Question

Consider the following pairs of solution which will be isotonic at the same temperature. The number of pairs of solutions is/are...... 
A. 1 M aq. NaCl and 2 M aq. Urea 
B. 1 M aq. CaCl₂ and 1.5 M aq. KCl 
C. 1.5 M aq. AlCl₃ and 2 M aq. Na₂SO₄ 
D. 2.5 M aq. KCl and 1 M aq. Al₂(SO₄)₃

Answer 1

Correct Answer: 4

Isotonic Solution Analysis 

Isotonic solutions have the same osmotic pressure. Osmotic pressure is directly proportional to the concentration of solute particles. Therefore, isotonic solutions have the same concentration of solute particles. We need to determine the concentration of particles in each solution, considering dissociation of ionic compounds.

• A. \( \text{NaCl} \) dissociates into 2 ions (\( \text{Na}^+ \) and \( \text{Cl}^- \)). So, 1 M \( \text{NaCl} \) gives \( 1 \text{ M} \times 2 = 2 \text{ M} \) ions. Urea does not dissociate, so 2 M urea remains 2 M particles. These solutions are isotonic.
• B. \( \text{CaCl}_2 \) dissociates into 3 ions (\( \text{Ca}^{2+} \) and \( 2\text{Cl}^- \)). So, 1 M \( \text{CaCl}_2 \) gives \( 1 \text{ M} \times 3 = 3 \text{ M} \) ions. \( \text{KCl} \) dissociates into 2 ions (\( \text{K}^+ \) and \( \text{Cl}^- \)). So, 1.5 M \( \text{KCl} \) gives \( 1.5 \text{ M} \times 2 = 3 \text{ M} \) ions. These solutions are isotonic.
• C. \( \text{AlCl}_3 \) dissociates into 4 ions (\( \text{Al}^{3+} \) and \( 3\text{Cl}^- \)). So, 1.5 M \( \text{AlCl}_3 \) gives \( 1.5 \text{ M} \times 4 = 6 \text{ M} \) ions. \( \text{Na}_2\text{SO}_4 \) dissociates into 3 ions (\( 2\text{Na}^+ \) and \( \text{SO}_4^{2-} \)). So, 2 M \( \text{Na}_2\text{SO}_4 \) gives \( 2 \text{ M} \times 3 = 6 \text{ M} \) ions. These solutions are isotonic.
• D. \( \text{KCl} \) dissociates into 2 ions (\( \text{K}^+ \) and \( \text{Cl}^- \)). So, 2.5 M \( \text{KCl} \) gives \( 2.5 \text{ M} \times 2 = 5 \text{ M} \) ions. \( \text{Al}_2\text{(SO}_4)_3 \) dissociates into 5 ions (\( 2\text{Al}^{3+} \) and \( 3\text{SO}_4^{2-} \)). So, 1 M \( \text{Al}_2\text{(SO}_4)_3 \) gives \( 1 \text{ M} \times 5 = 5 \text{ M} \) ions. These solutions are isotonic.

Conclusion:

All four pairs are isotonic. Therefore, the number of isotonic pairs is 4.

Answer 2

For two solutions to be isotonic, the total number of ions should be the same. Checking the pairs for ion concentration:
- A: 1 M NaCl gives 2 ions, and 2 M Urea gives 2 ions — isotonic.
- B: 1 M CaCl\(_2\) gives 3 ions, and 1.5 M KCl gives 3 ions — isotonic.
- C: 1.5 M AlCl\(_3\) gives 6 ions, and 2 M Na\(_2\)SO\(_4\) gives 6 ions — isotonic.
- D: 2.5 M KCl gives 5 ions, and 1 M Al\(_2\)(SO\(_4\))\(_3\) gives 5 ions — isotonic.
Thus, all 4 pairs are isotonic.