A mixture of hydrogen and carbon dioxide gases contains hydrogen at a partial pressure of 619 mm Hg and carbon dioxide at a partial pressure of 179 mm Hg. What is the mole fraction of each gas in the mixture? XH₂ CO₂

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When the equation

\[ 4.71x^2 + 2.86x - 1.80 = 0 \]

is solved, the two values of the unknown \( x \) are [textbox] and [textbox].

(Note: Textboxes are placeholders where students can input their answers on the educational website).
Transcribed Image Text:When the equation \[ 4.71x^2 + 2.86x - 1.80 = 0 \] is solved, the two values of the unknown \( x \) are [textbox] and [textbox]. (Note: Textboxes are placeholders where students can input their answers on the educational website).
**Question:**

A mixture of **hydrogen** and **carbon dioxide** gases contains hydrogen at a partial pressure of **619 mm Hg** and carbon dioxide at a partial pressure of **179 mm Hg**. What is the mole fraction of each gas in the mixture?

**Solution:**

To determine the mole fraction of each gas in the mixture:

1. Calculate the total pressure:
\[ P_{\text{total}} = P_{\text{H}_2} + P_{\text{CO}_2} \\
P_{\text{total}} = 619 \, \text{mm Hg} + 179 \, \text{mm Hg} = 798 \, \text{mm Hg} \]

2. Calculate the mole fraction for each gas:
\[ X_{\text{H}_2} = \frac{P_{\text{H}_2}}{P_{\text{total}}} = \frac{619 \, \text{mm Hg}}{798 \, \text{mm Hg}} \]

\[ X_{\text{CO}_2} = \frac{P_{\text{CO}_2}}{P_{\text{total}}} = \frac{179 \, \text{mm Hg}}{798 \, \text{mm Hg}} \]

These calculations will yield the mole fractions of hydrogen and carbon dioxide in the gas mixture. 

\[ X_{\text{H}_2} = \approx 0.776 \] (Value needs to be calculated)
\[ X_{\text{CO}_2} = \approx 0.224 \] (Value needs to be calculated)
Transcribed Image Text:**Question:** A mixture of **hydrogen** and **carbon dioxide** gases contains hydrogen at a partial pressure of **619 mm Hg** and carbon dioxide at a partial pressure of **179 mm Hg**. What is the mole fraction of each gas in the mixture? **Solution:** To determine the mole fraction of each gas in the mixture: 1. Calculate the total pressure: \[ P_{\text{total}} = P_{\text{H}_2} + P_{\text{CO}_2} \\ P_{\text{total}} = 619 \, \text{mm Hg} + 179 \, \text{mm Hg} = 798 \, \text{mm Hg} \] 2. Calculate the mole fraction for each gas: \[ X_{\text{H}_2} = \frac{P_{\text{H}_2}}{P_{\text{total}}} = \frac{619 \, \text{mm Hg}}{798 \, \text{mm Hg}} \] \[ X_{\text{CO}_2} = \frac{P_{\text{CO}_2}}{P_{\text{total}}} = \frac{179 \, \text{mm Hg}}{798 \, \text{mm Hg}} \] These calculations will yield the mole fractions of hydrogen and carbon dioxide in the gas mixture. \[ X_{\text{H}_2} = \approx 0.776 \] (Value needs to be calculated) \[ X_{\text{CO}_2} = \approx 0.224 \] (Value needs to be calculated)
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