Problem 70 - Chemistry and Chemical Reactivity

Question

Which should be the stronger Bronsted acid, \(\left[\mathrm{V}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\) or \(\left[\mathrm{V}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+} ?\)

Step-by-Step Solution

Answer

\([\mathrm{V}(\mathrm{H}_{2}\mathrm{O})_{6}]^{3+}\) is the stronger Brønsted acid.

Step 1: Understand the Components

Identify the key difference between the two complexes: the oxidation states. Here, the oxidation states are +2 and +3 respectively. This leads to different charge densities.

Step 2: Determine Charge Density Impact

A higher oxidation state in a complex ion generally implies a greater charge density on the central metal ion. This results in a stronger attraction between the metal ion and water molecules, making the complex more likely to release a proton, thus acting as a stronger acid.

Step 3: Analyze Proton Release Tendency

The complex \([\mathrm{V}(\mathrm{H}_{2}\mathrm{O})_{6}]^{3+}\) will have a higher charge density than \([\mathrm{V}(\mathrm{H}_{2}\mathrm{O})_{6}]^{2+}\). Therefore, in the 3+ complex, the water molecules are more polarizable, and it's easier for the complex to donate protons, acting as a stronger Brønsted acid.

Step 4: Conclusion

Based on the analysis, \([\mathrm{V}(\mathrm{H}_{2}\mathrm{O})_{6}]^{3+}\) is expected to be a stronger Brønsted acid than \([\mathrm{V}(\mathrm{H}_{2}\mathrm{O})_{6}]^{2+}\), due to its higher charge density and greater ability to donate protons.

Key Concepts

Oxidation States

Oxidation states are a way of keeping track of how electrons are distributed in a compound. They indicate the number of electrons an atom might gain, lose, or share when it forms chemical bonds.
For example, in the complexes \(\left[\mathrm{V}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\) and \(\left[\mathrm{V}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+}\), vanadium exhibits oxidation states of +2 and +3, respectively.

• The +2 oxidation state means vanadium ion has lost two electrons.
• The +3 oxidation state indicates the loss of three electrons, resulting in a higher positive charge on the vanadium ion.

A higher oxidation state corresponds to a higher positive charge on the central ion. This affects how strongly the central ion can attract electrons from surrounding ligands, such as water molecules.

Charge Density

Charge density refers to the concentration of electric charge in a given volume. In the context of chemistry, it particularly refers to how concentrated the charge is on an atomic or ionic scale.
When we discuss complexes like \(\left[\mathrm{V}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\) and \(\left[\mathrm{V}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+}\), the charge density is determined by the oxidation state of the metal ion.

• Higher oxidation states lead to higher charge densities.
• The complex with a charge of 3+ has a higher charge density than the 2+ complex.

This increased charge density in the 3+ complex results in a stronger pull on the water molecules. It polarizes the O-H bonds within the water, making them more likely to release protons.

Proton Release

Proton release is the process through which a molecule donates a proton to another species, characteristic of acids. In the framework of Bronsted acid-base theory, an acid is any substance capable of donating a proton (H⁺).

• In the case of \(\left[\mathrm{V}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+}\), due to its higher charge density, the bonds between water and vanadium are stronger.
• This interaction polarizes the water molecules, weakening their ability to hold onto protons.

Because the \(\left[\mathrm{V}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+}\) complex can release protons more easily than the \(\left[\mathrm{V}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\) complex, it behaves as a stronger Bronsted acid. This clearly establishes why the 3+ complex is more acidic - despite both complexes being similar, the increased capacity to donate protons differentiates them in terms of acidic strength.