Question

Which of the following pairs of solution is isotonic?
(Molar mass of urea = 60, sucrose = 342 g mol\(^{-1}\))

• A. 3.0 g L\(^{-1}\) urea and 17.19 g L\(^{-1}\) sucrose
• B. 0.3 g L\(^{-1}\) urea and 1.719 g L\(^{-1}\) sucrose
• C. 3.0 g L\(^{-1}\) urea and 1.719 g L\(^{-1}\) sucrose
• D. 0.3 g L\(^{-1}\) urea and 17.19 g L\(^{-1}\) sucrose

Hint:

To check if two solutions are isotonic, calculate the molarities of the solutes and ensure that they are equal.

Answer 1

The Correct Option is A

Step 1: Understanding Isotonic Solutions.
Isotonic solutions are those that have the same osmotic pressure. The osmotic pressure depends on the molarity and van't Hoff factor of the solute. The osmotic pressure can be calculated as: \[ \Pi = i \cdot M \cdot R \cdot T \] Where \( \Pi \) is osmotic pressure, \( i \) is the van't Hoff factor (which is 1 for urea and sucrose), \( M \) is molarity, \( R \) is the gas constant, and \( T \) is temperature. For urea and sucrose to be isotonic, their molarities must be equal.

Step 2: Analyzing the options.
(A) 3.0 g L\(^{-1}\) urea and 17.19 g L\(^{-1}\) sucrose: Correct. By calculating their molarities using their molar masses (60 g mol\(^{-1}\) for urea and 342 g mol\(^{-1}\) for sucrose), we find that both have the same molarity, making them isotonic.
(B) 0.3 g L\(^{-1}\) urea and 1.719 g L\(^{-1}\) sucrose: Incorrect. The molarity of urea and sucrose in this option would not match, so they are not isotonic.
(C) 3.0 g L\(^{-1}\) urea and 1.719 g L\(^{-1}\) sucrose: Incorrect. The molarities of urea and sucrose are not equal, so this pair is not isotonic.
(D) 0.3 g L\(^{-1}\) urea and 17.19 g L\(^{-1}\) sucrose: Incorrect. The molarity of sucrose is too high compared to urea, so they are not isotonic.

Step 3: Conclusion.
The correct answer is (A) 3.0 g L\(^{-1}\) urea and 17.19 g L\(^{-1}\) sucrose, as they are isotonic solutions.