Q.The equilibrium constant of a reaction is 10, what will be the sign of $\Delta G$? Will this reaction be spontaneous?

Step 1. The Van't Hoff equation (Section 7.11.2) relates $\Delta G^0$ and $K_{eq}$: $\Delta G^0=-RT\ln K_{eq}=-2.303RT\log K_{eq}$.

Step 2. Since $K_{eq}=10>1$, $\log K_{eq}=\log10=1$, a POSITIVE number.

Step 3. With the leading minus sign, $\Delta G^0=-2.303RT(1)$, which is NEGATIVE for any positive $T$. …

Check whether $K_{eq}$ is greater or less than 1, since that sign directly determines the sign o …

• Assuming $\Delta G$ is positive just because the question sounds like it's testing a 'trick' -- any $K_{eq}>1$ always gives a ne …