Problem 91 - Chemistry and Chemical Reactivity

Question

When salts of \(\mathrm{Mg}^{2+}, \mathrm{Ca}^{2+},\) and \(\mathrm{Be}^{2+}\) are placed in water, the positive ion is hydrated (as is the negative ion). Which of these three cations is most strongly hydrated? Which one is least strongly hydrated?

Step-by-Step Solution

Answer

\(\mathrm{Be}^{2+}\) is most strongly hydrated; \(\mathrm{Ca}^{2+}\) is least strongly hydrated.

Step 1: Understanding Ion Hydration

Ion hydration occurs when water molecules surround a cation due to electrostatic attraction. The strength of hydration depends on the charge density of the ion; ions with a high charge density are more strongly hydrated because they attract water molecules more effectively.

Step 2: Assess Charge Density

Charge density is determined by the charge-to-radius ratio. A higher charge and smaller atomic radius result in greater charge density. All three ions \((\mathrm{Mg}^{2+}, \mathrm{Ca}^{2+}, \mathrm{Be}^{2+})\) have the same +2 charge, so the key factor is the ionic radius.

Step 3: Compare Ionic Radii

The typical ionic radii for these ions are:- \(\mathrm{Be}^{2+}\): approximately 59 pm- \(\mathrm{Mg}^{2+}\): approximately 72 pm- \(\mathrm{Ca}^{2+}\): approximately 100 pmSince smaller ions have a higher charge density, \(\mathrm{Be}^{2+}\) will have the highest charge density, while \(\mathrm{Ca}^{2+}\) will have the lowest.

Step 4: Determine Hydration Strength

Given that \(\mathrm{Be}^{2+}\) has the smallest ionic radius and thus the highest charge density, it will be the most strongly hydrated. Conversely, \(\mathrm{Ca}^{2+}\), having the largest radius and lowest charge density, will be the least strongly hydrated.

Key Concepts

Charge Density

Charge density is a crucial factor in determining how an ion interacts with water molecules. It can be defined as the amount of charge per unit volume of a sphere of the ion. The higher the charge density, the stronger the ion's ability to attract surrounding water molecules. This is because a concentrated charge creates a significant electrostatic field, which water molecules, being polar, find very attractive. Let's look at why charge density matters:

• **Electrostatic Attraction:** Ions with higher charge densities create strong electrostatic attractions, pulling water molecules close.
• **Charge-to-Size Ratio:** The charge density increases with higher charges and smaller ionic radii.

When comparing ions such as Mg^{2+}, Ca^{2+}, and Be^{2+}, even though all have the same +2 charge, their charge densities differ due to their varying sizes. Be^{2+} has the highest charge density due to its small size, making it especially effective in attracting water molecules and thus, being more hydrated.

Ionic Radius

The ionic radius of an ion plays a significant role in its hydration because it affects the charge density. Ionic radius refers to the effective distance from the nucleus of an ion to the outer boundary of the surrounding electrons in a stable form. Here’s why it matters:

• **Direct Impact on Charge Density:** A smaller ionic radius results in higher charge density since the charge is concentrated over a smaller area.
• **Comparison of Sizes:** In the given scenario, Be^{2+} is about 59 pm, Mg^{2+} is approximately 72 pm, and Ca^{2+} is about 100 pm.

Be^{2+}, due to its tiny ionic radius, has much higher charge density compared to Ca^{2+}, leading to different hydration strengths. So, ionic radius is not just a number; it directly influences how ions interact with water molecules.

Cations in Water

When cations are dissolved in water, they become surrounded by water molecules in a process known as hydration. The process is influenced by the nature of the cation itself:

• **Polar Interaction:** Water molecules, being polar, are attracted to the charged cation surface, creating a hydration shell.
• **Impact of Ionic Properties:** Properties such as charge density and ionic radius affect how strong this interaction will be. Ions with higher charge densities create stronger hydration shells.

In terms of hydration strength among the cations Mg^{2+}, Ca^{2+}, and Be^{2+}, the Be^{2+} ion, having the highest charge density, will strongly attract water molecules and form a dense hydration shell. This makes it the most hydrated. Conversely, Ca^{2+} with its larger radius and lower charge density forms a weaker hydration shell, thus, is the least hydrated among these ions.