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Equilibrium Constant from Nernst Equation

In the acid-b...

Question

In the acid-base titration
$[H_{3} P O_{4} (0.1 M) + N a O H (0.1 M)]$ , the e.m.f of the solution is measured by coupling this electrode with a suitable reference electrode. When an alkali is added, the pH of the solution is in accordance with the equation:
$E_{cell} = E_{cell}^{\circ} + 0.059 pH$
For $H_{3} P O_{4} : K a_{1} = 10^{- 3}, K a_{2} = 10^{- 8}, K a_{3} = 10^{- 13}$
What is the e.m.f of the cell at the ${II}^{nd}$ end point of the titration if $E_{cell}^{\circ}$ at this stage is $1.3805 V$

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Solution

$p H$ for $N a_{2} H A$ = $\frac{1}{2} (p K a_{2} + p K a 3)$
= $\frac{1}{2} (8 + 13)$
= $\frac{21}{2}$
= 11.5
$E = E^{o} + 0.059 p H$
$E = 1.3805 + 0.059 \times 11.5$
$E = 2$

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