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

Question

The colligative properties of electrolytes require a slightly different approach than the one used for the colligative properties of non- electrolytes. The electrolytes dissociate into ions in solution. It is the number of solute particles that determine the colligative properties of a solution. The electrolyte solutions, therefore show abnormal colligative properties. To account for this effect we define a quantity; called the van't Hoff factor which is given by [solution] \(i=\) dissociation \(\mathrm{i}=1\) (for non - electrolytes); \(\mathrm{i}>1\) (for electrolytes, undergoing dissociation) \(\mathrm{i}<1\) (for solute, undergoing association) \(0.1 \mathrm{M} \mathrm{K}_{4}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]\) 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 is 3.4, which is option (a).

Step 1: Understand the ionization percentage

The compound K4[Fe(CN)6] ionizes in solution. It's given that the compound is 60% ionized. This means that 60% of the K4[Fe(CN)6] dissociates into ions, while the remaining 40% stays as the undissociated whole molecule.

Step 2: Determine dissociation products

The compound K4[Fe(CN)6] can dissociate into 4 K+ ions and one [Fe(CN)6]4- ion. This gives a total of 5 ions from a single formula unit when it completely dissociates.

Step 3: Calculate actual number of particles

The actual number of particles in solution combines the ions and undissociated units. - 60% of the compound dissociates into 5 ions, contributing 0.6 * 5 = 3 particles. - 40% remains undissociated, contributing 0.4 * 1 = 0.4 particles. The total number of particles per mole of formula unit is 3 + 0.4 = 3.4.

Step 4: Identify the van't Hoff factor formula

The van't Hoff factor \( i \) is the ratio of the actual number of particles in solution to the number of formula units initially present, which is: \[ i = \frac{\text{actual number of particles}}{\text{initial number of formula units}} \] Since initially there is 1 formula unit per mole.

Step 5: Calculate the van't Hoff factor

Using the formula from Step 4, substitute in the total number of particles calculated in Step 3 (which is 3.4):\[ i = \frac{3.4}{1} = 3.4 \] Therefore, the van't Hoff factor \( i \) is 3.4.

Key Concepts

Electrolytes

Electrolytes are substances that, when dissolved in water, dissociate into ions. These ions are charged particles that allow the solution to conduct electricity. This is why electrolytes are crucial in many biological and chemical processes. They come in the form of acids, bases, or salts, and are essential in maintaining the proper function of cells and organs in the body.

In chemistry, when a compound like K4[Fe(CN)6] is dissolved in water, it breaks down into individual ions. Here, the dissociation contributes positively to the unique properties of the solution, termed as colligative properties, which are significantly influenced by these ions. Knowing how compounds dissociate is essential to predicting and understanding how solutions will behave when electrolytes are present.

• Conductivity:** Solutions with dissolved electrolytes conduct electricity due to the presence of these ions.
• Colligative properties:** These include boiling point elevation, freezing point depression, vapor pressure lowering, and osmotic pressure.
• Dissociation grade:** The extent to which an electrolyte dissociates affects these properties. A higher ionization means more pronounced colligative properties.

Van't Hoff Factor

The van’t Hoff factor, denoted by \(i\), measures the effect of solute particles on the colligative properties of a solution. It is a critical component in understanding how electrolytes differ from non-electrolytes in their effects on colligative properties.

In simple terms, the van’t Hoff factor is the ratio of the total number of particles in solution after dissociation to the original number of formula units before dissociation. For non-electrolytes, which do not dissociate, \(i = 1\). However, for electrolytes, \(i\) is greater than 1 due to the formation of multiple ions from the dissociation of each formula unit. This is why solutions of electrolytes tend to behave differently than those of non-electrolytes.

The calculated van't Hoff factor informs us about the degree of dissociation and allows us to predict changes in colligative properties accurately. For example:

• Electrolyte solution:** Displays a van't Hoff factor greater than 1, increasing the solution's boiling point or lowering its freezing point more than an equivalent non-electrolyte solution.
• Dissociation impact:** An electrolyte that dissociates into three ions will have a van't Hoff factor approximating 3, assuming complete dissociation.

Dissociation

Dissociation is the process by which molecules or ionic compounds separate or split into smaller particles such as atoms, ions, or radicals. This process is vital in chemistry and biology because it allows the substances to participate in subsequent reactions or biological processes.

When electrolytes dissolve in water, they undergo dissociation, spreading evenly throughout the solution. The extent of this dissociation is typically a percentage, showing how much of the compound ionizes.

Consider the compound K4[Fe(CN)6], which dissociates into 4 K+ ions and one [Fe(CN)6]4- ion. If 60% of K4[Fe(CN)6] disassociates, it signifies that only 60% yields its total ion count while the rest remains as undissociated molecules.

This dissociation influences:

• Solution behavior:** The more the compound dissociates, the greater the number of particles in the solution, affecting the solution's colligative properties.
• Van’t Hoff factor calculation:** The degree of dissociation directly factors into calculating the van’t Hoff factor, shaping how dramatically the presence of solute affects the solution's properties.

Understanding dissociation helps in calculating and predicting the behavior of solutions, particularly when dealing with electrolytes. This provides insight into how different compounds impacts their surroundings, a focal point in both chemistry studies and practical applications.