Concept:According to Dalton's Law of Partial Pressures, the partial pressure of an individual gas in a mixture is equal to its mole fraction (or volume percentage in an ideal mixture) multiplied by the total pressure.
Formula:$$ P_{gas} = \left(\frac{\% \text{ of gas}}{100}\right) \times P_{total} $$
Solution:- We are given the volume percentage of \( \text{H}_2 \) gas as 67.8%.
- To find its mole fraction, we divide by 100: \( \frac{67.8}{100} \).
- The total pressure \( (P_{total}) \) of the mixture is 50 atm.
- Therefore, the partial pressure of \( \text{H}_2 \) is \( \frac{67.8}{100} \times 50 \), which matches the expression \( 67.8 \times \frac{50}{100} \).
Why other options are incorrect:- Option A: This formula incorrectly divides 100 by the total pressure, which breaks the mathematical definition of partial pressure.
- Option B: This ignores the specific percentage of Hydrogen gas entirely.
- Option D: Adding percentages and pressures is algebraically invalid in this context.
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