Question

What should be the molarity of aqueous solution of \(\text{K}_{2}\text{SO}_{4}\) so that it is isotonic with aqueous \(1\ \text{M}\) glucose at same temperature, assuming complete dissociation?

• A. \(1\ \text{M}\)
• B. \(3\ \text{M}\)
• C. \(0.333\ \text{M}\)
• D. \(0.5\ \text{M}\)

Hint:

Isotonic solutions have equal osmotic pressure, so the van't Hoff factor times molarity must be equal.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
Isotonic solutions have equal osmotic pressure. Since \(\pi = iCRT\), we need \(i_1C_1 = i_2C_2\) at the same temperature.

Step 2: Van't Hoff factors
Glucose does not dissociate, so \(i = 1\). \(\text{K}_2\text{SO}_4\rightarrow 2\text{K}^{+}+\text{SO}_4^{2-}\) dissociates completely, so \(i = 3\).

Step 3: Calculation
\(3\times C = 1\times 1\), so \(C = \dfrac{1}{3} = 0.333\ \text{M}\).

Final Answer:
The K2SO4 solution must be 0.333 M. \[ \boxed{\text{(C) }0.333\ \text{M}} \]