Problem 64 - A Complete Resource Book in Chemistry for JEE Main

Question

At same temperature, which pair of the following solutions are isotonic solutions? (a) \(0.2 \mathrm{M} \mathrm{BaCl}_{2}\) and \(0.2 \mathrm{M}\) urea (b) \(0.1 \mathrm{M}\) urea and \(0.1 \mathrm{MNaCl}\) (c) \(0.1 \mathrm{M} \mathrm{NaCl}\) and \(0.1 \mathrm{M} \mathrm{K}_{2} \mathrm{SO}_{4}\) (d) \(0.1 \mathrm{M} \mathrm{Ba}\left(\mathrm{NO}_{3}\right)_{2}\) and \(0.1 \mathrm{M} \mathrm{Na}_{2} \mathrm{SO}_{4}\)

Step-by-Step Solution

Answer

Option (d): 0.1 M \( \text{Ba(NO}_3)_2 \) and 0.1 M \( \text{Na}_2 \text{SO}_4 \) are isotonic.

Step 1: Understanding Isotonic Solutions

Isotonic solutions have the same osmotic pressure. The osmotic pressure depends on the total number of solute particles in the solution. To determine if two solutions are isotonic, we need to compare the concentration of particles they have in the solution.

Step 2: Analyzing the Solutions

For each solution, calculate the number of particles it dissociates into. - Urea does not dissociate, so a 0.2 M urea solution has 0.2 M particles.- \( \text{BaCl}_2 \) dissociates into \( \text{Ba}^{2+} \) and 2 \( \text{Cl}^- \), resulting in 3 particles. Therefore, 0.2 M \( \text{BaCl}_2 \) yields 0.6 M in particles.- \( \text{NaCl} \) dissociates into \( \text{Na}^+ \) and \( \text{Cl}^- \), giving 2 particles. Thus, 0.1 M \( \text{NaCl} \) results in 0.2 M in particles.- \( \text{K}_2 \text{SO}_4 \) dissociates into 2 \( \text{K}^+ \) and \( \text{SO}_4^{2-} \), giving 3 particles. A 0.1 M solution yields 0.3 M in particles.- \( \text{Ba(NO}_3)_2 \) dissociates into \( \text{Ba}^{2+} \) and 2 \( \text{NO}_3^- \), yielding 3 particles, hence 0.3 M in particles.- \( \text{Na}_2 \text{SO}_4 \) dissociates into 2 \( \text{Na}^+ \) and \( \text{SO}_4^{2-} \), also giving 3 particles, resulting in 0.3 M in particles.

Step 3: Comparing Solutions for Isotonicity

We compare the molar concentration of particles:(a) \( 0.2 \, \text{M} \, \text{BaCl}_2 \) = 0.6 M particles vs. 0.2 M urea = 0.2 M particles (Not Isotonic)(b) \( 0.1 \, \text{M} \, \text{urea} \) = 0.1 M particles vs. \( 0.1 \, \text{M} \, \text{NaCl} \) = 0.2 M particles (Not Isotonic)(c) \( 0.1 \, \text{M} \, \text{NaCl} \) = 0.2 M particles vs. \( 0.1 \, \text{M} \, \text{K}_2 \text{SO}_4 \) = 0.3 M particles (Not Isotonic)(d) \( 0.1 \, \text{M} \, \text{Ba(NO}_3)_2 \) = 0.3 M particles vs. \( 0.1 \, \text{M} \, \text{Na}_2 \text{SO}_4 \) = 0.3 M particles (Isotonic)

Key Concepts

Osmotic Pressure

Osmotic pressure is a vital concept when discussing solutions and their properties. It refers to the pressure required to prevent the flow of a solvent into a solution through a semipermeable membrane. This phenomenon is driven by the tendency of solvents to move towards areas of higher solute concentration. In simpler terms, the more solute particles present in a solution, the greater the osmotic pressure it exerts.

Osmotic pressure depends on the total number of solute particles, not on their identity. This ties into why isotonic solutions are essential in biological and chemical applications. Isotonic solutions have the same osmotic pressure, allowing them to maintain equilibrium without causing osmotic flow. This is imperative in medical solutions, where differences in osmotic pressure could cause cells to swell or shrink. By understanding osmotic pressure, one can determine whether solutions like those in the exercise are isotonic by comparing their solute particles.

Solute Dissociation

Solute dissociation plays a crucial role in calculating the actual molar concentration of particles in a solution. When certain solutes, especially salts and acids, dissolve in a solvent, they break apart into ions. This increases the total number of particles in the solution, affecting properties like osmotic pressure. Knowing how a solute dissociates helps predict its behavior in solutions.

For example, the compound \( \text{BaCl}_2 \) dissociates into one \( \text{Ba}^{2+} \) ion and two \( \text{Cl}^- \) ions, resulting in three particles per formula unit. On the other hand, a non-dissociating solute like urea remains as single particles in the solution. Calculating the total number of particles after dissociation is a necessary step in understanding if solutions are isotonic. This provides insight into their relative osmotic pressures.

Molar Concentration

Molar concentration is the number of moles of solute per liter of solution. This measurement is crucial in determining many aspects of a solution's behavior, such as its reactivity and colligative properties like osmotic pressure. When working with molar concentration in solutions involving dissociating solutes, it's important to consider how dissociation affects the total particle concentration.

The formula for molar concentration is straightforward: \( \text{C} = \frac{n}{V} \), where \( n \) is the number of moles and \( V \) is the volume in liters. However, when solute dissociation occurs, you must adjust the molar concentration to account for all particles. For instance, a 0.1 M solution of NaCl will have a total particle concentration of 0.2 M because it dissociates into two ions: \( \text{Na}^+ \) and \( \text{Cl}^- \). Thus, understanding molar concentration in context with solute dissociation is essential for accurate analysis of isotonicity in solutions.