Step 1: Understanding the Concept:
The color of transition metal ions in solution is usually due to d-d transitions. This requires an incompletely filled d-subshell (\(d^1\) to \(d^9\)). Ions with \(d^0\) or \(d^{10}\) configurations are typically colourless.
Step 2: Detailed Explanation:
1. \(ZnCl_2\): Contains \(Zn^{2+}\) ion. Configuration is \([Ar] 3d^{10}\). Because the d-shell is completely filled, no d-d transition is possible. It is colourless.
2. \(CuCl_2\): Contains \(Cu^{2+}\) ion. Configuration is \([Ar] 3d^9\). It has one unpaired electron, allowing for d-d transitions. It forms a blue/green coloured solution in water.
3. \(Cu_2Cl_2\): Contains \(Cu^+\) ion. Configuration is \([Ar] 3d^{10}\). Similar to \(Zn^{2+}\), it is colourless (and also largely insoluble in water).
4. \(AgCl\): Contains \(Ag^+\) ion. Configuration is \([Kr] 4d^{10}\). It is a white insoluble solid and gives a colourless supernatant if any dissolves.
Step 3: Final Answer:
\(CuCl_2\) gives a coloured solution when dissolved in water.