Which one of the following when dissolved in water gives coloured solution in nitrogen atmosphere?

We are asked: “Which one of the following when dissolved in water gives coloured solution in nitrogen atmosphere?” The four chlorides given are $$\text{Cu}_2\text{Cl}_2$$, $$\text{ZnCl}_2$$, $$\text{CuCl}_2$$ and $$\text{AgCl}$$. We must remember that the colour of an aqueous solution generally arises from the presence of ions capable of $$d$$-$$d$$ electronic transitions.

First, let us recall the electronic configurations of the relevant metal ions formed in water.

When $$\text{CuCl}_2$$ dissolves, it furnishes $$\text{Cu}^{2+}$$ ions. Copper in the +2 oxidation state has electronic configuration $$[ \text{Ar} ]\,3d^{9}$$. Because the $$3d$$ subshell is partly filled, the $$d$$-$$d$$ transitions fall in the visible region, and these transitions absorb certain wavelengths of light while transmitting the complementary colour, giving the solution its characteristic blue-green appearance.

Next, consider $$\text{Cu}_2\text{Cl}_2$$, commonly written as $$\text{CuCl}$$ (cuprous chloride). In aqueous medium, cuprous chloride tends to undergo disproportionation as per the reaction

$$2\,\text{Cu}^{+}\;(aq) \;\longrightarrow\; \text{Cu}^{2+}\;(aq) + \text{Cu}\;(s)$$

However, this reaction requires dissolved oxygen. The question specifically mentions a nitrogen atmosphere, that is, an oxygen-free environment. In the absence of oxygen the $$\text{Cu}^{+}$$ ion remains, and $$\text{Cu}^{+}$$ has configuration $$[ \text{Ar} ]\,3d^{10}$$, a completely filled $$d$$ subshell. Because there are no vacant $$d$$ levels with the proper energy gap for visible-light absorption, the solution of $$\text{Cu}^{+}$$ is colourless.

Now look at $$\text{ZnCl}_2$$. Dissolution yields $$\text{Zn}^{2+}$$ ions whose configuration is $$[ \text{Ar} ]\,3d^{10}$$. Again, the filled $$d$$ subshell precludes $$d$$-$$d$$ transitions in the visible range, so the solution is colourless.

Finally, $$\text{AgCl}$$ is practically insoluble in water, so it cannot give any appreciable ionic solution, coloured or otherwise.

Summarising, only $$\text{CuCl}_2$$ gives $$\text{Cu}^{2+}$$ ions with a partly filled $$d$$ subshell, leading to a distinctly coloured (blue-green) aqueous solution even when oxygen is excluded by a nitrogen atmosphere.

Hence, the correct answer is Option C.