1. Use the ionization data

The compound is written overall as $Co(NH_3)_5Cl_3$.

We are told that 1 mole of complex gives 3 moles of ions in water.

So on dissolution, the compound must dissociate like: $[\text{complex}]^{2+} + 2Cl^-$ or $[\text{complex}]^{+} + 2\text{other ions}$ with total number of ions $=3$.

Let us test the options.

2. Use the $AgNO_3$ test

$AgNO_3$ precipitates only those $Cl^-$ ions which are outside the coordination sphere.

Given: 1 mole of compound gives 2 moles of $AgCl$.

Therefore, the complex must contain 2 ionizable chloride ions outside the coordination sphere.

So the formula must be of the type: $[Co(NH_3)_5Cl]Cl_2$ where one $Cl^-$ is coordinated and two $Cl^-$ are outside.

3. Check each option

Option A: $[Co(NH_3)_3Cl_3]\cdot 2NH_3$

• No chloride outside the coordination sphere.
• So it would give 0 moles of $AgCl$ with $AgNO_3$.
• Also it behaves as a neutral complex, not giving 3 ions.

Option A is incorrect.

Option B: $[Co(NH_3)_4Cl_2]Cl\cdot NH_3$

• Only 1 chloride outside.
• So it would give 1 mole of $AgCl$.
• On dissolution, ions produced: $[Co(NH_3)_4Cl_2(NH_3)]^+ + Cl^-$ Total $=2$ ions.

Option B is incorrect.

Option C: $[Co(NH_3)_4Cl]Cl_2\cdot NH_3$

• This has 2 chloride outside, so it would give 2 moles of $AgCl$.
• But then inside the bracket there are only $4NH_3 + 1NH_3 = 5NH_3$, with one extra $NH_3$ outside as solvate.
• On dissolution it would produce: $[Co(NH_3)_4Cl]^{2+} + 2Cl^- + NH_3$ Depending on how written, the outside $NH_3$ is not ionic, so effective ions are 3, but this formulation is not the standard Werner structure for $Co(NH_3)_5Cl_3$ because the extra $NH_3$ is outside coordination sphere as molecular ammonia. The classical compound satisfying both conditions is the pentaamminechlorocobalt(III) chloride.

Option C is not the correct coordination structure.

Option D: $[Co(NH_3)_5Cl]Cl_2$

• Here 2 chloride ions are outside the coordination sphere.
• So with $AgNO_3$: $2Cl^- + 2AgNO_3 \rightarrow 2AgCl\downarrow + 2NO_3^-$ Hence 2 moles of $AgCl$ are formed.
• On dissolution: $[Co(NH_3)_5Cl]Cl_2 \rightarrow [Co(NH_3)_5Cl]^{2+} + 2Cl^-$ Total ions $= 3$.

This matches both given conditions.

4. Final answer

The correct structure is: $\boxed{[Co(NH_3)_5Cl]Cl_2}$ which is Option D.