How to calculate Ka given pH?

Steps to Solve

1. Use the pH to find the hydrogen ion concentration \([H^+]\)

Given the pH of the solution, we can find the hydrogen ion concentration using the formula:

$$[H^+] = 10^{-\text{pH}}$$

2. Set up the equilibrium expression for the weak acid

For a weak acid that dissociates as HA ⇌ H extsuperscript{+} + A extsuperscript{-}, we can express the equilibrium concentrations in terms of \[H^+]\ and the initial concentration of the acid \[HA]_0\ .

3. Write the expression for Ka

The acid dissociation constant \(K_a\) is given by:

$$K_a = \frac{[H^+][A^-]}{[HA]}$$

Assuming the initial concentration of HA is \[HA]_0\ and at equilibrium, the concentration of HA remaining is \[HA] = [HA]_0 - [H^+]\ (since \[H^+]\ is very small).

Therefore, we can approximate:

$$K_a = \frac{[H^+][H^+]}{[HA]_0 - [H^+]}$$

Since \[H^+]\ is very small compared to \[HA]_0\ , we usually approximate it as:

$$K_a \approx \frac{[H^+]^2}{[HA]_0}$$

4. Calculate Ka using the given pH and initial concentration of HA

If we know \[HA]_0\ (the initial concentration of the acid) and we have found \[H^+]\ in step 1, we can substitute these values into our simplified expression for \[K_a\) to find its value.