Problem 153 - A Complete Resource Book in Chemistry for JEE Main

Question

Which one of the following aqueous solutions will exhibit highest boiling point? (a) \(0.05 \mathrm{M}\) glucose (b) \(0.01 \mathrm{M} \mathrm{KNO}_{3}\) (c) \(0.015 \mathrm{M}\) urea (d) \(0.01 \mathrm{M} \mathrm{Na}_{2} \mathrm{SO}_{4}\)

Step-by-Step Solution

Answer

The 0.05 M glucose solution has the highest boiling point.

Step 1: Identify Colligative Properties

Boiling point elevation is a colligative property, meaning it depends on the number of solute particles in solution, not their identity. We calculate the boiling point elevation using the formula: \[ \Delta T_b = i \cdot K_b \cdot m \]where \( \Delta T_b \) is the boiling point elevation, \( i \) is the van 't Hoff factor, \( K_b \) is the ebullioscopic constant, and \( m \) is the molality of the solution.

Step 2: Determine van 't Hoff Factor

The van 't Hoff factor \( i \) represents the number of particles the solute dissociates into:- For glucose (\( \mathrm{C}_6\mathrm{H}_{12}\mathrm{O}_6 \)), \( i = 1 \) as it does not dissociate.- For \( \mathrm{KNO}_3 \), \( i = 2 \) as it dissociates into \( \mathrm{K}^+ \) and \( \mathrm{NO}_3^- \).- For urea (\( \mathrm{CO(NH}_2)_2 \)), \( i = 1 \) as it does not dissociate.- For \( \mathrm{Na}_2\mathrm{SO}_4 \), \( i = 3 \) as it dissociates into 2 \( \mathrm{Na}^+ \) and 1 \( \mathrm{SO}_4^{2-} \).

Step 3: Calculate Effective Molality

The effective molality \( m_{effective} \) is calculated by multiplying the molality \( m \) by \( i \):- For glucose: \( m_{effective} = 0.05 \times 1 = 0.05 \)- For \( \mathrm{KNO}_3 \): \( m_{effective} = 0.01 \times 2 = 0.02 \)- For urea: \( m_{effective} = 0.015 \times 1 = 0.015 \)- For \( \mathrm{Na}_2\mathrm{SO}_4 \): \( m_{effective} = 0.01 \times 3 = 0.03 \)

Step 4: Determine Highest Boiling Point Elevation

The solution with the highest \( m_{effective} \) will have the greatest boiling point elevation. Compare the values:- Glucose: 0.05- \( \mathrm{KNO}_3 \): 0.02- Urea: 0.015- \( \mathrm{Na}_2\mathrm{SO}_4 \): 0.03Since 0.05 is the highest, the solution with glucose exhibits the highest boiling point.

Key Concepts

Boiling Point Elevation

Boiling point elevation is a fascinating physical property of solutions that helps us understand how solutes affect the boiling point of a solvent. When a solute is dissolved in a solvent, it disrupts the solvent's ability to evaporate into vapor. Consequently, the solution will have a higher boiling point than the pure solvent. This occurrence is described by the formula for boiling point elevation: \[ \Delta T_b = i \cdot K_b \cdot m \] Here, \( \Delta T_b \) represents the increase in boiling point, \( i \) is the van 't Hoff factor, \( K_b \) is a constant specific to the solvent (called the ebullioscopic constant), and \( m \) refers to the solution's molality.
Boiling point elevation is categorized as one of the colligative properties because it relies on the number of solute particles in the solution rather than the type of solute. This means that regardless of the solute's nature, the key factor is how many particles it contributes to the solution. When more particles are present, the boiling point elevates further, making it a valuable concept in determining the boiling behavior of various solutions.

van 't Hoff Factor

The van 't Hoff factor, represented by \( i \), plays a crucial role in colligative properties, including boiling point elevation. It defines the number of particles that a solute releases when dissolved in a solution. Specifically, it accounts for the dissociation of ionic compounds.
For instance, when addressing non-electrolytes like glucose or urea, \( i \) equals 1 because these compounds do not break apart into ions. However, for ionic compounds such as \( \mathrm{KNO}_3 \) (which dissociates into \( \mathrm{K}^+ \) and \( \mathrm{NO}_3^- \)) and \( \mathrm{Na}_2\mathrm{SO}_4 \) (which dissociates into \( 2 \mathrm{Na}^+ \) and \( \mathrm{SO}_4^{2-} \)), \( i \) equals the number of resulting particles.
Understanding the van 't Hoff factor is central when calculating the colligative properties of a solution as it determines the effective concentration of solute particles. As a rule of thumb, the greater the number of particles produced upon dissociation, the bigger the effect on properties like boiling point elevation.

Molality

Molality is a concentration metric that is particularly useful in colligative property calculations. Unlike molarity, which depends on the volume of solution (and can change with temperature), molality is centered around the mass of the solvent, making it independent of temperature effects.
Defined as the number of moles of solute per kilogram of solvent, molality (\( m \)) is calculated using the formula: \[ m = \frac{\text{moles of solute}}{\text{kilograms of solvent}} \] Because of this, molality remains constant regardless of temperature changes, which is beneficial in experiments that involve heat, such as those studying boiling point elevation.
In boiling point elevation, the molality contributes directly to the calculation of \( \Delta T_b \), indicating how concentrated the solution is with solute particles. To determine the true impact of a solute on a solution, scientists often use effective molality, multiplying the molality by the van 't Hoff factor to reflect the actual particle concentration in cases where dissociation occurs.