Question

Which of the following pair of solutions is isotonic?
\[ A.\ 18\,g/L\ \text{of glucose solution and }6\,g/L\ \text{of urea solution} \] \[ B.\ 10\,g/L\ \text{of glucose solution and }10\,g/L\ \text{of urea solution} \] \[ C.\ 0.01\,M\ NaOH\ \text{solution and }0.02\,M\ \text{glucose solution} \] \[ D.\ 0.01\,M\ NaCl\ \text{solution and }0.01\,M\ \text{glucose solution} \] (Assume that NaCl undergoes complete dissociation)

• A. A and B
• B. A and C
• C. B and D
• D. B and C

Hint:

For isotonic solutions, \[ iC=\text{same} \] Non-electrolytes have \[ i=1 \] while electrolytes have higher \(i\) values because of dissociation.

Answer 1

The Correct Option is B

Step 1: Recall the condition for isotonic solutions.
Two solutions are isotonic if they have the same osmotic pressure: $\pi_1 = \pi_2$, i.e., $i_1 C_1 R T = i_2 C_2 R T$, which simplifies to $i_1 C_1 = i_2 C_2$, where $i$ = van't Hoff factor.
Step 2: Analyze Pair A.
Solution 1: 18 g/L glucose. Molar mass of glucose (C₆H₁₂O₆) = 180 g/mol. $C_1 = 18/180 = 0.1$ M. Glucose does not ionize, $i_1 = 1$. Effective osmolarity = $1 \times 0.1 = 0.1$ M. Solution 2: 6 g/L urea. Molar mass of urea (CH₄N₂O) = 60 g/mol. $C_2 = 6/60 = 0.1$ M. Urea does not ionize, $i_2 = 1$. Effective osmolarity = $1 \times 0.1 = 0.1$ M. Since both = 0.1 M, Pair A is ISOTONIC.
Step 3: Analyze Pair C.
Solution 1: 0.01 M NaOH. NaOH is a strong electrolyte, $i = 2$ (Na⁺ + OH^-). Effective osmolarity = $2 \times 0.01 = 0.02$ M. Solution 2: 0.01 M NaCl. NaCl is a strong electrolyte, $i = 2$ (Na⁺ + Cl^-). Effective osmolarity = $2 \times 0.01 = 0.02$ M. Both have effective osmolarity = 0.02 M, so Pair C is ISOTONIC.
Step 4: Check other pairs (if applicable).
Pairs B and D would have different effective osmolarities. For instance, a solution of a non-electrolyte at a different concentration, or one with $i > 1$ and a different molarity, would not match.
Step 5: Confirm the answer.
Pairs A and C are isotonic. Both pairs have equal effective molar concentrations (after accounting for ionization).
Step 6: State the final answer.
The isotonic pairs are A (glucose 0.1 M and urea 0.1 M) and C (0.01 M NaOH and 0.01 M NaCl, both giving effective 0.02 M).
\[ \boxed{\text{Pairs A and C are isotonic (option 2)}} \]