Units of equilibrium constant

The thermodynamic definition of the equilibrium constant is

\Delta_rG^{\: o}=-RTlnK

where ΔGo is the reaction Gibbs energy at standard conditions (a constant for a particular reaction), R is the gas constant, T is temperature.

Since logarithms only take pure numbers, K is a dimensionless number. However, when equilibrium constants are calculated as a quotient of concentrations or partial pressures,

K_c=\frac{\left [ C \right ]^p\left [ D \right ]^q...}{\left [ A \right ]^m\left [B \right ]^n...}\; \; \; or\; \; \; K_p=\frac{p_C^{ \; \; \; p}p_D^{ \; \; \;q}...}{p_A^{ \; \; \; m}p_B^{\; \; \; n}...}

the practice is to quote them in units of concentration or pressure according to the quotient, for example, the units of Kc for

K_c=\frac{\left [ CoCl_4^{\; 2-} \right ]}{\left [ Co\left ( H_2O \right )_6^{\; 2+} \right ]\left [ Cl^- \right ]^4}

is mol-4dm12.


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