Question

A \[5\% \]solution of cane sugar (molar mass\[342\]) is isotonic with \[1\% \] of a solution of an unlike solute. The molar mass of unknown in g/mol is:
A. \[136.2\]
B. \[171.2\]
C. \[68.4\]
D. \[34.2\]

Answer 1

Hint: Isotonic solutions are the solution which contains the same concentration of solute on both sides of the membrane so that no movement of molecules occurs from one side to another side. The movement of molecules from a side low concentration to the side of high concentration is called osmosis.

Complete step by step answer: The two solutions are isotonic which indicates that the concentrations of the solutions are equal. The concentration of cane sugar = concentration of unknown solution.
The solution of cane sugar is \[5\% \] and its molar mass is\[342\]. Therefore the moles of cane sugar will be:
Molar concentration = \[\dfrac{{5/100}}{{342/1000}}\]
                   = $\dfrac{5}{{342}} \times \dfrac{{1000}}{{100}}$
                   =$0.146mol{L^{ - 1}}$.
The concentration given of unknown solutions is\[1\% \]. Let the molar mass of this solution be \[M\].
Thus molar concentration = $\dfrac{{1/100}}{{M/1000}}$
                   =$\dfrac{1}{M} \times \dfrac{{1000}}{{100}}$
                   =$\dfrac{{10}}{M}mol{L^{ - 1}}$ .
Hence, for isotonic solution the equation of equality is, $0.146 = \dfrac{{10}}{M}$
                                            $M = \dfrac{{10}}{{0.146}}$
                                            $M = 68.4gmo{l^{ - 1}}$ .
Thus, the molar mass of unknown solution with concentration of \[1\% \] is$68.4g/mol$.
So, the correct answer is “Option C”.

Note: Isotonic solutions have the same molar concentrations. The properties associated with solutions like osmotic pressure, lowering of vapour pressure, elevation in boiling point and depression in freezing point are changeable when the solutions are isotonic with each other. These properties are known as colligative properties and they depend only on the number of molecules. The common saline used for medical purposes is an example of isotonic solution. It is isotonic with the blood stream of the patient and hence when it is administered it allows the movement of water across the cell so that the loss and gain of water fluid by the cell remains constant.