自由エネルギー及び平衡

Both the equilibrium constant and the standard free energy change can be used to determine whether a reaction is product or reactant favored. For any reaction mixture composition, the ΔG for the reaction is the sum of the standard free energy and RT times the natural log of the reaction quotient. When the reactants and products are at equilibrium, the free energy change is zero, and the reaction quotient equals the equilibrium constant. So the standard free energy change equals −RT ln K. If ΔG naught is less than zero, ln K is positive, meaning K is greater than 1. In this case, product formation is favored at equilibrium. The larger the equilibrium constant, the more negative the free energy.  Take, for example, the breakdown of dinitrogen tetroxide at 298 kelvin, in which K is 1.34 × 1017.  Substituting the known values into the equation, the standard free energy for the reaction equals −98 kJ/mole, and product formation is favored. Conversely, if ΔG naught is greater than zero, ln K is negative, meaning K is less than 1 and the reverse direction of the reaction is favored. Consider the breakdown of sulfur trioxide gas at 298 kelvin, which has a ΔG naught of 141.6 kJ/mole. The equation can be rearranged so ln K equals negative ΔG over RT. Substituting the known values into the equation, and raising e to the power of the result, K is very small—indicating that the reactant is favored. Notably, if the temperature varies, the equilibrium constant will also change. The temperature dependence of the equilibrium constant can be derived from the equation that directly relates K to the ΔG naught for the reaction. The ΔG naught can be replaced by the standard enthalpy minus temperature times the standard entropy. Dividing both sides by negative RT yields ln K equals negative ΔH over RT plus ΔS over R. This equation is in the form of a straight line where the natural log of K can be plotted against the inverse of the temperature in kelvins with a slope of negative ΔH over R and a y-intercept of ΔS over R. If the values of K are measured at two slightly different temperatures, then this graph can also be used to calculate the change in enthalpy, assuming it remains constant over a limited temperature range.