Gran Plot - Titrating Strong Acid With Strong Base

Titrating Strong Acid With Strong Base

For a strong acid-strong base titration monitored by pH, we have at any i'th point in the titration

where Kw is the water autoprotolysis constant.

If titrating an acid of initial volume and concentration with base of concentration, then at any i'th point in the titration with titrant volume ,

\frac{v_0 _0-v_i_0}{v_0+v_i} \begin{cases} \approx _i \text{ or } 10^{-pH_i} & \text{ when } v_{0^{ }} _0 > v_i_0 \text{ (acidic region)} \\ = 0 & \text{ when } v_{0^{ }} _0 = v_i_0 \text{ (equivalence point)} \\ \approx -_i \text{ or } -K_w 10^{pH_i} & \text{ when } v_{0^{ }} _0 < v_i_0 \text{ (alkaline region)} \end{cases}

At the equivalence point, the equivalence volume .

Thus,

  • a plot of will have a linear region before equivalence, with slope
  • and a plot of will have a linear region after equivalence, with slope
  • both plots will have as intercept

The equivalence volume is used to compute whichever of or is unknown.

The pH meter is usually calibrated with buffer solutions at known pH values before starting the titration. The ionic strength can be kept constant by judicious choice of acid and base. For instance, HCl titrated with NaOH of approximately the same concentration will replace H+ with an ion (Na+) of the same charge at the same concentration, to keep the ionic strength fairly constant. Otherwise, a relatively high concentration of background electrolyte can be used, or the activity quotient can be computed.

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