Question

A metal, M, of atomic weight 96 reacts with fluorine to form a salt that can be represented as MFx. In order to determine x and therefore the formula of the salt, a boiling point elevation experiment is performed. A 9.18-g sample of the salt is dissolved in 100.0 g of water and the boiling point of the solution is found to be 374.38 K.

(A) MF
(B) MF2
(C) MF3
(D) MF4

Answer 1

The correct answer is option 3.

Step-by-step explanation:

Molecular formula of the salt =
`MF_x`

The salt when dissolved in water will get dissociated into ions.

`MF_x\rightarrow M^(x+)+xF^-`

van't Hoff factor = i = 1+x

Boiling point of the solution =
`T_b=374.38 K`

Boiling point of pure solvent that water =
`T=373.15 K`

Elevation in boiling point =
`\Delta T_b`

`\Delta T_b=T_b-T=374.38 K-373.15 K=1.23 K`

`\Delta T_b=i* K_b* m`

`K_b`=molal elevation constant

m = molality of the solution

Molal elevation constant of water =0.52 K kg/mol

molality =
`\frac{\text{Mass of compound}}{\text{Molar mass of compound}* \text{mas of solvent in kg}}`

`m=(9.18 g)/((96 g/mol+x* 19 g/mol)* 0.100 kg)`

`1.23 K=i* 0.52 K kg/mol* (9.18 g)/((96 g/mol+x* 19 g/mol)* 0.100 kg)`

i = 2.47+0.48x

2.47+0.48x = 1+x

x =2.8 ≈ 3

Molecular formula of the salt =
`MF_3`