For a binary solution, the relation between the molality () of the solution and the mole fraction of — Solutions and Colligative Properties Chemistry Question
Question
For a binary solution, the relation between the molality ($m$) of the solution and the mole fraction of the solute ($\chi_B$) is given by which of the following expressions? (Where $M_A$ is the molar mass of the solvent $A$ in g/mol, and $\chi_A$ is the mole fraction of the solvent).
Answer: A
💡 Solution & Explanation
We know $\frac{\chi_B}{\chi_A} = \frac{n_B}{n_A} = \frac{n_B}{W_A / M_A}$. Molality $m = \frac{n_B \times 1000}{W_A}$. Therefore, $m = \frac{n_B}{W_A} \times 1000 = \frac{\chi_B}{\chi_A \times M_A} \times 1000$.
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