Question
How does $\mathrm{H}_2 \mathrm{O}_2$ behave as a bleaching agent?

Answer

$\mathrm{H}_2 \mathrm{O}_2$ acts as bleaching agent due to the release of nascent oxygen.
$\mathrm{H}_2 \mathrm{O}_2 \rightarrow \mathrm{H}_2 \mathrm{O}+[\mathrm{O}]$
Thus, the bleaching action of hydrogen peroxide is permanent and is due to oxidation. It oxidises the colouring matter to a colourless product.
$\text{Colouring matter}+[\text{O}]\xrightarrow{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\text{Colourless matter}\\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \text{(Bleached)}$

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