Question

when the following equation is balanced properly under acidic conditions, what are the coefficients of the species shown?
so₄²⁻ + mn²⁺ → h₂so₃ + mno₄⁻
water appears in the balanced equation as a (reactant, product, neither) with a coefficient of. (enter 0 for neither.)
which element is oxidized?

Explanation:

Step1: Assign oxidation numbers

• For \(SO_{4}^{2 - }\): S has an oxidation number of \(+6\) (since \(x+4\times(- 2)=-2\), \(x = +6\)). In \(H_{2}SO_{3}\), S has an oxidation number of \(+4\) (since \(2\times(+1)+x + 3\times(-2)=0\), \(x=+4\)).
• For \(Mn^{2+}\), Mn has an oxidation number of \(+2\). In \(MnO_{4}^{-}\), Mn has an oxidation number of \(+7\) (since \(x + 4\times(-2)=-1\), \(x = +7\)).

Step2: Write half - reactions

Reduction half - reaction (\(SO_{4}^{2-}\to H_{2}SO_{3}\)):

• \(SO_{4}^{2-}\to H_{2}SO_{3}\)
• Balance S (already balanced). Balance O by adding \(H_{2}O\): \(SO_{4}^{2-}\to H_{2}SO_{3}+H_{2}O\)
• Balance H by adding \(H^{+}\): \(SO_{4}^{2-}+4H^{+}\to H_{2}SO_{3}+H_{2}O\)
• Balance charge: \(SO_{4}^{2-}+4H^{+}+2e^{-}\to H_{2}SO_{3}+H_{2}O\)

Oxidation half - reaction (\(Mn^{2+}\to MnO_{4}^{-}\)):

• \(Mn^{2+}\to MnO_{4}^{-}\)
• Balance O by adding \(H_{2}O\): \(Mn^{2+}+4H_{2}O\to MnO_{4}^{-}\)
• Balance H by adding \(H^{+}\): \(Mn^{2+}+4H_{2}O\to MnO_{4}^{-}+8H^{+}\)
• Balance charge: \(Mn^{2+}+4H_{2}O\to MnO_{4}^{-}+8H^{+}+5e^{-}\)

Step3: Make electron transfer equal

Multiply the reduction half - reaction by \(5\) and the oxidation half - reaction by \(2\)

• Reduction: \(5SO_{4}^{2-}+20H^{+}+10e^{-}\to5H_{2}SO_{3}+5H_{2}O\)
• Oxidation: \(2Mn^{2+}+8H_{2}O\to2MnO_{4}^{-}+16H^{+}+10e^{-}\)

Step4: Add half - reactions

\(5SO_{4}^{2-}+20H^{+}+10e^{-}+2Mn^{2+}+8H_{2}O\to5H_{2}SO_{3}+5H_{2}O+2MnO_{4}^{-}+16H^{+}+10e^{-}\)
Cancel out \(H^{+}\) and \(H_{2}O\) and \(e^{-}\)
\(5SO_{4}^{2-}+4H^{+}+2Mn^{2+}+3H_{2}O\to5H_{2}SO_{3}+2MnO_{4}^{-}\)

Answer:

The coefficients of \(SO_{4}^{2-}\), \(Mn^{2+}\), \(H_{2}SO_{3}\), \(MnO_{4}^{-}\) are \(5\), \(2\), \(5\), \(2\) respectively.
Water appears as a reactant with a coefficient of \(3\).
The element that is oxidized is \(Mn\) (manganese).