Chapter 19, Problem 19.1P

Balance the following net ionic equation by the half-reaction method. The reaction takes place in acidic solution.
${\text{NO}}_{\text{3}}{}^{-}(aq)+Cu(s)\to NO(g)+C{u}^{2+}(aq)$ Unbalanced

Interpretation Introduction

Interpretation:

The given net ionic equation for the reaction which takes place in the acidic medium is to be balanced using the half reaction method.

Concept introduction:

The half-reaction method is also known as the ion-electron method makes use of the redox chemical equation. The redox equation is separated into two half equations where one shows the reduction reaction and the other shows the oxidation reaction.

Answer to Problem 19.1P

$\stackrel{}{\text{3Cu}}\text{(s)+}\stackrel{}{{\text{2NO}}_{\text{3}}^{\text{-}}}{\text{(aq)+8H}}^{\text{+}}\text{(aq)}\underset{}{\to }3{\text{Cu}}^{2+}\text{(aq)+}2\stackrel{}{\text{NO}}{\text{(g)+4H}}_{\text{2}}\text{O(l)}$

Explanation of Solution

The unbalanced chemical equation or the skeletal equation for the given reaction is written as follows:

${\text{NO}}_{\text{3}}^{\text{-}}\text{(aq)+Cu(s)}\underset{}{\to }{\text{NO(g)+Cu}}^{\text{2+}}\text{(aq)}$

The half-reactions are separated from the given redox chemical equation as follows:

$\stackrel{+5\text{ -2}}{{\text{NO}}_{\text{3}}^{\text{-}}}\text{(aq)+}\stackrel{0}{\text{Cu}}\text{(s)}\underset{}{\to }\stackrel{+2\text{ -2}}{\text{NO}}\text{(g)+}{\stackrel{+2}{\text{Cu}}}^{2+}\text{(aq)}$

The redox couples are as follows:

$\begin{array}{l}\stackrel{0}{\text{Cu}}\text{(s)}\underset{}{\to }{\stackrel{+2}{\text{Cu}}}^{\text{2+}}\text{(aq)}\\ \stackrel{+5\text{ -2}}{{\text{NO}}_{\text{3}}^{\text{-}}}\text{(aq)}\underset{}{\to }\stackrel{+2\text{ -2}}{\text{NO}}\text{(g)}\end{array}$

All the atoms in the half-reaction equations are balanced except hydrogen and oxygen.

$\begin{array}{l}\stackrel{0}{\text{Cu}}\text{(s)}\underset{}{\to }{\stackrel{+2}{\text{Cu}}}^{\text{2+}}\text{(aq)}\\ \stackrel{+5\text{ -2}}{{\text{NO}}_{\text{3}}^{\text{-}}}\text{(aq)}\underset{}{\to }\stackrel{+2\text{ -2}}{\text{NO}}\text{(g)}\end{array}$

The number of oxygen atoms is balanced by adding H₂Omolecules on the side of the equation which lacks in the number of oxygen atoms.

$\begin{array}{l}\stackrel{}{\text{Cu}}\text{(s)}\underset{}{\to }{\stackrel{}{\text{Cu}}}^{2+}\text{(aq)}\\ \stackrel{}{{\text{NO}}_{\text{3}}^{\text{-}}}\text{(aq)}\underset{}{\to }\stackrel{}{\text{NO}}{\text{(g)+2H}}_{\text{2}}\text{O(l)}\end{array}$

The number of hydrogens atoms is made equal by adding protons on adding the protons on either side of the equation as follows:

$\begin{array}{l}\stackrel{}{\text{Cu}}\text{(s)}\underset{}{\to }{\stackrel{}{\text{Cu}}}^{\text{2+}}\text{(aq)}\\ \stackrel{}{{\text{NO}}_{\text{3}}^{\text{-}}}{\text{(aq)+4H}}^{\text{+}}\text{(aq)}\underset{}{\to }\stackrel{}{\text{NO}}{\text{(g)+2H}}_{\text{2}}\text{O(l)}\end{array}$

The charge is balanced by adding electrons on the more positive side of the equation as follows:

$\begin{array}{l}\stackrel{}{\text{Cu}}\text{(s)}\underset{}{\to }{\stackrel{}{\text{Cu}}}^{\text{2+}}{\text{(aq)+2e}}^{-}\\ \stackrel{}{{\text{NO}}_{\text{3}}^{\text{-}}}{\text{(aq)+4H}}^{\text{+}}{\text{(aq)+3e}}^{-}\underset{}{\to }\stackrel{}{\text{NO}}{\text{(g)+2H}}_{\text{2}}\text{O(l)}\end{array}$

The number of electrons can be balanced as follows:

$\begin{array}{l}\stackrel{}{\text{3Cu}}\text{(s)}\underset{}{\to }3{\stackrel{}{\text{Cu}}}^{\text{2+}}{\text{(aq)+6e}}^{-}\\ \stackrel{}{{\text{2NO}}_{\text{3}}^{\text{-}}}{\text{(aq)+8H}}^{\text{+}}{\text{(aq)+6e}}^{-}\underset{}{\to }2\stackrel{}{\text{NO}}{\text{(g)+4H}}_{\text{2}}\text{O(l)}\end{array}$

The half-reaction equations are added as follows:

$\stackrel{}{\text{3Cu}}\text{(s)+}\stackrel{}{{\text{2NO}}_{\text{3}}^{\text{-}}}{\text{(aq)+8H}}^{\text{+}}{\text{(aq)+6e}}^{-}\underset{}{\to }3{\stackrel{}{\text{Cu}}}^{\text{2+}}{\text{(aq)+6e}}^{-}+2\stackrel{}{\text{NO}}{\text{(g)+4H}}_{\text{2}}\text{O(l)}$

The simplified equation is as follows:

$\stackrel{}{\text{3Cu}}\text{(s)+}\stackrel{}{{\text{2NO}}_{\text{3}}^{\text{-}}}{\text{(aq)+8H}}^{\text{+}}\text{(aq)}\underset{}{\to }3{\stackrel{}{\text{Cu}}}^{\text{2+}}\text{(aq)+}2\stackrel{}{\text{NO}}{\text{(g)+4H}}_{\text{2}}\text{O(l)}$

Conclusion

The net ionic equation can be defined as a type of chemical equation that describes only those elements, compounds and ions which get directly involved in the given chemical reaction.