In a binary liquid solution, the mass percentage of the solute is exactly , and the ratio of the mol — Mole Concept and Some Basic Concepts of Chemistry Chemistry Question
Question
In a binary liquid solution, the mass percentage of the solute is exactly $25/7 \%$, and the ratio of the mole fractions of the solute to the solvent is precisely $1 : 9$. If the stoichiometric ratio of the molar masses of the solute to the solvent is expressed as $1 : x$, determine the exact integer value of $x$.
💡 Solution & Explanation
Step 1: Let the mass of the solute be $w_1 = 25/7\text{ g}$. The mass of the solvent is $w_2 = 100 - 25/7 = 675/7\text{ g}$. Step 2: Find the mass ratio: $\frac{w_1}{w_2} = \frac{25/7}{675/7} = \frac{25}{675} = \frac{1}{27}$. Step 3: Relate mole fraction ratio to mole ratio and mass ratio. $\frac{x_1}{x_2} = \frac{n_1}{n_2} = \frac{w_1 / M_1}{w_2 / M_2} = \left(\frac{w_1}{w_2}\right) \times \left(\frac{M_2}{M_1}\right)$. Step 4: Substitute known values and solve for the molar mass ratio. $\frac{1}{9} = \left(\frac{1}{27}\right) \times \left(\frac{M_2}{M_1}\right) \implies \frac{M_2}{M_1} = \frac{27}{9} = 3$. Since $M_1 : M_2 = 1 : 3$, the value of $x$ is 3.