Question

$$ \begin{aligned} &\text { Which ion is expected to give the more acidic solution, }\\\ &\mathrm{Fe}^{2+} \text { or } \mathrm{Fe}^{3+} \text { ? Why? } \end{aligned} $$

Short answer

Fe^{3+} is expected to give a more acidic solution than Fe^{2+} because it has a higher charge and smaller ionic radius, leading to stronger polarization of the surrounding water molecules.

Step-by-step solution

Understand the Acidic Character

The acidic character of an aqueous solution containing cations is based on the cation's ability to polarize nearby water molecules. Higher charge and smaller radius increase the polarization, hence increasing the acidic character.

Compare Charges of the Ions

The charge on the iron ion affects its ability to polarize water molecules. Fe^{3+} has a higher charge than Fe^{2+}, which means it can polarize water molecules more strongly.

Consider the Size of the Ions

The size of the ion also affects its ability to polarize water molecules. The Fe^{3+} ion, being smaller due to the greater effective nuclear charge pulling the electrons closer, polarizes water molecules more effectively than Fe^{2+}.

Determine the More Acidic Solution

Since the greater charge and smaller size both enhance the capacity of the ion to polarize water molecules, Fe^{3+}, with its higher charge and smaller size compared to Fe^{2+}, is expected to give the more acidic solution.

Key concepts

Ion Polarization

Ion polarization plays a critical role in determining the acidic character of ions in aqueous solutions. In simple terms, it refers to the distortion of the electron cloud of the water molecules that are near a cation. This distortion is caused by the electrostatic interaction between the positively charged ion and the negative charges on the oxygen of the water molecules.

When a cation like iron exists in water, it can pull on the electrons of water, causing a shift in electron density. The greater the charge of the ion, the more powerful its ability to polarize surrounding water molecules. This effect can lead to the release of protons (H+) from the water, increasing the acidity of the solution. Therefore, a higher level of polarization indicates a higher acidity. In our exercise, between Fe²⁺ and Fe³⁺, the ion with the higher charge, Fe³⁺, will polarize water molecules more strongly.

Effective Nuclear Charge

The concept of effective nuclear charge (ENC) is central to understanding why ions of the same element can have different sizes and polarizing powers. ENC refers to the net positive charge experienced by an electron in an atom and is a result of the balance between the positive charge of the nucleus and the negative charges of the other electrons in the atom.

When an iron atom loses electrons to become Fe³⁺ rather than Fe²⁺, the ENC increases because there are more protons than electrons within the ion. This higher ENC pulls the remaining electrons closer to the nucleus, resulting in a smaller ionic radius. A smaller ion with a high charge density can more effectively polarize nearby water molecules causing an increase in the acidic character of the solution. This is the reason why the Fe³⁺ ion renders a more acidic solution compared to Fe²⁺.

Solution Acidity

Solution acidity is a measure of the concentration of hydrogen ions, H+, present in a solution. It is often expressed on the pH scale, where lower pH values indicate higher acidity. The acidity of a solution can be influenced by the presence of dissolved ions that can polarize water molecules and induce the liberation of H+ ions, thus increasing the solution's overall acidity.

Ions with higher charges and smaller atomic radii, such as Fe³⁺, have a stronger polarizing effect on water molecules leading to the formation of hydronium ions (H₃O⁺). This transformation enhances the acidity of the solution, as evidenced by a lower pH. Thus, in comparison to Fe²⁺, solutions containing Fe³⁺ are expected to be more acidic due to the ion's greater ability to polarize water and promote hydrogen ion release.