In a 10 text m ^ 3 container at 1000 text K , a mixture of 0.5 moles of gas A and x moles of gas B exerts a total pressure of 200 text Pa . If R is the gas constant, find the value of x.

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EEJ MAIN Chemistry QUESTION #7176

Question 1

In a $10 \text{ m}^{3}$ container at $1000 \text{ K}$, a mixture of $0.5$ moles of gas A and $x$ moles of gas B exerts a total pressure of $200 \text{ Pa}$. If $R$ is the gas constant, find the value of $x$.

$\frac{2R}{4+R}$
$\frac{2R}{4-R}$
$\frac{4+R}{2R}$
$\frac{4-R}{2R}$✔️

Correct Answer Explanation

Using the Ideal Gas Equation $PV = nRT$:

Total moles $n = 0.5 + x$
$200 \times 10 = (0.5 + x) \times R \times 1000$
$2000 = (0.5 + x)1000R$
$2 = (0.5 + x)R$
$2/R = 0.5 + x$
$x = \frac{2}{R} - \frac{1}{2} = \frac{4-R}{2R}$

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