Problem 27 - A Complete Resource Book in Chemistry for JEE Main

Question

The decreasing order of solubility of alkaline earth metal hydroxides \(\left[\mathrm{M}(\mathrm{OH})_{2}\right]\) is given as (a) \(\mathrm{Ba}>\mathrm{Sr}>\mathrm{Ca}>\mathrm{Mg}>\mathrm{Be}\) (b) \(\mathrm{Be}<\mathrm{Mg}<\mathrm{Ca}<\mathrm{Sr}<\mathrm{Ba}\) (c) \(\mathrm{Be}=\mathrm{Mg}>\mathrm{Ca}>\mathrm{Sr}>\mathrm{Ba}\) (d) \(\mathrm{Mg}<\mathrm{Be}<\mathrm{Ca}<\mathrm{Ba}<\mathrm{Sr}\)

Step-by-Step Solution

Answer

The correct answer is (b): \\ \( \text{Be} < \text{Mg} < \text{Ca} < \text{Sr} < \text{Ba} \).

Step 1: Understanding the Trend of Solubility

The solubility of alkaline earth metal hydroxides generally increases as you move down the group in the periodic table. This trend is due to the decrease in lattice energy and the relatively smaller decrease in the hydration energy of the hydroxides as the cation size increases. Hence, the hydroxides become more soluble as you move from beryllium to barium.

Step 2: Analyzing the Given Options

Let's analyze each statement: - (a) suggests decreasing order Ba > Sr > Ca > Mg > Be. - (b) suggests increasing order Be < Mg < Ca < Sr < Ba. - (c) suggests Be = Mg > Ca > Sr > Ba. - (d) suggests an incorrect sequence Mg < Be < Ca < Ba < Sr. We are looking for the order where solubility increases from Be to Ba.

Step 3: Selecting the Right Option

Given that solubility increases down the group from Be to Ba, option (b) correctly states this trend with Be < Mg < Ca < Sr < Ba. Therefore, option (b) reflects the correct increasing solubility order.

Key Concepts

Periodic Table Trends

The periodic table is a powerful tool for understanding the chemical behavior of elements. Elements are organized based on their atomic number, and group them into columns based on similar properties. One important aspect of the periodic table trends is how properties change as you move across periods (rows) or down groups (columns).

In the case of alkaline earth metals, which reside in group 2 of the periodic table, several properties show notable trends. One such trend is solubility, particularly in compounds like hydroxides. As you move down the group from beryllium (e{Be}) to barium (e{Ba}), the solubility of their hydroxides in water generally increases. This is significant because understanding this trend helps predict the reactivity and behavior of these elements in various chemical processes.

Lattice Energy

Lattice energy is a key concept when discussing the solubility of ionic compounds such as alkaline earth metal hydroxides. It is defined as the energy released when gaseous ions bind to form an ionic solid. The magnitude of lattice energy depends significantly on the sizes and charges of the ions involved.

As you move down the group of alkaline earth metals, the ionic size increases. Larger ions tend to form solids with lower lattice energies due to weaker attractions between the larger cations and their anions. Thus, as the lattice energy decreases, these hydroxides become more soluble in water. This decrease in lattice energy as we move from beryllium to barium makes the hydroxides of heavier alkaline earth metals dissolve more readily, reflecting an increase in solubility.

Hydration Energy

Hydration energy is another crucial concept impacting solubility. It refers to the energy released when ions are solvated or surrounded by water molecules. This energy varies depending on the charge and size of the ion.

In the case of alkaline earth metals, as you move down the group from beryllium to barium, the size of the metal ions increases. Although larger ions have lower hydration energies compared to smaller ions, the decrease in lattice energy as discussed earlier is more significant than the decrease in hydration energy.

Therefore, the net effect is an increase in solubility down the group, as the decrease in lattice energy outweighs the decrease in hydration energy. This is why compounds like magnesium hydroxide are less soluble than compounds like barium hydroxide.

Alkaline Earth Metals

Alkaline earth metals belong to group 2 of the periodic table and include beryllium, magnesium, calcium, strontium, and barium. These elements are characterized by having two electrons in their outermost energy level, leading to certain shared chemical properties such as forming +2 cations.

These metals form a variety of compounds, including hydroxides, which exhibit increasing solubility as you go down the group. This behavior is attributed to the periodic trends in lattice and hydration energies. Alkaline earth metals are reactive, though less so than their group 1 neighbors, the alkali metals.

They are commonly found in the earth's crust and are essential in various biological and industrial processes. Familiarity with these metals helps understand their applications in fields ranging from construction materials to aircraft and medical imaging technologies.