The synthesis of metabolite from precursors and is essential but thermodynamically…

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

Problem

The synthesis of metabolite

M

from precursors

X

and

Y

is essential but thermodynamically unfavorable in vitro, with a standard Gibbs free energy change

\Delta G^\circ_{\text{unfav}}=+56\,\text{kJ mol}^{-1}

. Cells overcome this barrier by coupling the reaction to the hydrolysis of

n

molecules of ATP, each with

\Delta G^\circ_{\text{ATP}}=-30.5\,\text{kJ mol}^{-1}

under the same conditions. Answer the following. (a) Derive an inequality that relates the integer

n

\Delta G^\circ_{\text{unfav}}

and

\Delta G^\circ_{\text{ATP}}

in order for the coupled overall reaction to be spontaneous under standard conditions. (b) Using the numerical values given, determine the minimum whole number of ATP molecules that must be hydrolyzed to render the overall reaction spontaneous. (c) Write the net chemical equation for the synthesis of one mole of

M

when it is coupled to the minimum number of ATP hydrolyses found in part (b). Clearly indicate and cancel all intermediates. (d) Discuss one biochemical advantage and one potential energetic disadvantage of employing multiple ATP hydrolyses to drive an otherwise unfavorable biosynthetic step.

Related theory

Browse the problem library