Mass–action ratio

The mass–action ratio,^[1] often denoted by $\Gamma$, is the ratio of product concentrations to reactant concentrations at one given time which may be at equilibrium or not.

$\Gamma = \frac{ P_1 P_2 \ldots}{ S_1 S_2 \ldots}$

This assumes that the stoichiometric amounts are all unity. If not, then each species must be raised to the power of its corresponding stoichiometric amount. If the product and reactant concentrations are at equilibrium then the mass–action ratio will equal the equilibrium constant. At equilibrium:

$\Gamma = K_{eq}$

The ratio of the mass–action ratio to the equilibrium constant is often called the disequilibrium ratio, denoted by the symbol $\rho$.

$\rho = \frac{\Gamma}{K_{eq}}$

At equilibrium $\rho = 1$. When the reaction is out of equilibrium $\rho < 1$ but always greater than zero.

References

1. B. Hess and K. Brand. (1965). Enzymes and metabolite profiles. In Control of energy metabolism. III. Ed. B. Chance, R. K. Estabrook and J. R. Williamson. New York: Academic Press.

Other sources

• Atkins, P.W. (1978). Physical Chemistry Oxford University Press ISBN 0-7167-3539-3
• Trevor Palmer (2001) Enzymes: biochemistry, biotechnology and clinical chemistry Chichester Horwood Publishing ISBN 1-898563-78-0