Molar concentration of $H^{+}$ in 0.01M $H_{2} O_{2}$ aqueous solution in the correct scientific notation is $P \times 10^{- Q} M$ . Sum of P and Q is (Given: $H_{2} O_{2} K a_{1} = 3 \times 10^{- 12}, K a_{2} ≃ 0$ )

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Detailed Solution

$H_{2} O_{2} + H_{2} O$
It can be considered as mixture of two weak acids
$[H^{+}] = \sqrt{K a_{1} C_{1} + K a_{2} C_{2}} = \sqrt{{(K a_{1})}_{H_{2} O_{2}} . C_{H_{2} O_{2}} + K a_{H_{2} O} . C_{H_{2} O}}$

$= \sqrt{3 \times 10^{- 12} \times 10^{- 2} + {(K w)}_{H_{2} O}} = \sqrt{3 \times 10^{- 14} + 10^{- 14}} = 2 \times 10^{- 7} M$

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