Answer:
Complete ionic: [tex]\begin{aligned}& \rm 2\, Ag^{+}\, (aq) + 2\, {NO_3}^{-} \, (aq) + Ca^{2+}\, (aq) + 2\, Cl^{-}\, (aq) \\ & \rm \to 2\, AgCl\, (s) + Ca^{2+}\, (aq) + 2\, {NO_3}^{-}\, (aq)\end{aligned}[/tex].
Net ionic: [tex]\begin{aligned}& \rm Ag^{+}\, (aq) + Cl^{-}\, (aq) \to AgCl\, (s)\end{aligned}[/tex].
Explanation:
Start by identifying species that exist as ions. In general, such species include:
All four species in this particular question are salts. However, only three of them are generally soluble in water: [tex]\rm AgNO_3[/tex], [tex]\rm CaCl_2[/tex], and [tex]\rm Ca(NO_3)_2[/tex]. These three salts will exist as ions:
On the other hand, [tex]\rm AgCl[/tex] is generally insoluble in water. This salt will not form ions.
Rewrite the original chemical equation to get the corresponding ionic equation. In this question, rewrite [tex]\rm AgNO_3[/tex], [tex]\rm CaCl_2[/tex], and [tex]\rm Ca(NO_3)_2[/tex] (three soluble salts) as the corresponding ions.
Pay attention to the coefficient of each species. For example, indeed each [tex]\rm AgNO_3\, (aq)[/tex] formula unit will exist as only one [tex]\rm Ag^{+}[/tex] ion and one [tex]\rm {NO_3}^{-}[/tex] ion. However, because the coefficient of [tex]\rm AgNO_3\, (aq)\![/tex] in the original equation is two, [tex]\!\rm AgNO_3\, (aq)[/tex] alone should correspond to two [tex]\rm Ag^{+}\![/tex] ions and two [tex]\rm {NO_3}^{-}\![/tex] ions.
Do not rewrite the salt [tex]\rm AgCl[/tex] because it is insoluble.
[tex]\begin{aligned}& \rm 2\, Ag^{+}\, (aq) + 2\, {NO_3}^{-} \, (aq) + Ca^{2+}\, (aq) + 2\, Cl^{-}\, (aq) \\ & \rm \to 2\, AgCl\, (s) + Ca^{2+}\, (aq) + 2\, {NO_3}^{-}\, (aq)\end{aligned}[/tex].
Eliminate ions that are present on both sides of this ionic equation. In this question, such ions include one unit of [tex]\rm Ca^{2+}[/tex] and two units of [tex]\rm {NO_3}^{-}[/tex]. Doing so will give:
[tex]\begin{aligned}& \rm 2\, Ag^{+}\, (aq) + 2\, Cl^{-}\, (aq) \to 2\, AgCl\, (s)\end{aligned}[/tex].
Simplify the coefficients:
[tex]\begin{aligned}& \rm Ag^{+}\, (aq) + Cl^{-}\, (aq) \to AgCl\, (s)\end{aligned}[/tex].
