Question

Balance the following equation using oxidation number method: $HNO_{3}(aq)+Cu_{2}O(s) \longrightarrow Cu(NO_{3})_{2}(aq)+NO(g)+H_{2}O(l)+2OH^{-}$

Answer 1

Write equation skeleton

${ HNO }_{ 3 }\quad +\quad { Cu }_{ 2 }O\quad \rightarrow \quad Cu{ \left( { NO }_{ 3 } \right) }_{ 2 }\quad +\quad NO\quad +\quad { H }_{ 2 }O$

Assign oxidation numbers

${ H }^{ +1 }{ N }^{ +5 }{ O }_{ 3 }^{ -2 }\quad +\quad { Cu }_{ 2 }^{ +1 }{ O }^{ -2 }\quad \rightarrow \quad { Cu }^{ +2 }{ \left( { N }^{ +5 }{ O }_{ 3 }^{ -2 } \right) }_{ 2 }\quad +\quad { N }^{ +2 }{ O }^{ -2 }\quad +\quad { H }_{ 2 }^{ +1 }{ O }^{ -2 }$

Identify the redox couples

$O:\quad { Cu }_{ 2 }^{ +1 }{ O }^{ -2 }\quad \rightarrow \quad { Cu }^{ +2 }{ \left( { N }^{ +5 }{ O }_{ 3 }^{ -2 } \right) }_{ 2 }\quad +\quad 2{ e }^{ - }$

$R:\quad { H }^{ +1 }{ N }^{ +5 }{ O }_{ 3 }^{ -2 }\quad +\quad 3{ e }^{ - }\quad \rightarrow \quad { N }^{ +2 }{ O }^{ -2 }$

Combine the redox couples

$O:\quad { Cu }_{ 2 }^{ +1 }{ O }^{ -2 }\quad \rightarrow \quad { Cu }^{ +2 }{ \left( { N }^{ +5 }{ O }_{ 3 }^{ -2 } \right) }_{ 2 }\quad +\quad 2{ e }^{ - }$

$R:\quad { H }^{ +1 }{ N }^{ +5 }{ O }_{ 3 }^{ -2 }\quad +\quad 3{ e }^{ - }\quad \rightarrow \quad { N }^{ +2 }{ O }^{ -2 }$

Balance all atoms except oxygen and hydrogen

$O:\quad { Cu }_{ 2 }^{ +1 }{ O }^{ -2 }\quad 4HN{ O }_{ 3 }\quad \rightarrow \quad { Cu }^{ +2 }{ \left( { N }^{ +5 }{ O }_{ 3 }^{ -2 } \right) }_{ 2 }\quad +\quad 2{ e }^{ - }$

$R:\quad { H }^{ +1 }{ N }^{ +5 }{ O }_{ 3 }^{ -2 }\quad +\quad 3{ e }^{ - }\quad \rightarrow \quad { N }^{ +2 }{ O }^{ -2 }$

Balance the charge

$O:\quad { Cu }_{ 2 }^{ +1 }{ O }^{ -2 }\quad 4HN{ O }_{ 3 }\quad \rightarrow \quad { Cu }^{ +2 }{ \left( { N }^{ +5 }{ O }_{ 3 }^{ -2 } \right) }_{ 2 }\quad +\quad 2{ e }^{ - }\quad +\quad 2{ H }^{ + }$

$R:\quad { H }^{ +1 }{ N }^{ +5 }{ O }_{ 3 }^{ -2 }\quad +\quad 3{ e }^{ - }\quad +\quad 3{ H }^{ + }\quad \rightarrow \quad { N }^{ +2 }{ O }^{ -2 }$

Balance the oxygen atoms

$O:\quad { Cu }_{ 2 }^{ +1 }{ O }^{ -2 }\quad 4HN{ O }_{ 3 }\quad \rightarrow \quad { Cu }^{ +2 }{ \left( { N }^{ +5 }{ O }_{ 3 }^{ -2 } \right) }_{ 2 }\quad +\quad 2{ e }^{ - }\quad +\quad 2{ H }^{ + }\quad +\quad { H }_{ 2 }O$

