Units of Thermodynamic Equilibrium Constant Explained

The thermodynamic equilibrium constant ($K$) for a reaction is defined using the activities of the reactants and products, not their concentrations or partial pressures directly.

Thermodynamic Equilibrium Constant ($K$)

Consider the reversible reaction: $A + B \rightleftharpoons C$

The thermodynamic equilibrium constant ($K$) is expressed as the ratio of the activities of the products to the activities of the reactants, each raised to the power of their stoichiometric coefficients:

Here, '$a$' denotes activity.

Activity Definition

Activity is a dimensionless quantity. It represents the effective concentration (or pressure) of a species relative to a standard state. For a species '$i$' in solution, its activity ($a_i$) is defined as:

Where:

• $[i]$ is the molar concentration of species $i$.
• $[i]^0$ is the standard state concentration, typically taken as 1 mol $L^{-1}$.

Since the activity is a ratio of concentration to a standard concentration (or pressure to a standard pressure), the units cancel out, making activity dimensionless.

Conclusion on Units of $K$

As $K$ is calculated as the ratio of dimensionless activities ($a_C$, $a_A$, $a_B$), the overall value of $K$ is also dimensionless.

Therefore, the correct unit for the thermodynamic equilibrium constant is dimensionless.