Question

Balance the following equation using half-reaction method in the acidic medium: $MnO_{4}^{-}+H_{2}C_{2}O_{4} \longrightarrow Mn^{2+}+CO_{2}$

Answer 1

Equation skeleton:

$Mn{ O }_{ 4 }^{ - }\quad +\quad { H }_{ 2 }{ C }_{ 2 }{ O }_{ 4 }\quad \rightarrow \quad { Mn }^{ 2+ }\quad +\quad { CO }_{ 2 }$

Assigning oxidation number:

${ Mn }^{ +7 }{ { O }^{ -2 } }_{ 4 }^{ - }\quad +\quad { H }_{ 2 }^{ +1 }{ C }_{ 2 }^{ +3 }{ O }_{ 4 }^{ -2 }\quad \rightarrow \quad { Mn }^{ +22+ }\quad +\quad { C }^{ +4 }{ O }_{ 2 }^{ -2 }$

Identify Redox couples:

$O:  { H }_{ 2 }^{ +1 }{ C }_{ 2 }^{ +3 }{ O }_{ 4 }^{ -2 }\quad \rightarrow \quad { C }^{ +4 }{ O }_{ 2 }^{ -2 }$

$R: { Mn }^{ +7 }{ O }_{ 4 }^{ -2 }\quad \rightarrow \quad { Mn }^{ +22+ }$

Combine into two half reactions

$O: { H }_{ 2 }^{ +1 }{ C }_{ 2 }^{ +3 }{ O }_{ 4 }^{ -2 }\quad \rightarrow \quad { C }^{ +4 }{ O }_{ 2 }^{ -2 }$

$R: { Mn }^{ +7 }{ O }_{ 4 }^{ -2 }\quad \rightarrow \quad { Mn }^{ +22+ }$

Balance all atoms

$O: { H }_{ 2 }{ C }_{ 2 }{ O }_{ 4 }\quad \rightarrow \quad 2{ CO }_{ 2 }$

$R: Mn{ O }_{ 4 }^{ - }\quad \rightarrow \quad { Mn }^{ 2+ }$

Balance oxygen atoms

$O: { H }_{ 2 }{ C }_{ 2 }{ O }_{ 4 }\quad \rightarrow \quad 2{ CO }_{ 2 }$

$R: Mn{ O }_{ 4 }^{ - }\quad \rightarrow \quad { Mn }^{ 2+ }\quad +\quad 4{ H }_{ 2 }O$

Balance hydrogen atoms

$O: { H }_{ 2 }{ C }_{ 2 }{ O }_{ 4 }\quad \rightarrow \quad 2{ CO }_{ 2 } +\quad { 2H }^{ + }$

$R: Mn{ O }_{ 4 }^{ - }\quad +\quad 8{ H }^{ + }\quad \rightarrow \quad { Mn }^{ 2+ }\quad +\quad 4{ H }_{ 2 }O$

Balance charge, electron gain, and electron lost

$O: { H }_{ 2 }{ C }_{ 2 }{ O }_{ 4 }\quad \rightarrow \quad 2{ CO }_{ 2 } +\quad { 2H }^{ + }\quad +\quad 2{ e }^{ - }$

$R: Mn{ O }_{ 4 }^{ - }\quad +\quad 8{ H }^{ + }\quad+\quad 5{ e }^{ - }\quad \rightarrow \quad { Mn }^{ 2+ }\quad +\quad 4{ H }_{ 2 }O$

$O: 5{ H }_{ 2 }{ C }_{ 2 }{ O }_{ 4 }\quad \rightarrow \quad10{ CO }_{ 2 }\quad +\quad 10{ H }^{ + }\quad +\quad 10{ e }^{ - }$

$R: 2Mn{ O }_{ 4 }^{ - }\quad +\quad 16{ H }^{ + }\quad+\quad 10{ e }^{ - }\quad \rightarrow \quad 2{ Mn }^{ 2+ }\quad +\quad 8{ H }_{ 2 }O$

Overall equation

$5{ H }_{ 2 }{ C }_{ 2 }{ O }_{ 4 }\quad+\quad 2Mn{ O }_{ 4 }^{ - }\quad +\quad 16{ H }^{ + }\quad+\quad 10{ e }^{ - }\quad \rightarrow \quad10{ CO }_{ 2 }\quad+\quad 2{ Mn }^{ 2+ }\quad+\quad 10{ H }^{ + }\quad+\quad 8{ H }_{ 2 }O+\quad 10{ e }^{ - }$

Simplified equation

$5{ H }_{ 2 }{ C }_{ 2 }{ O }_{ 4 }\quad+\quad 2Mn{ O }_{ 4 }^{ - }\quad +\quad 6{ H }^{ + }\quad \rightarrow \quad10{ CO }_{ 2 }\quad+\quad 2{ Mn }^{ 2+ }\quad+\quad 8{ H }_{ 2 }O$