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The reaction
$5 H_{2} O_{2} + {XClO}_{2} + 2 {OH}^{-} \to {XCl}^{-} + {YO}_{2} + 6 H_{2} O$
is balanced if

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X = 5, Y = 2

X = 2, Y = 5

X = 4, Y = 10

X = 5, Y = 5

answer is B.

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Detailed Solution

$H_{2} {\overset{- 1}{O}}_{2} + \overset{+ 4}{Cl} O_{2} + {OH}^{-} \to {Cl}^{-} + {\overset{0}{O}}_{2} + H_{2} O$

Change in oxidation state of ‘Cl’ = 5

Change in oxidation state of ‘O’ = 2(1) =2

By cross multiplying the changes ,

$5 H_{2} O_{2} + 2 {ClO}_{2} + {OH}^{-} \to 2 {Cl}^{-} + O_{2} + H_{2} O 5 H_{2} O_{2} + 2 {ClO}_{2} + 2 {OH}^{-} \to 2 {Cl}^{-} + 5 O_{2} + 6 H_{2} O$

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