Q. A 5% solution of cane sugar (molar mass 342) is isotonic with 1% of a solution of an unknown solute. The molar mass of unknown solute in g/mol is

A) 136.2
B) 171.2
C) 68.4
D) 34.2
Explanation

(c)
Two solutions are isotonic if their osmotic pressure are equal.
$\pi_{1} = \pi_{2}\$
$M_{1}ST_{1} = M_{2}ST_{2}$
($M_{1}and\ M_{2}\ are\ molarities$)
At a given temperature,
$\ \ \ \ \ \ \ \ \ \ \ \ M_{1} = M_{2}$
$\ \ \ \ \ \ \ \frac{\ 1000w_{1}}{m_{1}V_{1}} = \frac{1000w_{2}}{m_{2}V_{2}}\$ ($V_{1} = V_{2} = 100mL$)
Cane sugar unkown
$\therefore\ \ \ \ \ \frac{w_{1}}{m_{1}} = \frac{w_{2}}{m_{2}}\$
$\ \ \ \ \ \ \ \ \ \ \frac{5}{329} = \frac{1}{m_{2}}$
$m_{2} = \frac{342}{5}$=68.4 g $mol^{- 1}$

Dr. Abubacker
Reviewed by Dr. Abubacker

Physics Educator & NEET/JEE Specialist

Ph.D. in Physics with 19+ years of teaching experience.

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