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

The isotonic solutions are (d) 0.1 M Ba(NO₃)₂ and 0.1 M Na₂SO₄.

Step 1: Understanding Isotonic Solutions

Isotonic solutions have the same osmotic pressure, which means the number of solute particles in solution should be equal. Osmotic pressure is directly proportional to the van 't Hoff factor (i), which represents the number of particles that a compound dissociates into in solution.

Step 2: Calculating Van 't Hoff Factor

For ionic compounds, each molecule dissociates into ions. For example, in \( \text{BaCl}_2 \), \(i = 3\) because it dissociates into \(\text{Ba}^{2+}\) and two \(\text{Cl}^-\) ions. For nonelectrolytes like urea, \(i = 1\) because it does not dissociate.

Step 3: Analyzing Each Option

Let's analyze each option separately to determine the van 't Hoff factor:(a) \( \text{BaCl}_2: i = 3 \) and urea: \( i = 1 \)(b) \( \text{NaCl}: i = 2 \) and urea: \(i = 1\)(c) \(\text{NaCl}: i = 2\) and \(\text{K}_2\text{SO}_4: i = 3\)(d) \(\text{Ba(NO}_3)_2: i = 3\) and \(\text{Na}_2\text{SO}_4: i = 3\)We look for pairs with equal values of \( i \cdot C \) (where \( C \) is the concentration).

Step 4: Compare Concentration and Van 't Hoff Product

Now, multiply the concentration \( C \) by the van 't Hoff factor \( i \) for each solution to see which pair results in equal values:(a) \(0.2 \times 3 = 0.6\) and \(0.2 \times 1 = 0.2\)(b) \(0.1 \times 2 = 0.2\) and \(0.1 \times 1 = 0.1\)(c) \(0.1 \times 2 = 0.2\) and \(0.1 \times 3 = 0.3\)(d) \(0.1 \times 3 = 0.3\) and \(0.1 \times 3 = 0.3\)The pair that results in the same value is option (d): \(0.3 = 0.3\).

Step 5: Conclusion

Therefore, the isotonic solutions are option (d), where \(0.1\text{ M Ba(NO}_3)_2\) and \(0.1\text{ M Na}_2\text{SO}_4\) both have a van 't Hoff product of \(0.3\).

Key Concepts

Osmotic Pressure

Osmotic pressure is a crucial concept in understanding how solutions behave in relation to each other. It is the pressure required to stop the flow of a solvent through a semi-permeable membrane that separates two solutions of different concentrations. Higher osmotic pressure indicates a greater tendency for solvent to move into the solution to balance concentration differences.

In isotonic solutions, the osmotic pressure is equal, meaning the flow of solvent is balanced between the two solutions. This balance helps in processes like maintaining cell stability and drug formulation, where osmotic equilibrium is vital.

• Osmotic pressure depends on solute concentration and temperature.
• The presence and type of solute (ionic or non-electrolyte) directly affects the osmotic pressure.

Understanding osmotic pressure helps predict how solutions will interact, ensuring proper conditions in both natural and industrial processes.

Van 't Hoff Factor

The Van 't Hoff factor, denoted as \( i \), plays a vital role in determining the osmotic pressure of a solution. It represents the number of particles into which a compound dissociates when dissolved. This factor directly influences colligative properties, including osmotic pressure.

When a substance dissolves, ionic compounds separate into multiple ions, increasing the Van 't Hoff factor. For instance:

• For \( ext{BaCl}_2 \), \( i = 3 \) as it dissociates into one \( ext{Ba}^{2+} \) ion and two \( ext{Cl}^- \) ions.
• Non-electrolytes like urea have \( i = 1 \) since they do not dissociate.

The factor is crucial in calculations involving colligative properties, where \( i \) is multiplied by the concentration \( C \) to predict changes in properties, such as boiling point elevation, freezing point depression, and especially osmotic pressure. Understanding the Van 't Hoff factor helps in accurately assessing the behavior of solutions in various chemical and biological contexts.

Ionic and Non-Electrolyte Solutions

Solutions are classified as ionic or non-electrolytes based on whether they dissociate into ions. This distinction is fundamental to understanding their behavior and properties, including osmotic pressure.

Ionic solutions contain solutes that dissociate into ions, thus increasing the number of particles in the solution. Examples include:

• \( ext{NaCl} \): dissociates into \( ext{Na}^+ \) and \( ext{Cl}^- \), making \( i = 2 \).
• \( ext{K}_2 ext{SO}_4 \): dissociates into two \( ext{K}^+ \) ions and one \( ext{SO}_4^{2-} \), making \( i = 3 \).

Non-electrolytes, like urea, do not dissociate into ions, which means they have a Van 't Hoff factor \( i = 1 \).

The nature of the solute affects how solutions react in biological systems and industrial processes. For example, understanding whether a solution is ionic or a non-electrolyte allows chemists to predict its colligative effects and its interaction with biological tissues.