Problem 4 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

\(\mathrm{K}_{2} \mathrm{HgI}_{4}\) is \(40 \%\) ionised in aqueous solution. The value of its van't Hoff factor (i) is : (a) \(1.6\) (b) \(1.8\) (c) \(2.0\) (d) \(2.2\)

Step-by-Step Solution

Answer

The van't Hoff factor is 2.2.

Step 1: Understand the problem

The question asks to determine the van't Hoff factor (i) for the compound \(\mathrm{K}_2\mathrm{HgI}_4\) which is 40% ionised when dissolved in water. The van't Hoff factor reflects how many particles a solute forms in solution compared to the number of formula units initially present.

Step 2: Determine the initial dissociation

Before ionisation, \(\mathrm{K}_2\mathrm{HgI}_4\) is a single compound. If it were to completely dissociate, it would produce 3 ions (2 K+ and 1 HgI4^{2-}). This means if 100% ionised, the van't Hoff factor would be 3.

Step 3: Account for partial dissociation

Given that \(\mathrm{K}_2\mathrm{HgI}_4\) is 40% ionised, only 40% of the compound dissociates into ions. Therefore, the contribution to the additional number of particles from dissociation is 40% of the ideal situation. For 100 molecules, 40 would contribute additional ions, resulting in an increase of 0.4 * 3 = 1.2 in the number of particles.

Step 4: Calculate the van't Hoff factor

Initially, there is 1 particle since the compound is initially viewed as a single formula unit. The ionisation added 1.2 particles through dissociation. Therefore, the total number of particles after partial ionisation is 1 + 1.2 = 2.2. Thus, the van’t Hoff factor \(i\) is 2.2.

Key Concepts

Ionisation

Ionisation refers to the process where a neutral compound breaks apart into charged particles called ions when dissolved in a solution. This occurs in many chemical compounds when they are mixed with a solvent, like water. For example, the compound \(\mathrm{K}_2\mathrm{HgI}_4\) when ionised, partially breaks down to form ions. Ionisation is crucial for understanding how materials interact in solutions and is directly related to concepts like the van't Hoff factor. When \(40\%\) ionisation is mentioned, it means that out of \(100\) molecule units, \(40\) will split to form ions. In a solution that's not fully ionised, not all molecules separate into ions, affecting properties like boiling and freezing points.

Dissociation

Dissociation is a specific type of ionisation where compounds like salts split into their respective ions in a solution. For \(\mathrm{K}_2\mathrm{HgI}_4\), dissociation results in the formation of \(2\) potassium ions \(\text{(K}^+\text{)}\) and a single \(\text{mercuric iodate} (\text{HgI}_4^{2-})\). In this case, full dissociation would create three ions in total for each formula unit. Thus, if \(\mathrm{K}_2\mathrm{HgI}_4\) were \(100\%\) dissociated, it would form three particles from one. However, with \(40\%\) dissociation, not the entire compound converts into ions, leading to fewer new particles.

Aqueous Solution

An aqueous solution is one where water is the solvent. In chemistry, a solvent is a liquid in which substances (the solute) are dissolved to form a solution. Water is often used because of its ability to dissolve many substances due to its polar nature.When \(\mathrm{K}_2\mathrm{HgI}_4\) is dissolved in water, it forms an aqueous solution. This solution facilitates the ionisation process by allowing the molecules of \(\mathrm{K}_2\mathrm{HgI}_4\) to interact well with water molecules, promoting partial dissociation and formation of ions. The behavior of substances in an aqueous solution is essential for understanding their chemical properties and reactions.

Chemical Equilibrium

Chemical equilibrium is a state in which the forward and reverse reactions occur at the same rate, leading to the appearance of no net change in the concentrations of reactants and products.In the context of ionisation and dissociation, \(\mathrm{K}_2\mathrm{HgI}_4\)'s equilibrium in an aqueous solution demonstrates this balance. Even though \(40\%\) of \(\mathrm{K}_2\mathrm{HgI}_4\) dissociates, the remaining compound stays non-ionised, maintaining equilibrium between the ions formed and the undissociated molecules.Equilibrium is essential in understanding the extent to which a compound will ionise or dissociate in solution, and contributes to predicting properties like the van't Hoff factor, which reflects the effective number of particles present in solution.