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