Question

If a very small amount of phenolphthalein is added to 0.15mol/ litre solution of sodium benzoate, what fraction of the indicator will exist in the colored form?
State any assumption you make.
${{K}_{a}}(benzoic\_acid)=6.2X{{10}^{-5}},{{K}_{w}}({{H}_{2}}O)=1X{{10}^{-14}},{{K}_{\ln }}(phenolphthalein)=3.16X{{10}^{-10}}$

Answer 1

Hint: Acid base indicators may be better understood and explained by using Bronsted-Lowry definitions. Any acid-base indicator is really two entities for which the same name as a Bronsted-Lowry conjugate acid-base pair. The explanation of the behavior of acid-base indicators depends on both the Bronsted-Lowry concept and the equilibrium concept.

Complete step by step solution:
Apply formula of pH of salt hydrolysis sodium benzoate,
\[pH=\dfrac{1}{2}[p{{K}_{w}}+p{{K}_{a}}+\log C]=\dfrac{1}{2}[14+\log 6.2+\log 0.15]=8.6918\]
A typical acid base indicator for acid-base titrations is phenolphthalein. HIn is a protonated indicator and its conjugate base as $I{{n}^{-}}$ . In aqueous solution, phenolphthalein will present the following equilibrium,
\[HIn+{{H}_{2}}O\rightleftharpoons I{{n}^{-}}+{{H}_{3}}{{O}^{+}}\]
According to Le-chatlier principle, the equilibrium expressed in the above equation will shift to the left. Clearly there must be some intermediate situation where half the phenolphthalein is in the acid form and half in the colored conjugated-base form. [HIn]=[ $I{{n}^{-}}$ ]
According to the Henderson-Hasselbalch equation, the pH of indicator,
\[\begin{align}
& pH=p{{K}_{In}}+\log \dfrac{[I{{n}^{-}}]}{[HIn]} \\
& 8.6918=-\log 3.16X{{10}^{-10}}+\log \dfrac{[I{{n}^{-}}]}{[HIn]} \\
& 0.16=\dfrac{[I{{n}^{-}}]}{[HIn]}--(1) \\
\end{align}\]
The equation (1) is the fraction of indicator in colored form.

Note: The Henderson-Hasselbalch equation relates to the pH of a solution containing a mixture of the two components to the acid dissociation constant, ${{K}_{a}}$ , and the concentrations of the species in solution. To derive the equation a number of simplify assumptions have to be made. This equation is useful for estimating the pH of a buffer solution and finding the equilibrium pH in an acid-base reaction.