Which of the following will not be coloured?

The correct answer is option 1. \(TiO_2\).

Here is an explanation of why each compound is colored or not:

1. \(TiO_2\) (Titanium Dioxide): Titanium dioxide is a white solid and is widely used as a white pigment in paints, coatings, and food products. It does not have any unpaired d-electrons or charge transfer transitions that would absorb visible light, so it does not exhibit color.

2. \(CrO_3\) (Chromium Trioxide): Chromium trioxide is a compound where chromium is in the +6 oxidation state. In this oxidation state, chromium compounds often have charge transfer transitions that absorb visible light, leading to strong colors. \(CrO_3\) appears as a dark red to orange substance due to these transitions.

3. \(MnO_2\) (Manganese Dioxide): In \(MnO_2\), manganese is in the +4 oxidation state. The color of \(MnO_2\) is due to the presence of d-d transitions in the Mn(IV) ions and/or charge transfer from oxygen to manganese. This results in a dark brown to black color.

4. \(V_2O_5\) (Vanadium Pentoxide): In \(V_2O_5\), vanadium is in the +5 oxidation state. Vanadium pentoxide has charge transfer transitions between the vanadium and oxygen atoms that result in its yellow to orange color.

So, \(TiO_2\) is not colored because it lacks the electronic transitions responsible for color absorption in the visible spectrum.