Identify the reaction involved

White precipitate of silver chloride, $AgCl$, dissolves in aqueous ammonia because silver ion forms a soluble ammine complex.

Write the equilibrium

$AgCl(s) \rightleftharpoons Ag^+ + Cl^-$

In presence of ammonia:

$Ag^+ + 2NH_3 \rightleftharpoons [Ag(NH_3)_2]^+$

Therefore, overall:

$AgCl(s) + 2NH_3(aq) \rightleftharpoons [Ag(NH_3)_2]^+ + Cl^-$

Identify the compound formed

The soluble complex salt is written as:

$[Ag(NH_3)_2]Cl$

This is called diamminesilver(I) chloride.

Check the options

• A: $[Ag(NH_3)_4]Cl_2$
  Incorrect. Silver(I) commonly forms the coordination number 2 ammine complex, not this one here.

• B: $[Ag(Cl)_2(NH_3)_2]$
  Incorrect. This is not the complex responsible for dissolution of $AgCl$ in ammonia.

• C: $[Ag(NH_3)_2]Cl$
  Correct. This corresponds to the soluble complex formed.

• D: $[Ag(NH_3)Cl]Cl$
  Incorrect. This is not the standard ammine complex of silver responsible for dissolving $AgCl$.

Final answer

The white precipitate of $AgCl$ dissolves in aqueous ammonia due to formation of:

$\boxed{[Ag(NH_3)_2]Cl}$