A \(5\%\) solution of cane sugar (molecular weight \(= 342\)) is isotonic with \(1\%\) solution of substance \(X\). The molecular weight of \(X\) is?

68.4 g

The correct answer is option 2. \(68.4\, \ g\).

Solutions can have same osmotic pressure only if they have same molar concentration therefore,

\(\text{Molar concentration of cane sugar = Molar concentration of X}\)

\(5\%\) Solution means \(5 g\) of solute is present in \(100 g\) of water. Density of water is \(1\, \ g/cm^3\) therefore \(100 g\) of water is equal to \(100 ml\) of water. Same applies for \(1\%\) solution. For cane sugar

Mass of solute\(=\, \ 5 g\)

Volume of solution \(=\, \ 100 mL\)

Molecular mass of solute \(= 342\, \ g\)

For substance \(X\), let molecular mass be \(M_2\)

Given mass of solute \(=\, \ 1g\)

Volume of solution \(=\, \ 100 mL\)

Applying above mentioned formula

\(\text{Molarity of solution 1 = Molarity of solution 2}\) we will get

\(\frac{5 × 1000}{342 × 100} = \frac{1 × 1000}{M_2 × 100}\)

\(\frac{5}{342} = \frac{1}{M_2}\)

\(M_2 = \frac{342}{5}\)

\(M_2 = 68.4\, \ g\)