GATE 2024 BT Q.57: solution and answer

Official answer: -24Source: Official answer key, GATE 2024 BT (IISc Bengaluru)

1. Free energy changes of coupled reactions add, because $\Delta G$ is a state function: $\Delta G_{\text{total}}=\sum \Delta G_i$.

2. ATP hydrolysis: $\text{ATP}+{\text{H}}_2\text{O}\to \text{ADP}+{\text{P}}_i$, with $\Delta G_1=-32.2{\text{kJ mol}}^{-1}$.

3. Hydrolysis of $\alpha$-glycerophosphate: $\alpha \text{-glycerophosphate}+{\text{H}}_2\text{O}\to \text{glycerol}+{\text{P}}_i$, with $\Delta G=-8.2{\text{kJ mol}}^{-1}$.

4. Formation of $\alpha$-glycerophosphate from glycerol is the reverse of this hydrolysis: $\text{glycerol}+{\text{P}}_i\to \alpha \text{-glycerophosphate}+{\text{H}}_2\text{O}$. Reversing a reaction flips the sign, so $\Delta G_2=+8.2{\text{kJ mol}}^{-1}$.

5. Add the two reactions: $\text{glycerol}+\text{ATP}\to \alpha \text{-glycerophosphate}+\text{ADP}$. The ${\text{H}}_2\text{O}$ and ${\text{P}}_i$ cancel.

6. $\Delta G=-32.2+8.2=-24.0{\text{kJ mol}}^{-1}$, so the answer as an integer is $-24$. It is negative, so ATP can drive the phosphorylation of glycerol.