One difficulty in using entropy as a criterion of whether a biochemical process can occur spontaneously is that the entropy changes of chemical reactions are not readily measured. Furthermore the criterion of sponta neity given in equation 2 requires that both the entropy change of the surroundings and that of the system of interest be known. These difficu ties are obviated by using a different thermodynamic function called the free energy, which is denoted by the symbol G(or F, in the older literature
In 1878, Josiah Willard Gibbs created the free-energy function by com bining the first and second laws of thermodynamics. The basic equation is △G=△H-T△S (3) in which AG is the change in free energy of a system undergoing a trans- formation at constant pressure (P) and temperature (T),AH is the change in enthalpy(heat content) of this system, and AS is the change in entropy of this system
the Ag of a reaction depends both on the change in internal en ergy and on the change in entropy of the system. The change in free energy(AG)of a reaction, in contrast with the change in internal energy(AE) of a reaction, is a valuable criterion of whether it can occur spontaneously 1. A reaction can occur spontaneously only i/Ag ve 2.A system is at equilibrium and no net change can take place if Agis zero. 3. a reaction cannot occur spontaneously if AG is positive. An input of tree energy is required to drive such a reaction
Two additional points need to be emphasized here. First, the Ag of a reaction depends only on the free energy of the products(the final state minus that of the reactants(the initial state). The AG of a reaction is inde- pendent of the path(or molecular mechanism) of the transformation. The mecha- nism of a reaction has no effect on Ag Second, the Ag provides no informalion about the rale of a reaction. A negative A G indicates that a reaction can occur spontaneously, but it does not signify whether it will proceed at a perceptible rate. As will be dis cussed shortly(p. 188), the rate of a reaction depends on the free energy of activation(△G), which is unrelated to△G
STANDARD FREE-ENERGY CHANGE OF A REACTION AND ITS RELATION TO THE EQUILIBRIUM CONSTANT Consider the reaction A+B=C+D The AG of this reaction is given by [C][D] △G=△G°+ RTloge[A[B (6 in which AG is the standard free-energy change, R is the gas constant, Tis the absolute temperature, and [A], [B], [C], and [D] are the molar con centrations (more precisely, the activities) of the reactants. Ag is the free-energy change for this reaction under standard conditions-that is when each of the reactants A, B, C, and d is present at a concentration of 1.0 M(for a gas, the standard state is usually chosen to be I atmosphere Thus, the Ag of a reaction depends on the nature of the reactants(ex- pressed in the AG term of equation 6)and on their concentrations(ex- pressed in the logarithmic term of equation 6)
A convention has been adopted to simplify free-energy calculations for biochemical reactions. The standard state is defined as having a ph of 7 Consequently, when Ht is a reactant, its activity has the value I(corre- sponding to a pH of 7)in equations 6 and 9. The activity of water also is taken to be I in these equations. The standard free-energy change al pH 7, denoted by the symbol ago, will be used throughout this book. The kilocalorie(abbreviated kcal) will be used as the unit of energy
The relation between the standard free energy and the equilibrium constant of a reaction can be readily derived. At equilibrium. AG=0 Equation 6 then becomes 0=△G°+ RTog [CJ[D] A][B] and △G=- RT log ICJ[D [AJIB] (8) The equilibrium constant under standard conditions, Keo, is defined as K [C][D [A][B] (9) Substituting equation 9 into equation 8 gives AG.--RTloge Keq =-RT InKeq (10) △C"=-2.08r10Km△G!RT (11) hich can be rearranged to give Ken=e eq=10-42.303R7 K Substituting R= 1.987 X 10-3 kcal mol -I deg I and T=298K(corre- sponding to 25C) gives eq=10-4G°/1.36 K (13)
K´ e △G○′ /RT RT lnKeq ´ eq
Units of energy- A calorie(cal) is equivalent to the amount of heat required to raise the temperature of I gram of water from 14.5"C to15.5°C. a kilocalorie(kcal) is equal to 1000 cal A joule(d) is the amount of energy needed to apply a I newton force over a distance of I meter. A Kilojoule (k]) is equal to1000 I kcal= 4.184
Chapter 8 187 ENZYMES Table 8-1 Relation between AGo and K (at25°C) △G° kcal/mo/ kJ/ mol 10-5 6.82 28.53 10-4 5.46 22.84 10 4.09 17.11 10-2 2.73 11.42 10-1 1.36 5.69 10 1.36 -5.69 10 2.73 -11.42 10 4.09 17.11 10 5.46 22.84 10 -682 28.53
CHOH C=0 CHOPO, 2 Dihydroxyacetone phosphate H—C-0H CH2 OPO3 Glyceraldehyde 3-phosphate