Problem 29 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

Amongst the following hydroxides, the one which has the lowest value of \(K_{s p}\) at ordinary temperature (about \(25^{\circ} \mathrm{C}\) ) is [1990-1 Mark] (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 \( K_{sp} \) is \( \mathrm{Mg(OH)_2} \).

Step 1: Understanding Solubility Product

The solubility product constant \( K_{sp} \) is a measure of the solubility of a compound. A lower \( K_{sp} \) value indicates a less soluble compound, meaning it does not dissolve well in water. Our task is to find which of the given hydroxides has the lowest \( K_{sp} \) value at approximately room temperature (\( 25^{\circ} C \)).

Step 2: Evaluating Hydroxides

Check known \( K_{sp} \) values for the given hydroxides at \( 25^{\circ} C \): - \( \mathrm{Mg(OH)_2} \) has a \( K_{sp} \) of approximately \( 5.61 \times 10^{-12} \).- \( \mathrm{Ca(OH)_2} \) has a \( K_{sp} \) of approximately \( 5.02 \times 10^{-6} \).- \( \mathrm{Ba(OH)_2} \) is very soluble and thus has a much higher \( K_{sp} \).- \( \mathrm{Be(OH)_2} \) forms a complex ion and behaves differently, often being more soluble due to complexation.

Step 3: Identifying the Compound with Lowest \( K_{sp} \)

Comparing the \( K_{sp} \) values, \( \mathrm{Mg(OH)_2} \) has the lowest \( K_{sp} \) value. Therefore, it is the least soluble hydroxide among the options given. \( \mathrm{Be(OH)_2} \) does not have a simple \( K_{sp} \) due to its tendency to form complex ions, making it more soluble.

Key Concepts

Hydroxide Solubility

Hydroxide solubility refers to the ability of hydroxide compounds to dissolve in water. The solubility is often quantified by the solubility product constant, denoted as \( K_{sp} \). This constant provides insight into how readily a compound dissolves. For example, a smaller \( K_{sp} \) indicates lower solubility, which means the compound remains solid and undissolved in water.

Consider the hydroxides in the exercise: they are salts combining an alkaline earth metal with hydroxide ions \( (OH^-) \). Solubility varies depending on the interactions between these metal ions and hydroxide ions. This is why slight differences in chemical structure can lead to significant changes in their \( K_{sp} \) values.

In practical terms, understanding hydroxide solubility is crucial for predicting the behavior of these compounds in various chemical and environmental contexts. It helps in scenarios like calculating the concentration of ions in solutions, which is vital for reactions."},{

Inorganic Chemistry

Inorganic Chemistry is a branch of chemistry focusing on compounds that do not fit the criteria of organic compounds, which typically involve carbon-hydrogen bonds. This field covers a wide range of substances, including metals, minerals, and organometallic compounds.

One key aspect is understanding the relationships and reactivities between different elements and their compounds. For instance, the solubility and chemical behavior of hydroxides like those in the exercise are commonly examined under inorganic chemistry. These hydroxides are examples of simple inorganic ions interacting to form distinct structures with unique properties.

Inorganic chemistry also involves investigating the extraction, catalytic behaviors, and electron transport of various elements. Hence, it is fundamental not only for academic purposes but also for industrial applications, such as mining, material science, and environmental science."},{

Alkaline Earth Metals

Alkaline earth metals are a group of elements found in Group 2 of the periodic table. These elements include Beryllium (Be), Magnesium (Mg), Calcium (Ca), Strontium (Sr), Barium (Ba), and Radium (Ra). Known for their shiny surfaces and high melting points, they are less reactive than alkali metals but still play significant roles in chemistry and industry.

In terms of hydroxide compounds, each alkaline earth metal forms a specific hydroxide, like \( \mathrm{Mg(OH)_2} \) or \( \mathrm{Ca(OH)_2} \). The solubility of these hydroxides in water generally increases down the group. This trend is evident through observing the \( K_{sp} \) values—\( \mathrm{Mg(OH)_2} \) has a notably lower solubility than \( \mathrm{Ca(OH)_2} \) and \( \mathrm{Ba(OH)_2} \).

The properties of these metals make them suitable for various applications. For example, magnesium hydroxide is often used as an antacid and laxative. Understanding the differences in solubility among their compounds aids in these practical applications."}]} "],"sections":"