Chapter 11, Problem 11.65P

Interpretation Introduction

Interpretation:

The given equation for the titration of potassium hydrogen phthalate $\left({\text{K}}^{\text{+}}{\text{HP}}^{\text{-}}\right)$ with $\text{NaOH}$ has to be derived.

$\varphi \text{=}\frac{{\text{C}}_{\text{b}}{\text{V}}_{\text{b}}}{{\text{C}}_{\text{a}}{\text{V}}_{\text{a}}}\text{=}\frac{{\text{α}}_{{\text{HP}}^{\text{-}}}{\text{+2α}}_{{\text{P}}^{\text{2-}}}\text{-1-}\frac{\left[{\text{H}}^{\text{+}}\right]\text{-}\left[{\text{OH}}^{\text{-}}\right]}{{\text{C}}_{\text{a}}}}{\text{1+}\frac{\left[{\text{H}}^{\text{+}}\right]\text{-}\left[{\text{OH}}^{\text{-}}\right]}{{\text{C}}_{\text{b}}}}$

Concept Introduction:

Titration of weak acid with strong base:

When a strong base is titrated against weak base it involves the direct transfer of protons from the weak acid to the hydroxide ion.

Spreadsheet Equation for titration of titration of weak acid with strong base:

$\varphi \text{=}\frac{{\text{C}}_{\text{b}}{\text{V}}_{\text{b}}}{{\text{C}}_{\text{a}}{\text{V}}_{\text{a}}}\text{=}\frac{{\text{α}}_{{\text{HP}}^{\text{-}}}{\text{+2α}}_{{\text{P}}^{\text{2-}}}\text{-1-}\frac{\left[{\text{H}}^{\text{+}}\right]\text{-}\left[{\text{OH}}^{\text{-}}\right]}{{\text{C}}_{\text{a}}}}{\text{1+}\frac{\left[{\text{H}}^{\text{+}}\right]\text{-}\left[{\text{OH}}^{\text{-}}\right]}{{\text{C}}_{\text{b}}}}$

Where,

${\text{C}}_{\text{a}}$=initial concentration

${\text{C}}_b$=final concentration

${\text{V}}_{\text{a}}$=volume of the acid

${\text{V}}_{\text{b}}$= volume of the base

${\text{α}}_{{\text{HP}}^{\text{-}}}$=acid dissociation constant.

$\varphi$ =fraction way to equivalence point.