$$Cr(OH)_3+ClO^-+OH^- \rightarrow CrO_4^{2-}+Cl^-+H_2O$$
in a balanced chemical reaction number of all atoms at right side should be equal to the left side of the reaction.
Balancing a chemical reaction as:
Step 1: Assign oxidation numbers to each of the atoms in the equation and write the numbers above the atom as:
$$\overset {+3}{Cr}(OH)_3+ \overset {+1}{Cl}O^-+OH^- \rightarrow \overset {+6}{Cr}O_4^{2-} + \overset {-1}{Cl^-}+H_2O$$
Step 2: Identify the atoms that are oxidized and those that are reduced as:
Reduction: $$\overset {+1}{Cl}O^- \rightarrow \overset {-1}{Cl^-}$$
Oxidation: $$\overset {+3}{Cr}(OH)_3 \rightarrow \overset {+6}{Cr}O_4^{2-}$$
Step 3: oxidation-number change is:
Reduction: $$\overset {+1}{Cl}O^- \rightarrow \overset {-1}{Cl^-}$$: Gain of 2 electron
Oxidation: $$\overset {+3}{Cr}(OH)_3 \rightarrow \overset {+6}{Cr}O_4^{2-}$$: Loss of total 3 electrons
Step 4: Balance the total change in oxidation number as:
Reduction: $$\overset {+1}{Cl}O^- \rightarrow \overset {-1}{Cl^-} \times 3$$: Gain of 6 electron
Oxidation: $$\overset {+3}{Cr}(OH)_3 \rightarrow \overset {+6}{Cr}O_4^{2-} \times 2$$: Loss of total 6 electrons
OR
Reduction: $$3\overset {+1}{Cl}O^- \rightarrow 3\overset {-1}{Cl^-}$$
Oxidation: $$2\overset {+3}{Cr}(OH)_3 \rightarrow 2\overset {+6}{Cr}O_4^{2-}$$
Step 5: Balance O atoms in reduction reaction by adding $$H_2O$$ and then balance H by $$H^+$$ as:
Reduction: $$3\overset {+1}{Cl}O^- +6H^+ \rightarrow 3\overset {-1}{Cl^-}+3H_2O$$
Oxidation: $$2\overset {+3}{Cr}(OH)_3+2H_2O\rightarrow 2\overset {+6}{Cr}O_4^{2-}+4H^+$$
Step 6: For base catalysed reaction add $$OH^-$$ to both side to neutralize $$H^+$$ as:
Reduction: $$3\overset {+1}{Cl}O^- +6H^++6OH^- \rightarrow 3\overset {-1}{Cl^-}+3H_2O+6OH^-$$
Oxidation: $$2\overset {+3}{Cr}(OH)_3+2H_2O +4OH^-\rightarrow 2\overset {+6}{Cr}O_4^{2-}+4H^+ +4OH^-$$
OR
Reduction: $$3\overset {+1}{Cl}O^- +3H_2O \rightarrow 3\overset {-1}{Cl^-}+6OH^-$$
Oxidation: $$2\overset {+3}{Cr}(OH)_3 +4OH^-\rightarrow 2\overset {+6}{Cr}O_4^{2-}+2H_2O$$
Thus overall reaction is:
$$3\overset {+1}{Cl}O^- +3H_2O + 2\overset {+3}{Cr}(OH)_3 +4OH^- \rightarrow 3\overset {-1}{Cl^-}+6OH^- +2\overset {+6}{Cr}O_4^{2-}+2H_2O$$
OR
$$3ClO^- +H_2O + 2Cr(OH)_3 \rightarrow 3Cl^-+2OH^- +2CrO_4^{2-}$$
thus the values of coefficients of balanced reaction are:
$$Cr(OH)_3−(2),ClO^−−(3),CrO_4^{2−}-(2),Cl^−−(3)$$