What is the balanced molecular, ionic, and net ionic equation for: Solutions of acetic acid and sodium nitrite are mixed.?

The reaction between two solutions of acetic acid (#CH_3COOH# and sodium nitrite (#NaNO_2#) could be written in three different ways:

The Molecular equation:
#CH_3COOH(aq)+NaNO_2(aq)->CH_3COONa(aq)+HNO_2(aq)#

The ionic equation:
#CH_3COO^(-)(aq)+H^(+)(aq)+Na^(+)(aq)+NO_2^(-)(aq)->CH_3COO^(-)(aq)+H^(+)(aq)+Na^(+)(aq)+NO_2^(-)(aq)#

The net ionic equation:
#CH_3COO^(-)(aq)+H^(+)(aq)+Na^(+)(aq)+NO_2^(-)(aq)->CH_3COO^(-)(aq)+H^(+)(aq)+Na^(+)(aq)+NO_2^(-)(aq)#

In this case, since all ions are in solution, and remain in solution after mixing, the net ionic equation will be the same as the ionic equation.

Moreover, in a more complex way to explain this, since acetic acid is a weaker acid than nitrous acid, the reaction will favour the side where acetic acid is; which is the left side.

Note that reactions between an acid and a base favour the formation of the weaker acid.

An example where ionic equation would be different than the net ionic equation is the following.
If we mix a solution of silver nitrate (#AgNO_3#) and a solution of sodium chloride (#NaCl#):

The ionic equation:
#Ag^(+)(aq)+NO_3^(-)(aq)+Na^(+)(aq)+Cl^(-)(aq)->AgCl(s)+Na^(+)(aq)+NO_3^(-)(aq)#

The net ionic equation:
#Ag^(+)(aq)+Cl^(-)(aq)->AgCl(s)#

Here the two equations are different because #AgCl# precipitates out of the aqueous solution.

I hope you find this helpful.