Consider the expression $\Delta \mathrm{G}=-\mathrm{RTlnK}_{\mathrm{p}}+\mathrm{RTln}…
Consider the expression $\Delta \mathrm{G}=-\mathrm{RTlnK}_{\mathrm{p}}+\mathrm{RTln} \mathrm{Q}_{\mathrm{p}}$ and indicate the correct statement at equilibrium
$\Delta \mathrm{G}=0, \mathrm{Q}_{\mathrm{p}}>\mathrm{K}_{\mathrm{p}}$ the equilibrium reaction will shift from left to right
$\Delta \mathrm{G}=0, \mathrm{Q}_{\mathrm{p}}=\mathrm{K}_{\mathrm{p}}$ the equilibrium reaction will shift from left to right
$\Delta \mathrm{G}=\infty, \mathrm{Q}_{\mathrm{p}} < \mathrm{K}_{\mathrm{p}}$ the equilibrium reaction will shift from right to left
$\Delta \mathrm{G} < 0, \mathrm{Q}_{\mathrm{p}}>\mathrm{K}_{\mathrm{p}}$ the equilibrium reaction will shift from right to left where $Q_{p}$ and $K_{p}$ term refer to reaction quotient and equilibrium constant at constant pressure respectively.
Solution
The expression given is:
\(\Delta G=-R T \ln K_p+R T \ln Q_p\)
At equilibrium, \(\Delta \mathrm{G}=0\), so: \(0=-R T \ln K_p+R T \ln Q_p\)
Rearranging this, we get: \(\ln K_p=\ln Q_p\)
which implies: \(K_p=Q_p\)
Let's evaluate each statement
1. \(\Delta G=0, Q_p > K_{\mathrm{p}}\); the equilibrium reaction will shift from left to right.
- Incorrect. At equilibrium \((\Delta G=0) . Q_{\mathrm{p}}=K_{\mathrm{p}}\). If \(Q_{\mathrm{p}} > K_{\mathrm{p}} . \Delta G\) is positive, and the reaction shifts from right to left (toward reactants) to reach equilibrium.
2. \(\Delta G=0, Q_p=K_p\); the equilibrium reaction will shift from left to right.
- Incorrect. At equilibrium, when \(Q_{\mathrm{p}}=K_{\mathrm{p}}, \Delta G=0\), and there is no shift in the reaction direction; the system is at equilibrium.
3. \(\Delta G=\infty, Q_p < K_{\mathrm{p}}\); the equilibrium reaction will shift from right to left
- Incorrect. \(\Delta G\) cannot be \(\infty\) in practical terms; it implies an extreme situation where \(Q_p < K_p\) means the reaction will shift from left to right (toward products) to reach equilibrium.
4. \(\Delta G < 0, Q_{\mathrm{p}} > K_{\mathrm{p}}\); the equilibrium reaction will shift from right to left.
- Correct. When \(\Delta G < 0\), the reaction will proceed in the direction that decreases \(\Delta G\). If \(Q_{\mathrm{p}} > K_{\mathrm{p}} . \Delta G < 0\) indicates the reaction will shift from right to left (toward reactants) to reach equilibrium.
Correct statement: (4) \(\Delta G < 0, Q_p > K_p\); the equilibrium reaction will shift from right to left.
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