The Alkaline Equilibrium
While acids donate protons, weak bases (like ammonia or organic amines) act as proton acceptors. Because they are "weak," they do not dissociate completely. Instead, they must steal a hydrogen proton from a water molecule in a reversible equilibrium reaction, forcing the water to leave behind a hydroxide ion ([OH⁻]).
To calculate exactly how many hydroxide ions are produced in a basic solution, chemists use the Base Dissociation Constant (Kb).
Solving for [OH⁻]
Just like with weak acids, calculating the exact equilibrium state requires an ICE (Initial, Change, Equilibrium) table. However, if the base is weak enough that it ionizes less than 5%, we can bypass the complex quadratic math using the standard approximation formula.
The Equation
Example Calculation
You prepare a 0.5 M solution of Ammonia ($K_b = 1.8 \times 10^{-5}$). To find the [OH⁻]:
- Multiply $K_b$ by Concentration: $(1.8 \times 10^{-5}) \times 0.5 = 9.0 \times 10^{-6}$
- Take the square root: $\sqrt{9.0 \times 10^{-6}}$
- Result: $3.0 \times 10^{-3}$ M
The solution has an [OH⁻] of $0.003$ M. From here, you can easily calculate the pOH, and subsequently, the pH of the basic mixture.