Question

A $5\% $ solution of cane sugar $($molecular weight$ = 342)$ is isotonic with $1\% $ solution of substance X. The molecular weight of X is?
A: $171.2$
B: $68.4$
C: $34.2$
D: $136.2$

Answer 1

Hint: Isotonic solution refers to two solutions having same osmotic pressure across a semipermeable membrane. Semipermeable membrane is a type of biological or synthetic membrane that will allow certain molecules or ions to pass through it by diffusion.
Formula used: Molarity of solution $1$ $ = $Molarity of solution$2$
Molarity $ = \dfrac{{m \times 1000}}{{M \times V}}$ Where $m$ is given mass of solute, $M$ is molecular mass of solute, $V$ is volume of solution.

Complete step by step solution:
Solutions can have same osmotic pressure only if they have same molar concentration therefore,
Molar concentration of cane sugar $ = $ Molar concentration of X
$5\% $ Solution means $5g$ of solute is present in $100g$ of water. Density of water is $1g/c{m^3}$ therefore $100g$ of water is equal to $100ml$ of water. Same applies for $1\% $ solution. For cane sugar
Mass of solute$ = 5g$
Volume of solution$ = 100ml$
Molecular mass of solute$ = 342g$
For substance X, let molecular mass be ${M_2}$
Given mass of solute$ = 1g$
Volume of solution$ = 100ml$
Applying above mentioned formula
Molarity of solution $1$ $ = $Molarity of solution$2$
We will get
$\dfrac{{5 \times 1000}}{{342 \times 100}} = \dfrac{{1 \times 1000}}{{{M_2} \times 100}}$
$\dfrac{5}{{342}} = \dfrac{1}{{{M_2}}}$
${M_2} = \dfrac{{342}}{5}$
${M_2} = 68.4g$
Calculating we get mass of substance X to be $68.4g$ . So, the answer to this question is option B that is $68.4g$ .
Additional information: Terms related to isotonic solution are hypertonic solution and hypotonic solution
Hypertonic solutions are solutions which have comparatively high osmotic pressure. They have high concentration. In a hypertonic environment a cell tends to shrink, such kinds of solutions are helpful in food preservation.
Hypotonic solutions are solutions which have low osmotic pressure. Such solutions have low concentration. This environment causes a cell to swell. These solutions are not helpful in food preservation.
Isotonic solution has no effect on cells. In such environment cell neither shrink nor swell. This solution is also not helpful in food preservation.

Note: Don’t get confused with terms hypertonic and hypotonic. In hypotonic concentration of dissolved solute is less than that of other solution and in hypertonic concentration of dissolved solute is less than that of other solution.