What is the concentration of nitrate ions if equal volumes of 0.1 MAgNO3 and 0.1 M NaCl are mixed together

The correct answer is 0.05 M.

To find the final concentration of nitrate ions after mixing the two solutions, we can break down the process step-by-step:

Step 1: Understand the dissociation of the solutes
When silver nitrate (${\mathrm{AgNO}}_3$) dissolves in water, it dissociates completely into its constituent ions:
${\mathrm{AgNO}}_3\to {\mathrm{Ag}}^{+}+{\mathrm{NO}}_3^{-}$
Since the concentration of the ${\mathrm{AgNO}}_3$ solution is $0.1\text{ M}$, the initial concentration of nitrate ions (${\mathrm{NO}}_3^{-}$) is also $0.1\text{ M}$.

Similarly, sodium chloride ($\mathrm{NaCl}$) dissociates completely:
$\mathrm{NaCl}\to {\mathrm{Na}}^{+}+{\mathrm{Cl}}^{-}$
This solution does not contain any nitrate ions.

Step 2: Determine the effect of mixing
When the two solutions are mixed, the silver ions (${\mathrm{Ag}}^{+}$) react with chloride ions (${\mathrm{Cl}}^{-}$) to form a precipitate of silver chloride ($\mathrm{AgCl}$). However, the nitrate ions (${\mathrm{NO}}_3^{-}$) and sodium ions (${\mathrm{Na}}^{+}$) do not participate in any precipitation reaction; they are spectator ions and remain dissolved in the solution.

Step 3: Calculate the final concentration using the dilution formula
Let the volume of each solution mixed be $V$.
When equal volumes are mixed, the total volume of the mixture becomes:
$V_{\text{total}}=V+V=2V$

Since the total number of moles of nitrate ions remains constant during mixing, we can use the dilution equation:
$M_1{V}_1=M_2{V}_2$

Here:
• $M_1=0.1\text{ M}$ (initial concentration of nitrate ions in the ${\mathrm{AgNO}}_3$ solution)
• $V_1=V$ (initial volume of the ${\mathrm{AgNO}}_3$ solution)
• $V_2=2V$ (final total volume after mixing)
• $M_2$ is the final concentration of nitrate ions

Rearranging the formula to solve for $M_2$:
$M_2=\frac{M_1{V}_1}{V_2}$

Substituting the values:
$M_2=\frac{0.1\text{ M}\times V}{2V}$
$M_2=\frac{0.1}{2}\text{ M}=0.05\text{ M}$

Therefore, the concentration of nitrate ions in the final mixture is 0.05 M.