$R:\quad { H }^{ +1 }{ N }^{ +5 }{ O }_{ 3 }^{ -2 }\quad +\quad 3{ e }^{ - }\quad +\quad 3{ H }^{ + }\quad \rightarrow \quad { N }^{ +2 }{ O }^{ -2 }\quad +\quad 2{ H }_{ 2 }O$

Making electron gain equivalent to electron lost

$O:\quad { Cu }_{ 2 }^{ +1 }{ O }^{ -2 }\quad 4HN{ O }_{ 3 }\quad \rightarrow \quad 2{ Cu }^{ +2 }{ \left( { N }^{ +5 }{ O }_{ 3 }^{ -2 } \right) }_{ 2 }\quad +\quad 2{ e }^{ - }\quad +\quad 2{ H }^{ + }\quad +\quad { H }_{ 2 }O$

$R:\quad { H }^{ +1 }{ N }^{ +5 }{ O }_{ 3 }^{ -2 }\quad +\quad 3{ e }^{ - }\quad +\quad 3{ H }^{ + }\quad \rightarrow \quad { N }^{ +2 }{ O }^{ -2 }\quad +\quad 2{ H }_{ 2 }O$

$O:\quad 3{ Cu }_{ 2 }^{ +1 }{ O }^{ -2 }\quad 12HN{ O }_{ 3 }\quad \rightarrow \quad 6{ Cu }^{ +2 }{ \left( { N }^{ +5 }{ O }_{ 3 }^{ -2 } \right) }_{ 2 }\quad +\quad 6{ e }^{ - }\quad +\quad 6{ H }^{ + }\quad +\quad 3{ H }_{ 2 }O$

$R:\quad 2{ H }^{ +1 }{ N }^{ +5 }{ O }_{ 3 }^{ -2 }\quad +\quad 6{ e }^{ - }\quad +\quad 6{ H }^{ + }\quad \rightarrow \quad 2{ N }^{ +2 }{ O }^{ -2 }\quad +\quad 4{ H }_{ 2 }O$

Add the half-cell reactions

$3{ Cu }_{ 2 }^{ +1 }{ O }^{ -2 }\quad +\quad 2{ H }^{ +1 }{ N }^{ +5 }{ O }_{ 3 }^{ -2 }\quad +\quad 6{ e }^{ - }\quad +\quad 6{ H }^{ + }\quad 12HN{ O }_{ 3 }\quad \rightarrow \quad 6{ Cu }^{ +2 }{ \left( { N }^{ +5 }{ O }_{ 3 }^{ -2 } \right) }_{ 2 }\quad +\quad 2{ N }^{ +2 }{ O }^{ -2 }\quad +\quad 6{ e }^{ - }\quad +\quad 6{ H }^{ + }\quad +\quad 7{ H }_{ 2 }O$

Simplify the equation

$3{ Cu }_{ 2 }^{ +1 }{ O }^{ -2 }\quad +\quad 14{ H }^{ +1 }{ N }^{ +5 }{ O }_{ 3 }^{ -2 }\quad \rightarrow \quad 6{ Cu }^{ +2 }{ \left( { N }^{ +5 }{ O }_{ 3 }^{ -2 } \right) }_{ 2 }\quad +\quad 2{ N }^{ +2 }{ O }^{ -2 }\quad +\quad 7{ H }_{ 2 }O$

Final reaction is as follows,

$14HN{ O }_{ 3 }\quad +\quad 3{ Cu }_{ 2 }O\quad \rightarrow \quad 6Cu{ \left( { NO }_{ 3 } \right) }_{ 2 }\quad +\quad 2NO\quad +\quad 7{ H }_{ 2 }O$