Consider the reaction X->Y in a cell at 37°C. At equilibrium, the concentrations of X and Y are 50 ?M and 5 ?M, respectively. Use this information and the equations below to answer questions A–E

Question

?G° = –0.616 ln Keq
?G = ?G° + 0.

616 ln [Y]/[X]

Recall that the natural log of a number z will have a negative value when z< 1, positive when z> 1, and 0 when z = 1.

A. What is the value of Keq for this reaction?
B. Is the standard free-energy change of this reaction positive or negative? Is the reaction X->Y an energetically favorable or unfavorable reaction under standard conditions?
C. What is the value of the standard free energy? Refer to Table 3–1 in the textbook or use a calculator.
D. Imagine circumstances in which the concentration of X is 1000 ?M and that of Y is 1 ?M. Is conversion of X to Y favorable? Will it happen quickly?
E. Imagine starting conditions in which the reaction X->Y is unfavorable, yet the cell needs to produce more Y. Describe two ways in which this may be accomplished.

Answer 1

A. Keq = [Y]/[X] = 5 ?M/50 ?M = 0.1
B. The standard free-energy change, ?G°, is positive because Keq is less than 1. Under standard conditions (equal concentrations of X and Y), the reaction X->Y is unfavorable.
C. ?G° = –0.616 ln Keq = –0.616 ln 0.1 = (–0.616) (–2.3) = 1.4 kcal/mole.
D. Yes, the conversion is favorable because the value of [Y]/[X] is less than the equilibrium value. However, the speed of the reaction cannot be determined from the free-energy difference. For example, combustion of this piece of paper is a highly favorable reaction, yet it will not happen in our lifetime without a catalyst.
E. The cell may directly couple the unfavorable reaction to a second, energetically favorable reaction whose negative ?G has a value larger than the positive ?G of the X->Y reaction; the coupled reaction will have a ?G equal to the sum of the component reactions. Alternatively, more X will be converted to Y if the concentration of Y drops; this may happen if Y is converted to Z in a second reaction or if Y is exported from the cell or compartment where the X->Y reaction occurs.