Short Answer 
The acid dissociation constant (Ka) measures the strength of a weak acid in solution and can be simplified for weak acids that only slightly ionize. By calculating the concentration of hydrogen ions and using the formula pH = -log([H+]), the pH can be determined, for example, a 0.10 M weak acid with a Ka of 5 √ó 10-5 yields a pH of approximately 4.30.
Step 1: Understand the Acid Dissociation Constant (Ka)
The acid dissociation constant, denoted as Ka, indicates the strength of a weak acid in solution. It is represented by the formula:
- Ka = [HA] [H+] [A–]
In this equation, [H+] represents the concentration of hydrogen ions, [A–] is the concentration of the conjugate base, and [HA] is the concentration of the weak acid itself. Since weak acids do not fully dissociate, their concentrations can often be treated as approximately constant.
Step 2: Simplify the Equation for Calculation
For weak acids that only slightly ionize, we can simplify the formula. The equation can be approximated as:
- Ka ‚âà [HA]0 [H+] [A–]
This simplification allows us to assume that the change in concentration of the weak acid [HA] is negligible. Thus, at equilibrium, the concentrations of the conjugate base and hydrogen ions can be treated as equal, leading to further simplification. Now we can rearrange the equation to solve for [H+].
Step 3: Calculate the pH from [H+]
Once we have calculated the concentration of hydrogen ions, we can find the pH using the formula:
- pH = -log([H+])
For example, substituting our values, if [H+] = 5 √ó 10-5 M, then:
- pH ≈ -log(5 × 10-5) ≈ 4.30
This calculation shows that the approximate pH of a 0.10 M weak acid with a Ka of 5 √ó 10-5 is approximately 4.30.