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Why is the bleaching action of Chlorine permanent while that of sulphur dioxide is temporary?

Answer
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Hint :Bleaching is the process of eliminating natural and/or acquired colouring components from raw textile material in order to decolorize it. It gives the textile material a base whiteness that may be further whitened using optical brighteners or coloured/printed according to the intended end use.

Complete Step By Step Answer:
Chlorine's bleaching activity is permanent since it includes the oxidation process. Chlorine produces nascent oxygen when it combines with water. This oxygen reacts with the pigments in the substance, rendering it colourless. It has a strong oxidising effect. As a result, Chlorine's bleaching activity is irreversible. This is the reaction at hand.
Cl2 + H2O  HCl + HClO
Hypochlorous acid is a very unstable substance that readily dissociates into nascent oxygen.
HClO  HCl + [O]
The oxidising agent nascent oxygen is more potent. The bleaching characteristic of chlorine in the presence of moisture is due to its formation.
To summarise, Chlorine's bleaching activity is permanent since it includes the oxidation process. Chlorine produces nascent oxygen when it combines with water. This oxygen reacts with the pigments in the substance, rendering it colourless. It has a strong oxidising effect.
Because it includes a reduction process, sulphur di oxide's bleaching activity is very transient. Sulphur dioxide depletes the oxygen in the coloured material, rendering it colourless. Atmospheric oxygen gradually replaces the lost oxygen, allowing the substance to restore its colour. This is the reaction at hand.
SO2+2H2OH2SO4+2[H](nascent)
Colour material + [H]⟶Colourless Colour (in presence of air)
Chlorine bleaches a substance permanently owing to oxidation, whereas sulphur dioxide bleaches a substance briefly owing to reduction.

Note :
Bleaching is the next step in the decolorization of greige material to make it acceptable for further processing. Textile bleaching is divided into two types: oxidative bleaching and reductive bleaching. Sodium hypochlorite, sodium chlorite, or sulfuric acid are commonly used in oxidative bleachings. Cotton, ramie, jute, wool, and bamboo are all often bleached using oxidative techniques. Sodium hydrosulphite, a potent reducing agent, is used in reductive bleaching. Reductive bleaching technique may be used to bleach polyamides, polyacrylics, and poly acetates.