Physical Chemistry Third Edition

7.7 Chemical Equilibrium and Biological Systems 347

Processes other than nonspontaneous chemical reactions are also coupled to the

hydrolysis of ATP. Figure 7.4 depicts a proposed mechanism for theactive transport

of a hypothetical substance, A, through a biological membrane from a solution with

a low concentration and low chemical potential of A (on the left in the figure) to a

region with a high concentration and high chemical potential of A (on the right in the

figure).^7 This transport is opposite in direction to the spontaneous transport of A, which

is from a higher to a lower value of the chemical potential. The mechanism assumes the

existence inside the membrane of a carrier substance that has two forms. The first form

of the carrier, denoted by C, has a tendency to form a complex with the substance A,

whereas the second form, denoted by C′, has no such tendency.

External

fluid

Interior

of cell

Membrane

(2)

(1) (3)

CA

C

CA

C 9 C 9

C 9 A

(6) (4)

(5) A

ADP + Pi

ATP

A

Figure 7.4 A Proposed Mechanism

for Active Transport through a

Membrane.

Step (1) of the mechanism is the passage of A into the membrane and its combination

of C at the left surface of the membrane. This process is followed by step (2), the

spontaneous transport of the complex CA through the membrane from left to right to

a region where the concentration and chemical potential of CA are small. Step (3) is

the conversion of C to C′, which is coupled to the hydrolysis of ATP. The transported

molecule A is then released in step (4) because C′has no affinity for A. The conversion

of C to C′keeps the concentration of CA at a small value at the right side of the

membrane, which makes step (2) spontaneous. After the molecule A is released from

C′, the C′molecules move spontaneously from right to left in step (5), because they are

converted in step (6) back to the form C at the left side of the membrane by an enzyme

located there, keeping the concentration of C′small at the left side of the membrane.

The C molecules at the left side of the membrane are now available to complex again

with A molecules, and the process can be repeated. The process that causes the overall

process to transport A molecules from a lower to a higher chemical potential is step (3),

which consumes ATP. Although the chemical potential of A increases as it moves from

left to right, the Gibbs energy of the entire system decreases because of the negative

Gibbs energy change of hydrolysis of ATP.

PROBLEMS

Section 7.7: Chemical Equilibrium and Biological Systems

7.63 The hydrolysis of ATP to form ADP and phosphate has
∆G◦′− 29 .3kJmol−^1 and the hydrolysis of glycerol
1-phosphate to form glycerol and phosphate has
∆G◦′− 9 .6kJmol−^1 at 298.15 K. The reactions are
coupled by the enzyme glycerol kinase. If a solution
initially contains some of the enzyme and 0.0100 mol L−^1
ATP and 0.012 mol L−^1 glycerol at 298.15 K, find the final
concentrations of ATP, ADP, glycerol, and glycerol
1-phosphate.

7.64 Creatine phosphate is another substance in addition to
phosphoenolpyruvate that can regenerate ATP. If the
temperature equals 25◦C, if pH 7 .00, and if
pMg 4 .00, the value of∆G◦′for its hydrolysis is

equal to− 43 .1 kJ mol−^1. Assuming that a mechanism

exists to couple the reactions, find the value of the

equilibrium constant for the combined reaction to

regenerate ATP.

7.65 Just as the active transport of a substance through a

membrane can be driven by the hydrolysis of ATP, the

regeneration of ATP can also be driven by a spontaneous

transport of hydrogen ions through a membrane.^8

Assuming the existence of a suitable mechanism, calculate

the minimum difference in pH on the two sides of the

membrane that would be required to drive this regeneration

at 298.15 K.

(^8) E. D. P. DeRobertis and E. M. F. DeRobertis, Jr.,Cell and Molecular
Biology, Saunders College, Philadelphia, 1980, p. 267ff.
(^7) Ibid., p. 487ff.