Problem 83 - A Complete Resource Book in Chemistry for JEE Main

Question

The correct order of solubility of fluorides of alkaline earth metals is (a) \(\mathrm{BeF}_{2}>\mathrm{MgF}_{2}>\mathrm{CaF}_{2}>\mathrm{SrF}_{2}>\mathrm{BaF}_{2}\) (b) \(\mathrm{MgF}_{2}>\mathrm{BaF}_{2}>\mathrm{SrF}_{2}>\mathrm{CaF}_{2}>\mathrm{BeF}_{2}\) (c) \(\mathrm{BaF}_{2}>\mathrm{SrF}_{2}>\mathrm{CaF}_{2}>\mathrm{MgF}_{2}>\mathrm{BeF}_{2}\) (d) \(\mathrm{BeF}_{2}^{2}>\mathrm{Mg}^{2} \mathrm{~F}_{2}>\mathrm{SrF}_{2}^{2}>\mathrm{BaF}_{2}^{2}>\mathrm{CaF}_{2}^{2}\)

Step-by-Step Solution

Answer

The correct order is (c): BaF₂ > SrF₂ > CaF₂ > MgF₂ > BeF₂.

Step 1: Understanding Solubility in Alkaline Earth Metals

The solubility of alkaline earth metal fluorides in water generally decreases as we move down the group from beryllium to barium. This is due to the decreasing lattice energy being offset by the relatively small decrease in hydration energy. Hence, the solubility order is influenced more by lattice energy than hydration energy as we move down the group.

Step 2: Comparing Given Options

We compare each provided option to the general trend known for alkaline earth metal fluorides: (a) Shows solubility decreasing down the group. (b) Incorrect as it shows BeF₂ as least soluble, which is inaccurate. (c) Correctly indicates decreasing solubility from BaF₂ to BeF₂. (d) There are irregular terms like BeF₂² and SrF₂², which do not match the standard representation of these compounds.

Step 3: Identify the Correct Option

By matching the general trend of solubility (decreasing from BaF₂ to BeF₂), the correct answer choice that follows this trend closely is (c), where it decreases in order of BaF₂ > SrF₂ > CaF₂ > MgF₂ > BeF₂.

Key Concepts

Lattice Energy

Lattice energy is a crucial concept in understanding why some metal fluorides dissolve more easily than others. It is the energy required to separate a mole of a solid ionic compound into gaseous ions. This energy relies heavily on the strength of the electrostatic force between the oppositely charged ions. These forces are stronger when the ions are closer together or when they carry higher charges. In the case of alkaline earth metal fluorides, which are mostly composed of +2 cations and -1 fluoride anions, lattice energy plays a pivotal role. As we move down Group 2 in the periodic table, from beryllium to barium, the size of the cations increases. This increase in size results in less electrostatic attraction between the cations and anions due to a greater distance between them, thus decreasing the lattice energy. Understanding this:

• Higher lattice energy means the compound is harder to break apart, thus less soluble.
• Lattice energy decreases as we move down the group from BeF₂ to BaF₂, making the compounds more soluble.

Hydration Energy

Hydration energy is another significant force determining solubility. Unlike lattice energy, hydration energy is the energy released when ions from a solid are dissolved and surrounded by water molecules. This energy helps to pull apart the solid ionic compound. What's important to remember?

• Smaller ions with higher charges have a higher charge density, attracting water molecules more strongly.
• As we move down the group, the size of the alkaline earth metal cations increases, resulting in a decrease in hydration energy.
• This means that lower hydration energy makes fluoride compounds less soluble in water.

In the bigger picture, as you proceed down the group, both lattice and hydration energies decrease. However, with alkaline earth metal fluorides, the decrease in lattice energy is more significant. Thus, generally, lattice energy has a more substantial effect on solubility trends.

Group Trend in Periodic Table

The periodic table can tell us a lot about how elements and their compounds will behave, and this is particularly true for solubility trends of alkaline earth metal fluorides. Key observations in group trends:

• Group 2 metals become larger as you move from top to bottom, from beryllium to barium.
• The increase in ionic size generally decreases the charge density and thus affects both lattice and hydration energies.
• Because the lattice energy more significantly decreases than hydration energy, solubility usually decreases down the group.

Thus, with these trends, the solubility order for alkaline earth fluorides is generally decreasing from BaF₂ to BeF₂. This reflects both the changes in lattice and hydration energies as well as the general periodical group trends.