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Reduction half reaction-

\(Cl_2 \rightarrow Cl^-\)

Balancing chlorine atom-

\(Cl_2 \rightarrow 2Cl^-\)

Balancing charges-

\(Cl_2 + 2e^-\rightarrow 2Cl^-\)   ....(i)

Oxidation half reaction-

\(Cl_2 \rightarrow Cl{O_3}^-\)

Balancing Cl atom-

\(Cl_2 \rightarrow 2Cl{O_3}^-\)

Balancing O atom-

\(Cl_2 + 6OH^- \rightarrow 2Cl{O_3}^-\) 

Balancing H atom-

\(Cl_2 + 12OH^- \rightarrow 2Cl{O_3}^- + 6H_2O\)

Balancing charges-

\(Cl_2 + 12OH^- \rightarrow 2Cl{O_3}^- + 6H_2O+ 10e^-\)   ....(ii)

Adding equation (i) after multiply by 5, to option (ii)-

\(\begin {array}{l}{5 Cl_2 + 10e^- \rightarrow 10Cl^-}\\{Cl_2 + 12OH^- \rightarrow 2Cl{O_3}^- + 6H_2O + 10e^-}\\\hline 6Cl_2 + 12OH^- \rightarrow 10Cl^- + 2Cl{O_3}^- + 6H_2O\end{array}\)

or

\(3Cl_2 + 6OH^- \rightarrow 5Cl^- + Cl{O_3}^- + 3H_2O\)   ...(iii)

Hence equation (iii) is a balance chemical equation.

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