If we go a little farther in thermodynamics than this book will, it is not hard to prove the logarithmic relationship between and . In the equation above In is the natural logarithm, not log, or logarithm to base 10. R is the gas constant discussed in Chapter 2, with a numerical value of 1.987 cal deg or 0.08205 liter atm deg . It also is Avogadro's number times the Boltzmann constant, k, of Chapter 13. The superscript zero on G indicates that the free energy change in this equation is the standard free energy change of the reaction-the value at the given temperature when all gases are at

one atmosphere partial pressure and all solution components are at concentrations of one mole per liter. In contrast, is the ratio of products to reactants at equilibrium, which may be quite different from standard conditions. The equation above compares the strength of the drive toward equilibrium from the standard state, with the ratio of products to reactants once equilibrium is attained. The more that equilibrium is skewed toward an excess of products (large ), the greater the initial impetus of movement (large negative ) if the reaction is begun from standard concentrations.