Question

Balance the following in basic medium:

$As{O}_3^{3+}+{MnO}_4^{-}\to As{O}_4^{3-}+Mn{O}_2$

• A. $3As{O}_3^{3+}+2{MnO}_4^{-}+H_{2}O\to 3As{O}_4^{3-}+2Mn{O}_2+2O{H}^{-}$
• B. $3As{O}_3^{3+}+2{MnO}_4^{-}+4H_{2}O\to 3As{O}_4^{3-}+3Mn{O}_2+2O{H}^{-}$
• C. $3As{O}_3^{3+}+4{MnO}_4^{-}+3H_{2}O\to 3As{O}_4^{3-}+2Mn{O}_2+4O{H}^{-}$
• D. None of these

Answer 1

The correct option is A $3As{O}_3^{3+}+2{MnO}_4^{-}+H_{2}O\to 3As{O}_4^{3-}+2Mn{O}_2+2O{H}^{-}$

The unbalanced redox equation is as follows:
$As{O}_3^{3-}+{MnO}_4^{-}\to As{O}_4^{3-}+Mn{O}_2+H_{2}O$
All atoms other than H and O are balanced.
The oxidation number of As changes from +3 to +5. The change in the oxidation number of As is +2.
The oxidation number of Mn changes from +7 to +4. The change in the oxidation number of Mn is 3.
The increase in the oxidation number is balanced with decrease in the oxidation number by multiplying
$As{O}_3^{3-}$ and $As{O}_4^{3-}$ with 3 and multiplying ${MnO}_4^{-}$ and $Mn{O}_2$ with 2.
$3As{O}_3^{3-}+2{MnO}_4^{-}\to 3As{O}_4^{3-}+2Mn{O}_2+H_{2}O$
O atoms are balanced.
$3As{O}_3^{3-}+2{MnO}_4^{-}\to 3As{O}_4^{3-}+2Mn{O}_2+H_{2}O$
Hydrogen atoms are balanced by adding 2 $H^{+}$ atoms on the LHS.
$3As{O}_3^{3-}+2{MnO}_4^{-}+2H^{+}\to 3As{O}_4^{3-}+2Mn{O}_2+H_{2}O$
Since the reaction occurs in basic medium, add 2 hydroxide ions on both sides of the equation.
$3As{O}_3^{3-}+2{MnO}_4^{-}+2H^{+}+2O{H}^{-}\to 3As{O}_4^{3-}+2Mn{O}_2+H_{2}O+2O{H}^{-}$
On LHS, 2 $H^{+}$ ions combine with 2 $O{H}^{-}$ ions to form 2 water molecules out of which, one water molecule cancels with one water molecule on RHS..
$3As{O}_3^{3-}+2{MnO}_4^{-}+H_{2}O\to 3As{O}_4^{3-}+2Mn{O}_2+2O{H}^{-}$
This is the balanced chemical equation.