Reaction Quotient Calculator

The reaction quotient has the same algebraic form as the equilibrium constant but is evaluated with whatever concentrations exist at the moment of measurement. For aA + bB in equilibrium with cC + dD, Q = [C]^c [D]^d divided by [A]^a [B]^b, each term raised to its stoichiometric coefficient. Comparing Q against K tells the system which way to move: Q below K means products are under-represented and net reaction runs forward, Q above K means it runs in reverse, and Q equal to K means no net change. The thermodynamic link is delta-G = delta-G-standard + RT ln Q, and since delta-G-standard equals minus RT ln K this collapses to delta-G = RT ln(Q/K), so at 298.15 K a Q ten times below K corresponds to about minus 5.7 kJ per mole of driving force. Two conventions must be respected. Pure solids and pure liquids have unit activity and are omitted, so for CaCO3 decomposing to CaO and CO2 the quotient is simply the CO2 pressure; water acting as solvent is dropped for the same reason, its concentration of about 55.5 mol per litre being effectively constant. Q must also be built on the same standard state as the K it is compared against: Qc from molar concentrations belongs with Kc, Qp from partial pressures with Kp, and the two differ by RT raised to the change in moles of gas. Strictly, Q is dimensionless because each term is a ratio to a standard state of 1 M or 1 bar, which is what makes taking its logarithm legitimate. Finally, Q says nothing about speed: a mixture can sit far from equilibrium indefinitely when the kinetic barrier is high, as hydrogen and oxygen do at room temperature.

Cato Guldberg and Peter Waage, working in Christiania, now Oslo, published the law of mass action in 1864, stating that the rate of a reaction depends on the active masses of the reactants and that equilibrium represents the balance of forward and reverse tendencies. Their paper appeared in Norwegian and attracted little notice; a French version in 1867 and a German one in 1879 finally spread it. Jacobus Henricus van't Hoff reached the same relation independently in the early 1880s and gave it a thermodynamic reading, while Josiah Willard Gibbs had already, in his 1876 to 1878 memoir on the equilibrium of heterogeneous substances, supplied the free-energy framework that explains why the constant takes the form it does. The distinction between the constant and the same expression evaluated away from equilibrium follows from Gibbs's result that free energy depends on composition through a logarithmic term. Van't Hoff's reaction isotherm, published in the 1880s, is precisely the relation between delta-G, delta-G-standard and RT ln Q used here. Henry Le Chatelier stated his qualitative displacement principle in 1884, with Karl Ferdinand Braun adding a version in 1887, and the Q against K comparison is the quantitative form of that principle for changes in composition. Gilbert Lewis introduced activity and fugacity in 1907 to replace concentrations and pressures in non-ideal systems, which is why rigorous treatments define Q in terms of activities rather than molarities. The symbol Q itself, and its explicit teaching as a separate quantity from K, is a later textbook convention.