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

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.