Question

A 1.17 $\%$ solution of $ {\text{NaCl}} $ is isotonic with $ 7.2\% $ solution of glucose. Calculate the value of “i” of $ {\text{NaCl}} $ .
(A) 1
(B) 2
(C) 3
(D) 4

Answer 1

Hint: The Van’t Hoff factor or “i” is a relation between the ideal value of ideal value of the solution’s colligative properties and the observed colligative properties. For most of the non-electrolytes, the Van’t Hoff factor is essentially 1 while for most ionic compounds, the Van’t Hoff factor is equal to the discrete ions in the formula unit of the substance.
 $ {{\pi = iCRT}} $
where $ {{\pi }} $ is the osmotic pressure, C is the concentration of the solution, R is a universal gas constant, T is the temperature on the kelvin scale.

Complete Stepwise solution
As per the question, it can be written that,
 $ 1.17\% $ Solution of $ {\text{NaCl}} $ = $ 7.2\% $ solution of glucose
Number of moles of sodium chloride in $ 1.17\% $ Solution of $ {\text{NaCl}} $ = $ \dfrac{{1.17}}{{58.5}} = 0.02 $ moles of sodium chloride, where $ 58.5 $ grams is the molecular weight of sodium chloride.
Number of moles of glucose in $ 7.2\% $ solution of glucose = $ \dfrac{{7.2}}{{180}} = 0.04 $ moles of glucose, the molecular weight of glucose being 180 grams.
From the formula of osmotic pressure we know that, $ {{\pi = iCRT}} $
As the two solutions are isotonic, the osmotic pressure of both the solutions are equal and hence,
Osmotic pressure of sodium chloride = Osmotic pressure of glucose
 $ {{i}} 0.02 {\text{R T = 1}} 0.04 {\text{R T}} $
Rearranging:
 $ \Rightarrow {\text{i = }}\dfrac{{{{1}} 0.04}}{{0.02}} $ = 2.
Calculate the value of “i” of $ {\text{NaCl}} $ is 2.
Hence, the correct answer is option B.

Note:
If two solutions are separated from each other by a semipermeable membrane then, an isotonic solution is one that has the same solute concentration as the other solution on the other side of the membrane. Here the two solutions in questions are, sodium chloride solution and glucose solution. Among them, sodium chloride is an electrolyte and thus its Van’t Hoff factor will be greater than one.