Oncogenes, Tumor Suppressor Genes, and Programmed Cell Death:- Actual Free-Energy Changes Depend on Reactant and Product Concentrations
We must be careful to distinguish between two different quantities: the free-energy change, ΔG0, and the standard free-energy change, ΔG0. Each chemical reaction has a characteristic standard free-energy change, which may be positive, negative, or zero, depending on the equilibrium constant of the reaction. The standard free energy change tells us in which direction and how far a given reaction must go to reach equilibrium when the initial concentration of each component is 1.0 M, the pH is 7.0, the temperature is 25 C, and the pressure is 101.3 kPa. Thus, ΔG0 is a constant: it has a characteristic, unchanging value for a given reaction. But the actual free-energy change, ΔG0, is a function of reactant and product concentrations and of the temperature pre vailing during the reaction, which will not necessarily match the standard conditions as defined above. Moreover, the ΔG0 of any reaction proceeding spontaneously toward its equilibrium is always negative, becomes less negative as the reaction proceeds, and is zero at the point of equilibrium, indicating that no more work can be done by the reaction.
ΔG and ΔG0 for any reaction A+B ⇌C+D are related by the equation
in which the terms in red are those actually prevailing in the system under observation. The concentration terms in this equation express the effects commonly called mass action, and the term [C][D]/[A][B] is called the mass-action ratio, Q. As an example, let us sup pose that the reaction A+B ⇌C+D is taking place at the standard conditions of temperature (25 C) and pressure (101.3 kPa) but that the concentrations of A, B, C, and D are not equal and none of the components is present at the standard concentration of 1.0 M. To determine the actual free-energy change, ΔG, under these nonstandard conditions of concentration as the reaction proceeds from left to right, we simply enter the actual concentrations of A, B, C, and D in Equation 13–3; the values of R, T, and ΔG0 are the standard values. ΔG is negative and approaches zero as the reaction proceeds because the actual concentrations of A and B decrease and the concentrations of C and D increase. Notice that when a reaction is at equilibrium—when there is no force driving the reaction in either direction and ΔG is zero—Equation 13–3 reduces to
which is the equation relating the standard free-energy change and equilibrium constant given earlier.
The criterion for spontaneity of a reaction is the value of ΔG, not ΔG0. A reaction with a positive ΔG0 can go in the forward direction if ΔG is negative. This is possible if the term RT ln ([products]/[reactants]) in Equation 13–3 is negative and has a larger absolute value than ΔG0. For example, the immediate removal of the products of a reaction can keep the ratio [products]/[reactants] well below 1, such that the term RT ln ([products]/[reactants]) has a large, negative value.
ΔG0 and ΔG are expressions of the maximum amount of free energy that a given reaction can theoretically deliver—an amount of energy that could be realized only if a perfectly efficient device were available to trap or harness it. Given that no such device is possible (some free energy is always lost to entropy during any process), the amount of work done by the re action at constant temperature and pressure is always less than the theoretical amount. Another important point is that some thermody namically favorable reactions (that is, reactions for which ΔG0 is large and negative) do not occur at measurable rates. For example, combustion of firewood to CO2 and H2O is very favorable thermodynamically, but firewood remains stable for years because the activation energy (see Figs 6–2 and 6–3) for the combustion re action is higher than the energy available at room temperature. If the necessary activation energy is provided (with a lighted match, for example), combustion will begin, converting the wood to the more stable products CO2 and H2O and releasing energy as heat and light. The heat released by this exothermic reaction provides the activation energy for combustion of neighboring regions of the firewood; the process is self-perpetuating.
In living cells, reactions that would be extremely slow if uncatalyzed are caused to proceed, not by sup plying additional heat but by lowering the activation en ergy with an enzyme. An enzyme provides an alternative reaction pathway with a lower activation energy than the uncatalyzed reaction, so that at room temperature a large fraction of the substrate molecules have enough thermal energy to overcome the activation barrier, and the re action rate increases dramatically. The free-energy change for a reaction is independent of the pathway by which the reaction occurs; it depends only on the nature and concentration of the initial reactants and the final products. Enzymes cannot, therefore, change equilibrium constants; but they can and do increase the rate at which a reaction proceeds in the direction dictated by thermodynamics.
