13.1 Bioenergetics and Thermodynamics 491 TABLE 13-1 Some Physical Constants and Units Used in Thermodynamics stant temperature. Boltzmann constant k= 1.381 x 10<3J/K Avogadro's number, N=6.022 X 1023mol-1 The Standard Free-Energy Change Is Directly Related Faraday constant, J=96, 480 J/. mol to the equilibrium Constant Gas constant, R=8.315 J/mol- K (=1.987ca/mol·8 The composition of a reacting system (a mixture of chemical reactants and products) tends to continue Units of△Gand△ H are j/mol(ca/mo changing until equilibrium is reached. At the equilibrium Units of△ S are j/mol·k(rca/mol·K) concentration of reactants and products, the rates of the 1ca=4.184」 forward and reverse reactions are exactly equal and no Units of absolute temperature, I, are Kelvin, K further net change occurs in the system. The concen- 25° trations of reactants and products at equilibrium A25°CRT=2.479k/mol define the equilibrium constant, Keg(p. 26). In the (0.592 kcal/mon) general reaction aA+ bB=c+ dD, where a, b, c, and d are the number of molecules of A, B. C, and D par ticipating, the equilibrium constant is given by in which AG is the change in Gibbs free energy of the ing system, AH is the change in enthalpy of th system, T is the absolute temperature, and AS is the change in entropy of the system. By convention, A Shas where [Al. [B. Cl and [D] are the molar concentrations a positive sign when entropy increases and A H, as noted of the reaction components at the point of equilibrium. above, has a negative sign when heat is released by the When a reacting system is not at equilibrium, the system to its surroundings. Either of these conditions tendency to move toward equilibrium rep which are typical of favorable processes, tend to make ing force, the magnitude of which can be expressed as AGnegative. In fact, AGof a spontaneously reacting sys. the ree-energy change for the reaction, AG. Under stan ons tem is always negative The second law of thermodynamics states that the products are initially present at 1 M concentrations or. entropy of the universe increases during all chemical and physical processes, but it does not require that the or I atm, the force driving the system toward equilib entropy increase take place in the reacting system it rium is defined as the standard free-energy change, AGo self. The order produced within cells as they grow ar By this definition, the standard state for reactions that divide is more than compensated for by the disorder involve hydrogen ions is[H]=l M, or pH 0. Most bio- chemical reactions however. occur in well-buffered they create in their surroundings in the course of growth aqueous solutions near pH 7: both the ph an and division(see Box 1-3, case 2). In short, living id the con- centration of water(55.5 M) essentially constant ganisms preserve their internal order by taking from the For convenience of calculations, biochemists therefore light, and returning to their surroundings an equal define a different standard state, in which the concen- amount of energy as heat and entropy tration of H is 10-M(pH 7)and that of water is 55.5 M; for reactions that involve Mgt(including n Cells Require Sources of Free Energy in which ATP is a reactant), its concentration in solu tion is commonly taken to be constant at 1 mM. phy Cells are isothermal systems-they function at essen- cal constants based on this biochemical standard stat tially constant temperature(they also function at con- are called standard transformed constants and e). Heat flow is not a of (such as AG and Keg) to dist cells, because heat can do work only as it passes to a guish them from the untransformed constants used by zone or object at a lower temperature. The energy that chemists and physicists. (Notice that most other text cells can and must use is free energy, described by the books use the symbol AG rather than AGo. Our use of Gibbs free-energy function G, which allows prediction AG, recommended by an international committee of of the direction of chemical reactions, their exact equi- chemists and biochemists, is intended to emphasize that librium position, and the amount of work they can in the transformed free energy G is the criterion for equi theory perform at constant temperature and pressure. librium )By convention, when H20, H*, and/or Mg2 Heterotrophic cells acquire free energy from nutrient are reactants or products, their concentrations are not molecules, and photosynthetic cells acquire it from ab- included in equations such as Equation 13-2 but are in- sorbed solar radiation. Both kinds of cells transform this stead incorporated into the constants Keg and AGin which G is the change in Gibbs free energy of the reacting system, H is the change in enthalpy of the system, T is the absolute temperature, and S is the change in entropy of the system. By convention, S has a positive