Question

Which of the following hydrated cations are colorless: ${\mathrm{Fe}}^{2+}(aq),{\mathrm{Zn}}^{2+}(aq),{\mathrm{Cu}}^{+}(aq),{\mathrm{Cu}}^{2+}(aq),{\mathrm{V}}^{5+}(aq)$ ${\mathrm{Ca}}^{2+}(aq),{\mathrm{Co}}^{2+}(aq),{\mathrm{Sc}}^{3+}(aq),{\mathrm{Pb}}^{2+}(aq)?$ Explain your choice.

Short answer

The colorless cations are ${\mathrm{Zn}}^{2+}$, ${\mathrm{Cu}}^{+}$, ${\mathrm{V}}^{5+}$, ${\mathrm{Ca}}^{2+}$, ${\mathrm{Sc}}^{3+}$, and ${\mathrm{Pb}}^{2+}$.

Step-by-step solution

Understand the Concept of Color in Transition Metals

The color of hydrated cations often arises due to d-d transitions, which occur in transition metals that have partially filled d-orbitals. These transitions allow the metal ions to absorb certain wavelengths of light, which result in colors visible to the eye.

Identify Cations with Partially Filled d-Orbitals

List the given cations and determine whether they have partially filled d-orbitals. Transition metals with completely filled or empty d-orbitals often appear colorless. 1. ${\mathrm{Fe}}^{2+}$: d⁶ (not colorless)2. ${\mathrm{Zn}}^{2+}$: d¹⁰ (completely filled, potentially colorless)3. ${\mathrm{Cu}}^{+}$: d¹⁰ (completely filled, potentially colorless)4. ${\mathrm{Cu}}^{2+}$: d⁹ (not colorless)5. ${\mathrm{V}}^{5+}$: d⁰ (empty, potentially colorless)6. ${\mathrm{Ca}}^{2+}$: d⁰ (empty, potentially colorless)7. ${\mathrm{Co}}^{2+}$: d⁷ (not colorless)8. ${\mathrm{Sc}}^{3+}$: d⁰ (empty, potentially colorless)9. ${\mathrm{Pb}}^{2+}$: non-transition (potentially colorless as main group element)

List Potential Colorless Cations

Based on the analysis of d-orbital configurations, the colorless cations are likely those with completely filled or completely empty d-orbitals. Examine the list:- ${\mathrm{Zn}}^{2+}$ (d¹⁰)- ${\mathrm{Cu}}^{+}$ (d¹⁰)- ${\mathrm{V}}^{5+}$ (d⁰)- ${\mathrm{Ca}}^{2+}$ (d⁰)- ${\mathrm{Sc}}^{3+}$ (d⁰)- ${\mathrm{Pb}}^{2+}$ (not a transition metal)

Key concepts

d-d transitions

In transition metals, color often arises from something called d-d transitions. These involve the movement of electrons between different energy levels within the d-orbitals of a metal ion. When light hits a transition metal, certain wavelengths are absorbed to facilitate these transitions. This absorption results in the appearance of color, as the non-absorbed light is what we perceive.

For example, the vivid blue of copper sulfate is a result of such transitions. It's important to note that these occur only if d-orbitals are partially filled, giving space for electrons to shift between levels.

partially filled d-orbitals

Partially filled d-orbitals are key to the colorful properties of transition metals. When the d-orbitals have unfilled spaces (meaning not all available spots for electrons are occupied), they can absorb visible light and cause color changes.

Metals like ${\mathrm{Fe}}^{2+}$ and ${\mathrm{Cu}}^{2+}$ have such configurations, fully engaging in these transitions and showing rich colors. If d-orbitals are entirely full $\text{(e.g., }{\mathrm{Zn}}^{2+})$ or empty $\text{(e.g., }{\mathrm{V}}^{5+})$, no such transitions occur, often making the ions appear colorless.

transition metals

Transition metals are elements found in the d-block of the periodic table, known for their ability to exhibit various oxidation states and form colored compounds. These elements have an incomplete d sub-shell, which allows them to form complex ions with intriguing properties such as magnetism and variable color.

Some common characteristics include high melting points, density, and the ability to form complex ions with other elements. Examples are $\mathrm{Fe}$, $\mathrm{Co}$, and $\mathrm{Cu}$. They make exceptional catalysts due to their variable oxidation states.

hydrated cations

Hydrated cations are metal ions surrounded by water molecules, forming what chemists call coordination complexes. This occurs when the lone pairs of electrons on the oxygen atoms in water coordinate, or attach, to the metal ion.

Such complexation often affects the electronic configuration and is responsible for the observed color changes in transition metals. The presence of water can alter the energies of the d-orbitals, facilitating d-d transitions. In essence, the hydration environment plays a crucial role in determining the optical properties of the metal ion.

orbital configurations

Orbital configurations determine how electrons are arranged in an atom or ion. For transition metals, the configuration of the d-orbitals is particularly important in explaining color properties.

In ions like ${\mathrm{Zn}}^{2+}$ $(d^{10})$ and ${\mathrm{Sc}}^{3+}$ $(d^0)$, their filled or empty d-orbitals don't allow for electronic transitions that absorb visible light, resulting in no color. Conversely, partially filled configurations like ${\mathrm{Co}}^{2+}$ $(d^7)$ often result in rich colors. Understanding these configurations is essential for predicting the behavior of transition metal ions in various chemical environments.