Question

A solution is made with Solvent A (molar mass 40 g/mol) by slowly adding solute B. A curve is plotted between molality of the solution vs $\frac{x_B}{x_A}$ where $x_B$ and $x_A$ represents the mole fraction of solute and solvent respectively.
Calculate the slope of the curve.

• A. 10 mol/g
• B. 10 g/mol
• C. 25 g/mol
• D. 25 mol/g

Answer 1

The correct option is D 25 mol/g

Molality is given by
$m=\frac{1000\times n_B}{n_A\times m_A}$ (i)
Where $n_A$ and $n_B$ are moles of solvent and solute respectively and $M_A$ is molar mass of solvent in g/mol
Also mole fraction of the solute is given by
$x_B=\frac{n_B}{n_A+n_B}$ (ii)
Substituting the value of $n_A$ from eq (ii)
we will get
$m=\frac{1000}{M_A}\times \frac{x_B}{x_A}$
$\therefore slope=\frac{1000}{M_A}=25mol/g$