A mixture of $1.57 \mathrm{~mol}$ of $\mathrm{N}_2, 1.92 \mathrm{~mol}$ of $\mathrm{H}_2$ and $8.13 \mathrm{~mol}$ of $\mathrm{NH}_3$ is introduced into a $20 \mathrm{~L}$ reaction vessel at $500 \mathrm{~K}$. At this temperature, the equilibrium constant, $K_c$ for the reaction $\mathrm{N}_2(\mathrm{~g})+3 \mathrm{H}_2(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NH}_3(\mathrm{~g})$ is $1.7 \times 10^2$. Is the reaction mixture at equilibrium ? If not, what is the direction of the net reaction ?

Question

A mixture of $1.57 \mathrm{~mol}$ of $\mathrm{N}_2, 1.92 \mathrm{~mol}$ of $\mathrm{H}_2$ and $8.13 \mathrm{~mol}$ of $\mathrm{NH}_3$ is introduced into a $20 \mathrm{~L}$ reaction vessel at $500 \mathrm{~K}$. At this temperature, the equilibrium constant, $K_c$ for the reaction $\mathrm{N}_2(\mathrm{~g})+3 \mathrm{H}_2(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NH}_3(\mathrm{~g})$ is $1.7 \times 10^2$. Is the reaction mixture at equilibrium ? If not, what is the direction of the net reaction ?,

MARKS App · Accepted Answer

Given reaction is: $\begin{aligned} &\mathrm{N}_2(\mathrm{~g})+3 \mathrm{H}_2(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NH}_3(\mathrm{~g}) \ &\mathrm{Q}_{\mathrm{c}}=\frac{\left[\mathrm{NH}_3\right]^2}{\left[\mathrm{~N}_2\right]\left[\mathrm{H}_2\right]^3} \ &=\frac{\left(8.13 / 20 \mathrm{~mol} \mathrm{~L}^{-1}\right)^2}{\left(1.57 / 20 \mathrm{molL}^{-1}\right)\left(1.92 / 20 \mathrm{~mol} \mathrm{~L}^{-1}\right)^3} \ &=2394.20 \ &\text { As } \mathrm{Q}_{\mathrm{c}} \neq \mathrm{K}_{\mathrm{c}} \text {, the reaction mixture is not in equilibrium. } \ &\text { As } \mathrm{Q}_{\mathrm{c}}>\mathrm{K}_{\mathrm{c}} \text {, the net reaction will be in the backward } \ &\text { direction. } \end{aligned}$

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