We now must be careful, for the numerical value of given was for these units only:



If we used this numerical value but expressed concentrations in moles per liter, the results of the calculation would be meaningless.

We could just as well have written the combustion reaction as

(g) + (g) (g)
= -54.6 kcal per mole of

in which case the equilibrium-constant expression would be

If we halve the coefficients of a chemical reaction, we must halve the corresponding free energy change of the reaction, and take the square root of the equilibrium-constant expression (which is the same as halving the exponents).

We also must take the square root of the value of the equilibrium constant, . If we double the coefficients of a reaction, we must double the free energy change and square the equilibrium expression and .

Whenever you use either equilibrium constants or free energies, you must be careful to be sure that you know the chemical reaction and the concentration units to which the numerical values of apply.