Problem 137 - A Complete Resource Book in Chemistry for JEE Main

Question

\(0.1 \mathrm{M} \mathrm{K}_{4}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]\) is \(60 \%\) ionized. What will be its van't Hoff factor? (a) \(3.4\) (b) \(1.7\) (c) \(2.4\) (d) \(2.2\)

Step-by-Step Solution

Answer

The van't Hoff factor for the ionized compound is 3.4, corresponding to option (a).

Step 1: Understanding the Problem

We are given a complex compound, \( \mathrm{K}_{4}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right] \), which is \(60\%\) ionized in solution. We need to determine its van't Hoff factor (\(i\)). The van't Hoff factor represents the effective number of particles in solution after dissociation or ionization.

Step 2: Write Ionization Equation

Write the dissociation equation for \( \mathrm{K}_{4}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right] \). Upon ionization, it dissociates into 4 potassium ions \( (\mathrm{K}^+) \) and one \( \left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{4-} \) complex ion. Thus, the equation is:\[ \mathrm{K}_{4}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right] \rightarrow 4 \mathrm{K}^+ + \left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{4-} \]

Step 3: Calculate Expected Number of Particles

In a complete ionization scenario, the compound would dissociate into 5 particles: 4 potassium ions and 1 \( \left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{4-} \). Thus, the theoretical van't Hoff factor \(i_0\) would be \(5\).

Step 4: Determine Degree of Ionization

Given that \(60\%\) of the compound is ionized, it means \(0.6\) fraction of the compound dissociates completely. Calculate the number of actual dissociated particles:\[ \text{Dissociated particles} = 0.6 \times 5 = 3 \]

Step 5: Calculate Van't Hoff Factor

The van't Hoff factor \(i\) is the total number of particles in solution per formula unit initially put into solution. Since \(3\) particles result from ionization, and \(1\) molecule remains undissociated, it results in \(3 + 0.4\) (undissociated particles remain as one identity forming 0.4 based on non-dissociation of 40%) = \(3.4\) total effective particles.Thus, \[ i = \frac{\text{particles from dissociation} + \text{undissociated fraction}}{\text{formula units initially}} = 3.4 \]

Step 6: Select the Correct Option

Compare our calculated van't Hoff factor with the provided options. The correct choice is (a) \(3.4\).

Key Concepts

Ionization

Ionization is a fundamental chemical process where a compound dissolves or breaks apart into ions when added to a solvent, like water. When a substance ionizes, its neutral compounds split into charged particles called ions. For example, when potassium hexacyanoferrate(II), given as \( \mathrm{K}_{4}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right] \), dissolves, it ionizes to produce:

• Four potassium ions \( (\mathrm{K}^+) \)
• One hexacyanoferrate(II) ion \( \left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{4-} \)

Each ion in the solution contributes to various properties like electrical conductivity. Thus, understanding ionization helps us predict these behaviors.

Dissociation Equation

The dissociation equation is a key tool in chemistry to understand how complex compounds break into simpler ions in solution. Writing this equation requires knowing the chemical structure and composition of the compound.For our example, the dissociation equation for potassium hexacyanoferrate(II) operates as follows:\[ \mathrm{K}_{4}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right] \rightarrow 4 \mathrm{K}^+ + \left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{4-} \]This equation shows that, upon complete dissociation, 5 ions are produced per formula unit:

• 4 potassium ions \( (\mathrm{K}^+) \)
• 1 negatively charged hexacyanoferrate ion \( \left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{4-} \)

The dissociation equation thereby helps us calculate the potential impact of ionization on properties like freezing point and boiling point changes.

Degree of Ionization

The degree of ionization is an important concept that quantifies the fraction or percentage of a compound that ionizes in solution. When a compound is not fully ionized, as in our example where ionization is 60%, a certain percentage remains undissociated.Here is how it works:

• Total potential dissociated particles if fully ionized = 5
• Given ionization level = 60% or 0.6
• Dissociated particles = \(0.6 \times 5 = 3\)

The degree of ionization reveals how much of the compound actually contributes to ion forming in the solution, affecting the van't Hoff factor used to predict colligative properties changes.

Complex Compound

Complex compounds, also known as coordination compounds, are central to fields like chemistry and biology. These structures consist of a central atom or ion, typically metallic, bonded to surrounding molecules or ions known as ligands.For instance, in \(\mathrm{K}_{4}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]\), "\([\mathrm{Fe}(\mathrm{CN})_{6}]^{4-}\)" is a metal complex.Complex compounds feature:

• Central atom: Typically a metal, here Iron (Fe)
• Ligands: Atoms or molecules, like cyanide ions \((\mathrm{CN}^-)\), that bind to the metal atom

These compounds often have specific geometric configurations and exhibit unique reactivity and properties, like color, magnetism, and solubility. Recognizing these features aids in understanding many chemical behaviors and applications.