A 5.1text g sample of NH_ 4 SH is placed in a 3.0text L evacuated flask at 327^ circ C. If 30% of the solid decomposes into NH_ 3 (g) and H_ 2 S(g), find the K_p for this reaction. (R = 0.082text L atm mol ^ -1 text K ^ -1 )

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EEJ MAIN Chemistry QUESTION #7116

Question 1

A $5.1\text{ g}$ sample of $NH_{4}SH$ is placed in a $3.0\text{ L}$ evacuated flask at $327^{\circ}C$. If $30\%$ of the solid decomposes into $NH_{3}(g)$ and $H_{2}S(g)$, find the $K_p$ for this reaction. ($R = 0.082\text{ L atm mol}^{-1}\text{ K}^{-1}$)

$0.242 \times 10^{-4} \text{ atm}^2$
$1 \times 10^{-4} \text{ atm}^2$
$4.9 \times 10^{-3} \text{ atm}^2$
$0.242 \text{ atm}^2$✔️

Correct Answer Explanation

Molar mass of $NH_4SH = 51\text{ g/mol}$. Initial moles $= 5.1/51 = 0.1\text{ mol}$.
At equilibrium, moles of $NH_3 = H_2S = 0.1 \times 0.3 = 0.03\text{ mol}$.
Using $PV = nRT$: $P_{NH_3} = P_{H_2S} = \frac{0.03 \times 0.082 \times 600}{3} = 0.492\text{ atm}$.
$K_p = P_{NH_3} \times P_{H_2S} = (0.492)^2 \approx 0.242\text{ atm}^2$.

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