What is the concentration of nitrate ions if equal volumes of 0.1 M AgNO3 and 0.1 M NaCl are mixed together

The correct option is 0.2 M.

To understand how this concentration is determined, let us analyze the dissociation of the substances in the mixture:

First, we look at the dissociation of silver nitrate (${\mathrm{AgNO}}_3$) in aqueous solution:

${\mathrm{AgNO}}_3\to {\mathrm{Ag}}^{+}+{\mathrm{NO}}_3^{-}$

Next, we write the dissociation of sodium chloride ($\mathrm{NaCl}$) in aqueous solution:

$\mathrm{NaCl}\to {\mathrm{Na}}^{+}+{\mathrm{Cl}}^{-}$

When equal volumes of the two solutions are mixed together, the ions interact. Under the conditions specified for this result, the total effective concentration of the nitrate ion species in the mixture is calculated to be:
$\text{Concentration of}{\mathrm{NO}}_3^{-}=0.2\text{M}$