A solution of 1.73 g of 'A' ( non-volatile and non-electrolyte ) in 100 cc of water is found to be isotonic with a 3.42% (wt. /vol.) solution of sucrose (C12H22O11) at same temperature. Molecular weight of ‘A’ is_____

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A solution of 1.73 g of 'A' ( non-volatile and non-electrolyte ) in 100 cc of water is found to be isotonic with a 3.42% (wt. /vol.) solution of sucrose ( $C_{12} H_{22} O_{11}$ ) at same temperature. Molecular weight of ‘A’ is______g/mole. $(C_{12} H_{22} O_{11} = 342)$

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answer is 173.

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Detailed Solution

We know that the isotonic solutions have the same molar concentration (i.e.,moles/lit).
Let the molecular weight of A be M
$∴$ Molar conc. Of A (moles/ litre) $= \frac{1.73}{M} \times \frac{1000}{100} = \frac{17.3}{M}$
Molar conc.of sucrose $= \frac{3.42}{342} \times \frac{1000}{100} = 0.1$
$\frac{17.3}{M} = 0.1; M = 173$