0.5 moles of gas A and x moles of gas B together exert a pressure of 200 Pa in a 10 m^3 container at 1000 K. Given that R is the gas constant in J K^ -1 mol^ -1 , the value of x is:

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EEJ MAIN Chemistry QUESTION #7508

Question 1

0.5 moles of gas A and $x$ moles of gas B together exert a pressure of 200 Pa in a 10 m$^3$ container at 1000 K. Given that $R$ is the gas constant in J K$^{-1}$ mol$^{-1}$, the value of $x$ is:

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

Correct Answer Explanation

Apply the ideal gas law: $PV = n_{\text{total}}RT$

$n_{\text{total}} = 0.5 + x$

$200 \times 10 = (0.5 + x) \times R \times 1000$

$2000 = 1000R(0.5 + x)$

$2 = R(0.5 + x) = 0.5R + Rx$

$Rx = 2 - 0.5R$

$x = \dfrac{2 - 0.5R}{R} = \dfrac{4 - R}{2R}$

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