The reaction
`5H_(2)O_(2)+XClO_(2)+2OH^(-) rarr XCl^(-)+YO_(2)+6H_(2)O`
is balanced if

Options

A. ` x=5, y=2`
B. ` x=2, y=5`
C. ` x=4, y=10`
D. ` x=5 , y=5`

Answer

B

Explanation

Consider the reduction half-reaction
`overset(+4)(ClO_(2))+5e^(-) rarr overset(-1)(Cl^(-))`
To balance the charge, we add `OH^(-)` ions
` ClO_2 + + 5e^(-) rarr Cl^(-) + 4OH^(-)`
Add `H_2O` molecules to balance H and O atoms :
(a) `ClO_2 +2H_2O +5e^(-) rarr Cl^(-) + 4OH^(-)`
Consider oxidation half-reaction:
`H_(2)overset(-1)(O_(2))rarr overset(0)O_(2)+2e^(-)`
Balance the charge by adding ` OH^(-)` ions :
`H_2O_2 +2OH^(-) rarr O_2+2e^(-)`
balance the H and O atoms by adding `H_(2)O` molecules:
(b) `H_(2)O_(2)+2OH^(-) rarr O_(2) +2H_(2)O+2e^(-)`
Now multiply Equation (a) by 2 and Equation (b) by 5. Finally add them:
`{:(2ClO_(2)+4H_(2)O+10 e^(-) rarr2Cl^(-)+8OH^(-)),(5H_(2)O_(2)+10OH^(-) rarr 5O_(2)+10H_(2)O+10e^(-)),(bar(5H_(2)O_(2)+2ClO_(2)+2OH^(-) rarr 2Cl^(-)+5O_(2)+6H_(2)O)):}`