Problem 5 - A Complete Resource Book in Chemistry for JEE Main

Question

Which one of the following forms a colourless solution in aqueous medium? (a) \(\mathrm{V}^{3+}\) (b) \(\mathrm{Cr}^{3+}\) (c) \(\mathrm{Ti}^{3+}\) (d) \(\mathrm{Sc}^{3+}\) Atomic number \(\mathrm{Sc}=21, \mathrm{Ti}=22, \mathrm{~V}=23, \mathrm{Cr}=24\)

Step-by-Step Solution

Answer

Sc³⁺ forms a colorless solution in water.

Step 1: Understand the Color Conditions

Ions are typically colorless in an aqueous medium if they have completely filled or completely empty d-orbitals. This is because electronic transitions between d-orbitals, which give rise to color, are not possible in these cases.

Step 2: Analyze Electronic Configuration

We first identify the electronic configurations of each metal in its +3 oxidation state by removing 3 electrons from the neutal atom configuration. - Scandium (Sc): Atomic number = 21, Configuration = [Ar] 3d¹ 4s². For Sc³⁺, the configuration becomes [Ar]. - Titanium (Ti): Atomic number = 22, Configuration = [Ar] 3d² 4s². For Ti³⁺, the configuration becomes [Ar] 3d¹. - Vanadium (V): Atomic number = 23, Configuration = [Ar] 3d³ 4s². For V³⁺, the configuration becomes [Ar] 3d². - Chromium (Cr): Atomic number = 24, Configuration = [Ar] 3d⁵ 4s¹. For Cr³⁺, the configuration becomes [Ar] 3d³.

Step 3: Identify the Colorless Configuration

The Sc³⁺ ion has the electronic configuration [Ar], indicating it has empty d-orbitals (3d⁰ configuration), which do not allow for d-d electronic transitions and therefore do not exhibit color. In contrast, Ti³⁺, V³⁺, and Cr³⁺ ions have partially filled d-orbitals, contributing to color formation.

Step 4: Verify Answer

Since Sc³⁺ has an electron configuration with empty d-orbitals, it will form a colorless solution in an aqueous medium. Confirming the consistency between the observed and theoretical conditions for colorlessness.

Key Concepts

Colorless Solution

A colorless solution is one that does not exhibit any apparent color when viewed in an aqueous medium. In the context of transition metal ions, the appearance of color is heavily influenced by the arrangement and condition of d-orbitals. When d-orbitals are completely empty or fully filled, there's no available route for electronic transitions that typically produce color. These transitions usually happen as electrons jump between energy levels within these d-orbitals. Without them, the ion absorbs no visible light to show any particular color and hence appears colorless.
This is why Sc³⁺, which has an electronic configuration that leads to an empty set of d-orbitals, appears colorless in a solution. Since there are no electrons in its 3d-orbital to make any transitions, there are no light absorption events that would impart color.

d-Orbital Filling

The concept of d-orbital filling concerns the distribution of electrons within the d-sub shell of transition metal ions. A d-orbital can hold up to 10 electrons given its five specific orbitals. How these electrons fill these orbitals strongly influences the properties of the ions, particularly their color.

• If a d-orbital is completely empty (as in Sc³⁺), no electronic transitions can occur, which results in a colorless solution.
• Similarly, if a d-orbital is completely filled (d¹⁰ configuration), it will also typically result in a colorless compound because no further electronic transitions are possible.
• Partial filling (such as in Ti³⁺, V³⁺, and Cr³⁺) usually allows for electronic transitions, which can absorb certain wavelengths of light and impart color to the solution.

The observed color is the result of these transitions not being available, which fundamentally relates to changes in energy levels within these d-orbitals.

Transition Metal Ions

Transition metals are unique in their ability to form ions with various oxidation states, primarily due to the involvement of d-orbitals. They reside in the central block of the periodic table, and are characterized by having an incomplete d-sub shell in one of their common oxidation states.
These metals can lose electrons to form positively charged ions. In the +3 oxidation state, electrons are typically removed from the s-orbital and then the d-orbitals. The specific configuration after this removal determines the behavior of the ion in a solution.

• For Scandium ( 3^+ or Sc³⁺), removal of its three outermost electrons results in an empty d-orbital, leading to a colorless solution.
• Titanium, Vanadium, and Chromium form partially filled d-orbitals in their respective +3 states, each contributing to a characteristic colored solution because of potential d-d electronic transitions.

Recognizing these patterns helps in predicting the color of solutions containing these metal ions and understanding their chemical behavior.