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Nernst Equation

Calculate the...

Question

Calculate the $p H$ (nearest integer) of a solution containing $1.8 g$ $N a H {S O}_{4}$ per $100 m L$ . $K_{a}$ for $H {S O}_{4}^{-} ⇌ H^{+} + {S O}_{4}^{-}$ is $1.26 \times 10^{- 2}$ .

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Solution

The molar mass of sodium bisulphate is 120 g/mol.
The molarity of sodium bisulphate is $\frac{1.8}{120 \times 0.1} = 0.15 M$ .

$H S O_{4}^{-}$
$H^{+}$
$S O_{4}^{2 -}$
Initial molarity (M)
0.15
0
0
Equilibrium molarity (M)
0.15-x
x
x
The expression for the acid dissociation constant $K_{a}$ is $K_{a} = \frac{[H^{+}] [S O_{4}^{2 -}]}{[H S O_{4}^{-}]}$
Substitute values in the above equation.
$\frac{x \times x}{0.15 - x} = 1.26 \times 10^{- 2}$
$x = [H^{+}] = 0.0436$
$p H = - l o g [H^{+}] = - l o g 0.0436 = 1.36$ .

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