)) of \( \text{CO}_2 \approx 0.030 \), Partial pressure (\( p_{\text{CO}_2} \)) \( \approx 0.172 \, \text{atm} \) (or more accurate values based on precise calculations: \( x \approx 0.0299 \), \( p_{\text{CO}_2} \approx 0.173 \, \text{atm} \))