We shall make two assumptions:
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- [H+] from water is negligible, i.e. H+ in the flask containing the weak acid is solely due to that of the acid, [H+]a, as the dissociation of water is suppressed at this stage.
- For a weak acid, [HA] is approximately equal to the concentration of the undissociated acid, [HA]ud, i.e. the dissociation of the weak acid HA is negligible.
The equation for the dissociation of a weak monoprotic acid is:
with the equilibrium constant at the start of the titration as:
Taking the logarithm on both sides of the above equation and rearranging, we have:
Eq1 is the general formula for determining the pH of a strong base to weak acid titration at the start point.
The second assumption becomes less valid when the weak monoprotic acid or weak monoprotic base has Ka ≥ 10-3 or Kb ≥ 10-3 respectively. Removing the second assumption, the equilibrium constant expression becomes:
The corresponding pH equation is obtained by rearranging the above equation into a quadratic equation in terms of [H+]a, finding the latter’s roots and taking the logarithm of the root:
Question
Do both the above equation and eq1 give the same pH value for the titration of 10 cm3 of 0.200 M of CH3COOH (Ka = 1.75 x 10-5) with NaOH?
Answer
Yes, both formulae give pH = 2.73. This validates the applicability of eq1 for acids with Ka in the region of 10-5.
If we disregard both assumptions, we will end up deriving the complete pH titration curve for a strong base to weak acid titration. See this article in the advanced section for details.
Question
Show that pKa + pKb = 14.
Answer