Question

A metal M of molar mass 96 $\text{g mo}{{\text{l}}^{-1}}$ reacts with fluorine to form a salt that can be represented as $\text{M}{{\text{F}}_{x}}$. In order to determine x, 9.18g 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: ${{\text{K}}_{b}}(water)\text{ = 0}\text{.512 K kg mo}{{\text{l}}^{-1}}$
Assume complete dissociation of salt.
(A) x = 2
(B) x = 4
(C) x = 5
(D) x = 7

Answer 1

Substitute the values given in the formula to calculate elevation in boiling point. It is important to consider the Van't Hoff factor. Once you calculate the Van't Hoff factor, you will know the number of ions formed after dissociation. With this you can determine the value of x.

Complete step-by-step answer:
Colligative properties are the properties of solutions that depend on the ratio of the number of solute particles to the number of solvent molecules in a solution, and not on the nature of the chemical species present.
The number ratio can be related to the various units for concentration of a solution, for example, molarity, molality, normality etc.
The colligative properties are:
Relative lowering of vapor pressure Elevation of boiling point Depression of freezing point Osmotic pressure
When a nonvolatile solute is dissolved in a liquid solvent, the boiling point temperature of the solution becomes greater than the boiling point of the pure liquid solvent. The formula to find elevation in boiling point is:
$\Delta {{T}_{b}}\text{ = i }\text{. }{{\text{K}}_{b}}\text{ }\text{. m}$
Where,
$\Delta {{T}_{b}}$ is the difference in freezing point
i is the Van't Hoff factor
${{K}_{b}}$ is the ebullioscopic constant
m is the molality of solution
It is given to us that,
${{\text{K}}_{b}}(water)\text{ = 0}\text{.512 K kg mo}{{\text{l}}^{-1}}$
$\Delta {{T}_{b}}$ = (374.38 - 373) K = 1.38 K
$\text{m = }\frac{\text{9}\text{.18 x 10}}{\text{96}}\text{ = 0}\text{.95625}$
Substituting the values in the equation we get,
$\Delta {{T}_{b}}\text{ = i }\text{. }{{\text{K}}_{b}}\text{ }\text{. m}$
$\text{1}\text{.38 = i x (0}\text{.512) x (0}\text{.95625)}$
$\text{i = }\frac{1.38}{0.512\text{ x 0}\text{.95625}}$
$\text{i = 2}\text{.91 }\approx \text{ 3}$
Since 3 ions are formed after dissociation of 1 molecule of the compound, the number of fluoride ions attached to the metal atom is 3 - 1 = 2.
The value of x thus becomes equal to 2. Therefore, the correct answer is option (A).
Note: Van't Hoff factor is the ratio between the actual concentration of particles produced when the substance is dissolved and the concentration of a substance as per its mass. The value of the Van't Hoff factor is greater than 1 for dissociation of ionic compounds. The factor is used when the solute undergoes dissociation or association in the solvent.