Question

A metal $M$ of molar mass 96 g $mo{l}^{-1}$ reacts with fluorine to form a salt that can be represented as $M{F}_x$. In order to determine $x$. 9.18 g of the sample of the salt is dissolved in 100 g of water and its boiling point was determined to be 374.38 K. What is the value of $x$?

Given: $K_b\left(water\right)=0.512Kkgmo{l}^{-1}$.

Assume complete dissociation of salt.

• A. $x=2$
• B. $x=4$
• C. $x=5$
• D. $x=7$

Answer 1

The correct option is B $x=4$

Elevation of boiling-point describes that the boiling point of a liquid (a solvent) will be higher when another compound is added to it, meaning that a solution has a higher boiling point than a pure solvent. This happens whenever a non-volatile solute, such as a salt, is added to a pure solvent, such as water.

Elevation of boiling point ( $\Delta T_b$ ) is the difference between the boiling points of the solution and the pure solvent:

$\Delta T_b=T_b-{T_b}^0$

Elevation of boiling point can be calculated as

$\Delta T_b=i.m.K_b$

Here, $m$ is the concentration of the solute expressed in molality and $K_b$ is the molal boiling point elevation constant of the solvent.

$i$ is van't hoff factor $=1$ for complete dissociation.

Molality of solute is $\frac{\frac{9.18}{96+18x}}{\frac{100}{1000}}=\frac{91.8}{96+18x}$

$K_b=0.512$

$\Delta T_b=374.38-373=1.38$

So,

$1.38=\frac{91.8}{96+18x}\times 0.512⟹x=4$