sign when entropy increases and H, as noted above, has a negative sign when heat is released by the system to its surroundings. Either of these conditions, which are typical of favorable processes, tend to make G negative. In fact, G of a spontaneously reacting sys￾tem is always negative. The second law of thermodynamics states that the entropy of the universe increases during all chemical and physical processes, but it does not require that the entropy increase take place in the reacting system it￾self. The order produced within cells as they grow and divide is more than compensated for by the disorder they create in their surroundings in the course of growth and division (see Box 1–3, case 2). In short, living or￾ganisms preserve their internal order by taking from the surroundings free energy in the form of nutrients or sun￾light, and returning to their surroundings an equal amount of energy as heat and entropy. Cells Require Sources of Free Energy Cells are isothermal systems—they function at essen￾tially constant temperature (they also function at con￾stant pressure). Heat flow is not a source of energy for cells, because heat can do work only as it passes to a zone or object at a lower temperature. The energy that cells can and must use is free energy, described by the Gibbs free-energy function G, which allows prediction of the direction of chemical reactions, their exact equi￾librium position, and the amount of work they can in theory perform at constant temperature and pressure. Heterotrophic cells acquire free energy from nutrient molecules, and photosynthetic cells acquire it from ab￾sorbed solar radiation. Both kinds of cells transform this free energy into ATP and other energy-rich compounds capable of providing energy for biological work at con￾stant temperature. The Standard Free-Energy Change Is Directly Related to the Equilibrium Constant The composition of a reacting system (a mixture of chemical reactants and products) tends to continue changing until equilibrium is reached. At the equilibrium concentration of reactants and products, the rates of the forward and reverse reactions are exactly equal and no further net change occurs in the system. The concen￾trations of reactants and products at equilibrium define the equilibrium constant, Keq (p. 26). In the general reaction aA bB cC dD, where a, b, c, and d are the number of molecules of A, B, C, and D par￾ticipating, the equilibrium constant is given by Keq   [ [ C A ] ] c a [ [ D B ] ] d b (13–2) where [A], [B], [C], and [D] are the molar concentrations of the reaction components at the point of equilibrium. When a reacting system is not at equilibrium, the tendency to move toward equilibrium represents a driv￾ing force, the magnitude of which can be expressed as the free-energy change for the reaction, G. Under stan￾dard conditions (298 K  25 C), when reactants and products are initially present at 1 M concentrations or, for gases, at partial pressures of 101.3 kilopascals (kPa), or 1 atm, the force driving the system toward equilib￾rium is defined as the standard free-energy change, G . By this definition, the standard state for reactions that involve hydrogen ions is [H]  1 M, or pH 0. Most bio￾chemical reactions, however, occur in well-buffered aqueous solutions near pH 7; both the pH and the con￾centration of water (55.5 M) are essentially constant. For convenience of calculations, biochemists therefore define a different standard state, in which the concen￾tration of H is 107 M (pH 7) and that of water is 55.5 M; for reactions that involve Mg2 (including most in which ATP is a reactant), its concentration in solu￾tion is commonly taken to be constant at 1 mM. Physi￾cal constants based on this biochemical standard state are called standard transformed constants and are written with a prime (such as G and K eq) to distin￾guish them from the untransformed constants used by chemists and physicists. (Notice that most other text￾books use the symbol G rather than G . Our use of G , recommended by an international committee of chemists and biochemists, is intended to emphasize that the transformed free energy G is the criterion for equi￾librium.) By convention, when H2O, H, and/or Mg2 are reactants or products, their concentrations are not included in equations such as Equation 13–2 but are in￾stead incorporated into the constants K eq and G . yz 13.1 Bioenergetics and Thermodynamics 491 Boltzmann constant, k  1.381 1023 J/K Avogadro’s number, N  6.022 1023 mol1 Faraday constant,  96,480 J/V  mol Gas constant, R  8.315 J/mol  K ( 1.987 cal/mol  K) Units of G and H are J/mol (or cal/mol) Units of S are J/mol
K (or cal/mol
K) 1 cal  4.184 J Units of absolute temperature, T, are Kelvin, K 25 C  298 K At 25 C, RT  2.479 kJ/mol ( 0.592 kcal/mol) TABLE 13–1 Some Physical Constants and Units Used in Thermodynamics