Question

Nitrous acid $\left({\mathrm{HNO}}_2\right)$ disproportionates in acidic solution to nitrate ion $\left({\mathrm{NO}}_3^{-}\right)$ and nitrogen oxide (NO). Write a balanced equation for this reaction.

Short answer

The balanced equation is:

${\text{2HNO}}_{\text{3}}\left(\text{aq}\right)\to {\text{NO}}_{\text{3}}^{\text{-}}\left(\text{aq}\right)\text{+ NO}\left(\text{g}\right){\text{+ 2H}}^{\text{+}}\left(\text{aq}\right)$

Step-by-step solution

Disproportionation reaction

Disproportionation reactions are termed dismutation reactions.A simultaneous oxidation and reduction of a specific element takes place in the reaction.

Writing a balanced equation for the reaction

Nitrous acid disproportionate into nitrite ion and nitrogen monoxide in the acidic solution. The balanced equation can be found by writing the half reactions. One equation is for species being oxidized and the other one is for the reduced species. Nitrous acid is reduced to nitrogen monoxide and is oxidized to nitrite ion.

The half reaction for the reduction is shown below:

${\text{e}}^{\text{-}}{\text{+H}}^{\text{+}}\left(\text{aq}\right){\text{+ HNO}}_{\text{2}}\left(\text{aq}\right)\to \text{NO}\left(\text{g}\right){\text{+H}}_{\text{2}}\text{O}\left(\text{l}\right)$

The oxidation half reaction is shown below:

${\text{H}}_{\text{2}}\text{O}\left(\text{l}\right){\text{+ HNO}}_{\text{2}}\left(\text{aq}\right)\to {\text{NO}}_{\text{3}}^{\text{-}}\left(\text{aq}\right){\text{+ 3H}}^{\text{+}}\left(\text{aq}\right){\text{+e}}^{\text{-}}$

To find the overall equation, both the reactions are kept together.

$$\begin{gathered} {\text{e}}^{\text{-}}{\text{+H}}^{\text{+}}\left(\text{aq}\right){\text{+ HNO}}_{\text{2}}\left(\text{aq}\right)\to \text{NO}\left(\text{g}\right){\text{+H}}_{\text{2}}\text{O}\left(\text{l}\right) \\ {\text{H}}_{\text{2}}\text{O}\left(\text{l}\right){\text{+ HNO}}_{\text{2}}\left(\text{aq}\right)\to {\text{NO}}_{\text{3}}^{\text{-}}\left(\text{aq}\right){\text{+ 3H}}^{\text{+}}\left(\text{aq}\right){\text{+e}}^{\text{-}} \end{gathered}$$

Add all the species on the same side of the arrow and subtract like species on opposite sides of the equation. The combined equation can be given as:

${\text{2HNO}}_{\text{3}}\left(\text{aq}\right)\to {\text{NO}}_{\text{3}}^{\text{-}}\left(\text{aq}\right)\text{+ NO}\left(\text{g}\right){\text{+ 2H}}^{\text{+}}\left(\text{aq}\right)$

The balanced equation is:

${\text{2HNO}}_{\text{3}}\left(\text{aq}\right)\to {\text{NO}}_{\text{3}}^{\text{-}}\left(\text{aq}\right)\text{+ NO}\left(\text{g}\right){\text{+ 2H}}^{\text{+}}\left(\text{aq}\right)$