Problem 44 - A Complete Resource Book in Chemistry for JEE Main

Question

Amongst the following hydroxides, the one which has the lowest value of \(K_{s p}\) at ordinary temperature (about \(\left.25^{\circ} \mathrm{C}\right)\) is (a) \(\mathrm{Mg}(\mathrm{OH})_{2}\) (b) \(\mathrm{Ca}(\mathrm{OH})_{2}\) (c) \(\mathrm{Ba}(\mathrm{OH})_{2}\) (d) \(\mathrm{Be}(\mathrm{OH})_{2}\)

Step-by-Step Solution

Answer

The hydroxide with the lowest value of \(K_{sp}\) is \(\mathrm{Mg(OH)}_{2}\).

Step 1: Understand Solubility Product Constant

The solubility product constant (K_{sp}) of a compound is a reflection of its solubility. A lower value of K_{sp} indicates lower solubility of the ionic compound in water. Therefore, to find the compound with the lowest K_{sp}, we need to consider the one with the least solubility.

Step 2: Assess Solubility Trends of Hydroxides

Typically, the solubility of alkaline earth metal hydroxides ( ext{Group II}) increases as we move down the group in the periodic table. Hence,  ext{Mg(OH)}_{2} will generally have a lower solubility and thus a lower K_{sp} value than hydroxides like  ext{Ca(OH)}_{2} or  ext{Ba(OH)}_{2}.

Step 3: Compare With Beryllium Hydroxide

 ext{Be(OH)}_{2} is unique because beryllium's behavior differs from other Group II elements due to its smaller atomic size and higher charge density, which makes its hydroxide less soluble than others. However, it's not as straightforward because complex ion formation can affect its apparent K_{sp}. Nevertheless, without such formation, it generally also has a low K_{sp}.

Step 4: Combine Known Information

Given the common trends and noted peculiarities in solubility and K_{sp} values,  ext{Mg(OH)}_{2} and  ext{Be(OH)}_{2} will have smaller K_{sp} compared to other options. Published data show that  ext{Mg(OH)}_{2} has particularly low K_{sp} at room temperature.

Key Concepts

Alkaline Earth Metal Hydroxides

Alkaline earth metal hydroxides are substances formed when alkaline earth metals, like magnesium, calcium, and barium, react with water to produce metal hydroxide compounds. These compounds have the general formula of \( M(OH)_2 \), where \( M \) represents the metal. These hydroxides are known for their role in various chemical processes and are often encountered in high school chemistry.

• They have varying solubility in water, which is influenced by periodic trends.
• Examples of alkaline earth metal hydroxides include magnesium hydroxide \(\text{Mg(OH)}_2\), calcium hydroxide \(\text{Ca(OH)}_2\), and barium hydroxide \(\text{Ba(OH)}_2\).

Understanding these hydroxides helps in grasping broader concepts in chemistry, such as solubility and chemical reactions. Their solubility trends can be used to predict how these compounds will behave in reactions.

Periodic Table Trends

The periodic table is an excellent tool for predicting the behavior of elements, including their hydroxides. Within the alkaline earth metals (group 2), there are trends that can help us understand changes in properties as we move from one element to another.

• Solubility: As you move down group 2 from beryllium to barium, the solubility of their hydroxides generally increases.
• Reactivity: With increasing atomic number, these metals become more reactive. Beryllium and magnesium are less reactive compared to calcium or barium.

These trends are essential because they provide a framework for predicting solubility patterns, which are useful for educational purposes and practical applications in chemistry.

Solubility Trends

Solubility trends help us understand how much of a substance will dissolve in a liquid, typically water. For alkaline earth metal hydroxides, solubility is quite important when discussing the solubility product constant \(K_{sp}\), which is a measure of this property.

• Solubility generally increases for alkaline earth metal hydroxides as you move down the periodic table.
• A lower \(K_{sp}\) value signifies less solubility, meaning that the compound is less likely to dissolve in water.

For example, magnesium hydroxide \(\text{Mg(OH)}_2\) has a lower \(K_{sp}\) than calcium hydroxide \(\text{Ca(OH)}_2\), making it less soluble. Recognizing these patterns helps students predict the behavior of different hydroxides in solution.

Beryllium

Beryllium is the first element in group 2 of the periodic table and is somewhat distinct compared to other metals in this group. Its small atomic size and high charge density give it unique properties.

• Beryllium forms chemical bonds that are more covalent in nature, compared to the largely ionic bonds of the other alkaline earth metals.
• Beryllium hydroxide \(\text{Be(OH)}_2\) has a low solubility due to these covalent characteristics, contributing to its lower \(K_{sp}\).

Understanding beryllium's behavior helps explain why it doesn’t follow some of the same trends as other alkaline earth metals, which is valuable in various chemical applications.

Magnesium Hydroxide

Magnesium hydroxide, \(\text{Mg(OH)}_2\), is one of the most recognizable compounds of the alkaline earth metals. Often known as "milk of magnesia," it is commonly used in medicine as an antacid to relieve indigestion and as a laxative.

• It has a low solubility in water, which results in a low \(K_{sp}\).
• This low solubility makes it less likely to dissolve, which is why it is effective in forming suspensions in liquids.

By understanding the solubility of magnesium hydroxide, students can grasp how it behaves in various chemical contexts, reinforcing key concepts in chemistry.