From observing the reaction ,
[tex]NO_2^{-}--->NO_3^{-}[/tex]
we see that the equation is balanced as far as charge is concerned in its present form. The problem with this equation is that there is oxygen is not balanced.
The first step step in balancing the equation for oxygen is realizing that if we add water to the left hand side it will balance the equation for oxygen. This step is shown below,[tex]H_2O+NO_2^- ----->NO_3^-+2H^+.[/tex]
The equation above is balanced for all elements involved. It is worth noting that the equation above violates conservation of charge. There is an overall charge of negative 1 on the left hand side, and a charge of positive 1 on the right hand side. To balance the charge,w e have to add 2 electrons on the right. The final equation is shown below,
[tex]H_2O+NO_2^----->NO_3^-+2H^++2e.[/tex]
The equation above is balanced for elements and electrons. Note that [tex]e[/tex] is the symbol for the electron which is a particle that has a charge of negative 1.
