pKb Calculator

Linking Thermodynamics to Equilibrium

In advanced physical chemistry, equilibrium constants (like Kb) are not just random numbers derived from concentrations. They are fundamentally driven by the Thermodynamics of the molecule—specifically, the Standard Gibbs Free Energy of Dissociation ($\Delta G^\circ$).

By calculating the pKb directly from the Gibbs Free Energy, chemists can seamlessly link the physical thermodynamic stability of a basic molecule to its resulting macroscopic pH in water.

The Thermodynamic Derivation

The core equation linking free energy and equilibrium is $\Delta G^\circ = -RT \ln(K_b)$. To find the pKb, we must first isolate $K_b$ using the natural exponential ($e$), and then convert it into the base-10 logarithmic pKb scale.

The Full Equation

Example Calculation

A weak base has a $\Delta G^\circ$ of +27.1 kJ/mol at standard room temperature (298.15 K).

1. Convert kJ to J: $27.1 \times 1000 = 27,100$ J/mol
2. Calculate RT: $8.314 \times 298.15 = 2478.8$ J/mol
3. Divide $-\Delta G$ by RT: $-27,100 / 2478.8 = -10.93$
4. Raise $e$ to that power to find $K_b$: $e^{-10.93} = 1.79 \times 10^{-5}$
5. Take negative base-10 log for pKb: $-\log_{10}(1.79 \times 10^{-5})$
6. Result: $4.75$

The pKb is 4.75, which proves that the positive $\Delta G$ corresponds to a non-spontaneous, weak dissociation process (like Ammonia).