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Step 1: Calculate the mole fraction of each gas.
• For N₂
[tex]\begin{aligned} X_{\text{N}_2} & = \frac{n_{\text{N}_2}}{n_{\text{N}_2} + n_{\text{O}_2} + n_{\text{other}}} \\ & = \frac{\text{0.390 mol}}{\text{0.390 mol + 0.102 mol + 0.0085 mol}} \\ & = 0.779 \end{aligned}[/tex]
• For O₂
[tex]\begin{aligned} X_{\text{O}_2} & = \frac{n_{\text{O}_2}}{n_{\text{N}_2} + n_{\text{O}_2} + n_{\text{other}}} \\ & = \frac{\text{0.102 mol}}{\text{0.390 mol + 0.102 mol + 0.0085 mol}} \\ & = 0.204 \end{aligned}[/tex]
• For other
[tex]\begin{aligned} X_{\text{other}} & = \frac{n_{\text{other}}}{n_{\text{N}_2} + n_{\text{O}_2} + n_{\text{other}}} \\ & = \frac{\text{0.0085 mol}}{\text{0.390 mol + 0.102 mol + 0.0085 mol}} \\ & = 0.017\end{aligned}[/tex]
Step 2: Calculate the partial pressures of each gas.
• For N₂
[tex]\begin{aligned} P_{\text{N}_2} & = X_{\text{N}_2}P_{\text{T}} \\ & = \text{(0.779)(754 mm Hg)} \\ & = \boxed{\text{587 mm Hg}} \end{aligned}[/tex]
• For O₂
[tex]\begin{aligned} P_{\text{O}_2} & = X_{\text{O}_2}P_{\text{T}} \\ & = \text{(0.204)(754 mm Hg)} \\ & = \boxed{\text{154 mm Hg}} \end{aligned}[/tex]
• For other
[tex]\begin{aligned} P_{\text{other}} & = X_{\text{other}}P_{\text{T}} \\ & = \text{(0.017)(754 mm Hg)} \\ & = \boxed{\text{13 mmHg}} \end{aligned}[/tex]
Hence, the partial pressures of N₂, O₂, and other gases are 587 mm Hg, 154 mm Hg, and 13 mm Hg, respectively.
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