Problem 46 - Chemistry and Chemical Reactivity

Question

In which salts does the cation bind most strongly to water molecules? In which is the binding less strong in comparison? Explain your reasoning. (a) \(\mathrm{Fe}\left(\mathrm{NO}_{3}\right)_{3}\) (b) \(\mathrm{CoCl}_{2}\) (c) \(\mathrm{NaCl}\) (d) \(\mathrm{Al}\left(\mathrm{NO}_{3}\right)_{3}\)

Step-by-Step Solution

Answer

Fe(NO₃)₃ binds most strongly, NaCl binds the weakest.

Step 1: Understand the Trend

The strength of a cation binding to water molecules in a solution is related to its charge and size. Small cations with higher charges exhibit stronger binding due to higher charge density. The charge density is the ratio of the charge of the ion to its volume.

Step 2: Analyze Cations

Identify the cations present in each salt:- (a) \(\mathrm{Fe}^{3+}\)- (b) \(\mathrm{Co}^{2+}\)- (c) \(\mathrm{Na}^{+}\)- (d) \(\mathrm{Al}^{3+}\)Observe that (a) and (d) have cations with a charge of +3, while (b) and (c) have lower charges.

Step 3: Assess Charge Density

The cations with higher charges (\(\mathrm{Fe}^{3+}\) and \(\mathrm{Al}^{3+}\)) will generally have stronger interactions with water than those with lower charges (\(\mathrm{Co}^{2+}\) and \(\mathrm{Na}^{+}\)). Between \(\mathrm{Fe}^{3+}\) and \(\mathrm{Al}^{3+}\), \(\mathrm{Fe}^{3+}\) typically has a slightly higher effective charge density because of its smaller ionic radius.

Step 4: Rank the Binding Strength

Rank the cations based on the expected strength of their binding to water:1. \(\mathrm{Fe}^{3+}\) (in \(\mathrm{Fe}\left(\mathrm{NO}_{3}\right)_{3}\)) - strongest binding due to highest charge density2. \(\mathrm{Al}^{3+}\) (in \(\mathrm{Al}\left(\mathrm{NO}_{3}\right)_{3}\)) - also very strong, but slightly less than \(\mathrm{Fe}^{3+}\)3. \(\mathrm{Co}^{2+}\) (in \(\mathrm{CoCl}_{2}\)) - moderate binding, higher than \(\mathrm{Na}^{+}\)4. \(\mathrm{Na}^{+}\) (in \(\mathrm{NaCl}\)) - weakest binding, due to low charge and larger size.

Key Concepts

Charge Density

The concept of charge density is crucial in understanding how strongly a cation binds to water molecules. Charge density refers to the ratio of a cation's electric charge to its volume.
High charge density means that the charge is concentrated over a smaller area, leading to stronger interactions with surrounding molecules like water.

Factors affecting charge density include:

• The amount of charge on the ion (ionic charge)
• The size of the cation (radius)

Cations with high charge density are generally smaller and have a higher ionic charge. For example, \( ext{Fe}^{3+}\) has a high charge density because of a +3 charge distributed over a relatively small atomic radius. As a result, it binds more strongly to water compared to cations like \( ext{Na}^{+}\), which has a +1 charge and a larger radius, resulting in lower charge density.

Cation Size

The size of a cation plays a significant role in determining its interaction with water. Smaller cations can pack their positive charge into a smaller volume, thereby increasing their charge density.
This higher density results in a stronger attraction to the negative dipoles of water molecules.

Considerations for cation size include:

• Directly affects charge density: Smaller ions mean larger charge-to-volume ratios.
• Comparative examples: \( ext{Na}^+\) is larger than \( ext{Fe}^{3+}\) resulting in weaker water binding.

As a cation decreases in size, the electric field around it becomes more concentrated, allowing it to attract more water molecules around it more strongly. Therefore, cations like \( ext{Fe}^{3+}\) and \( ext{Al}^{3+}\) exhibit stronger water binding compared to larger ions.

Ionic Charge

Ionic charge is another key factor that affects the binding strength of cations to water. This refers to the actual positive charge a cation carries.
Higher charged ions have more robust electrostatic attractions with the partial negative charge of water molecules.

Crucial points about ionic charge include:

• Higher charge leads to stronger attraction: \( ext{Fe}^{3+}\) and \( ext{Al}^{3+}\) each have high charges, drawing water molecules more effectively than lower charged ions.
• Influences hydration pattern: Stronger ionic charges can lead to more organized water molecule arrangements surrounding the cation.

Thus, cations with higher ionic charges, like \( ext{Fe}^{3+}\) and \( ext{Al}^{3+}\), will naturally hydrate more strongly and extensively than those with lower charges such as \( ext{Na}^+\).

Hydration of Ions

Hydration refers to how water molecules orient themselves around a dissolved ion. This process is influenced by both charge density and ionic charge; stronger interactions lead to a more well-defined hydration shell.
It's through hydration that ions become stabilized in a solution.

Key elements of ion hydration are:

• Ions with high charge density and high ionic charge like \( ext{Fe}^{3+}\) have tightly bound water molecules creating a stable hydration shell.
• This shell assists in stabilizing ions in an aqueous environment, preventing them from aggregating.

In general, ions with high charge and density, such as \( ext{Fe}^{3+}\) and \( ext{Al}^{3+}\), are effective at attracting multiple water molecules, leading to highly stabilized ions when dissolved.