Question

$ 3\% $ solution of glucose is isotonic with $ 1\% $ of a non-volatile non-electrolyte substance the molecular mass of the substance would be
 $ A. $ $ 30 $
 $ B. $ $ 60 $
 $ C. $ $ 90 $
 $ D. $ $ 120 $

Answer 1

Hint: There are three types of solution such as isotonic solution, hypertonic solution and hypotonic solution. An isotonic solution is a solution that has the same concentration as another solution and their osmotic pressures are equal.

Complete step by step solution
In the given it is given that the $ 3\% $ solution of glucose is isotonic with $ 1\% $ of a non-volatile non-electrolyte substance. So, the osmotic pressure is equal. Osmotic pressure is denoted by $ \left( \pi \right) $
We know osmotic pressure $ \left( \pi \right) $ $ = CRT $ , where $ C $ is the concentration, $ R $ is a gas constant and $ T $ is a temperature
So, according to the isotonic condition,
 $ {\pi _{glu\cos e}} = {\pi _{solute}} $ $ \left( 1 \right) $
Where $ {\pi _{glu\cos e}} $ is the osmotic pressure of glucose and $ {\pi _{solute}} $ is the osmotic pressure of solute.
By relation, $ \pi = CRT $ , we get equation $ 1 $ as
 $ {C_{glu\cos e}}RT = {C_{solute}}RT $
 $ \Rightarrow $ $ {C_{glu\cos e}} = {C_{solute}} $
 $ \left( 2 \right) $
 $ \Rightarrow $ $ \dfrac{{{W_{glu\cos e}} \times 1000}}{{{M_{glu\cos e}} \times V}}\dfrac{{{W_{solute \times }}1000}}{{{M_{solute}} \times V}} $ $ \left( 3 \right) $ $ \left[ {\because C = \dfrac{{W \times 1000}}{{M \times V}}} \right] $
Where $ {W_{gluo\cos e}} $ and $ {W_{solute}} $ is the weight of glucose and solute whereas $ {M_{glu\cos e}} $ and $ {M_{solute}} $ molar mass of glucose and solute.
Now, by solving equation $ \left( 3 \right) $ .we get the final relation to solve the given question, we get
 $ \dfrac{{{W_{glu\cos e}}}}{{{M_{glu\cos e}}}} = \dfrac{{{W_{solute}}}}{{{M_{solute}}}} $ $ \left( 4 \right) $
In our question $ 3\% $ of glucose solution means $ 3g $ of solution present in $ 100g $ of solution. Similarly, $ 1\% $ of solution means $ 1g $ of solute present in $ 100g $ of solution. We also know the molar mass of glucose is $ 180g/mol $
By using the above equation $ \left( 4 \right) $ , we get
 $ \dfrac{3}{{180}} = \dfrac{1}{{{M_{solute}}}} $
 $ \Rightarrow $ $ {M_{solute}} = 60g/mol $
Thus, the molar mass of solute is $ 60g/mol $ . So, the correct answer is $ B. $

Additional Information
Hypertonic solution: Hypertonic solutions are solutions having comparatively high osmotic pressure. Hypertonic solutions are helpful for food preservation.
Hypotonic solution: It is defined as the solution having lower osmotic pressure. Hypotonic solutions are not helpful for food preservation.

Note:
Osmotic pressure is the minimum pressure that is required to be applied to a solution to prevent the inward flow of its pure solvent across a semipermeable membrane. It is also defined as the pressure required stopping the osmosis.