In a biosynthetic pathway

CHEMISTRY · Multi-part · AP · Chemistry · Thermodynamics and Electrochemistry · Thermodynamics and Electrochemistry

Problem

In a biosynthetic pathway, formation of compound C from reactants A and B is endergonic. The cell couples this step to two separate phosphate-transfer reactions derived from ATP to make the overall process favorable. Relevant data at 298 K298\,\text{K} are provided. (1) A+B→CΔG1∘=+40 kJ mol−1A + B \to C \quad \Delta G^\circ_1 = +40\,\text{kJ mol}^{-1} (2) ATP+H2O→ADP+PiΔG2∘=−31 kJ mol−1\text{ATP} + \text{H}_2\text{O} \to \text{ADP} + P_i \quad \Delta G^\circ_2 = -31\,\text{kJ mol}^{-1} (3) ADP+Pi→AMP+PPiΔG3∘=−10 kJ mol−1\text{ADP} + P_i \to \text{AMP} + \text{PP}_i \quad \Delta G^\circ_3 = -10\,\text{kJ mol}^{-1} Assume that each hydrolysis step consumes one molecule of ATP or ADP as written. Answer the following questions. (a) Determine the minimum integer number of ATP molecules that must be hydrolyzed, using Reactions (2) and (3) as provided, so that coupling with Reaction (1) makes the overall standard Gibbs free energy change negative. (b) Write a balanced overall chemical equation that includes Reaction (1) and the appropriate number of hydrolysis reactions you identified in part (a). Cancel all species that appear unchanged on both sides. (c) Calculate the standard Gibbs free energy change, ΔGoverall∘\Delta G^\circ_{\text{overall}}, for the balanced equation you wrote in part (b). (d) Assuming the reaction is carried out reversibly at 298 K298\,\text{K}, determine the maximum amount of non-pressure–volume work (in kJ mol−1\text{kJ mol}^{-1} of C produced) that could, in principle, be extracted from the overall process.

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