When 19g of a certain molecular compound X are dissolved in of benzonitrile , the freezing point of the solution is measured to be . Calculate the molar mass of X.

When 19 mg of a certain molecular compound X are dissolved in 200 g of benzonitrile , the freezing point of the solution is measured to be [tex]-13.4^0C[/tex]. Calculate the molar mass of X. Freezing point of pure benzonitrile = [tex]-13^0C[/tex]

Answer: Molar mass of X is 1271 grams

Explanation:

Depression in freezing point = [tex]0.4^0C[/tex]

Mass of solute (X) = 19 g

Mass of solvent (benzonitrile) = 200.0 g = 0.2 kg (1 kg = 1000 g)

Formula used :

[tex]\Delta T_f=i\times k_f\times m\\\\\Delta T_f=i\times K_f\times\frac{\text{Mass of solute}}{\text{Molar mass of solute}\times \text{Mass of solvent in Kg}}[/tex]

where,

[tex]\Delta T_f[/tex] = change in freezing point = [tex]13.4^oC-(-13^0C)=0.4^0C[/tex]

i = Van't Hoff factor = 1

[tex]K_f[/tex] = freezing point constant = 5.35 K.kg/mole

m = molality

Now put all the given values in this formula, we get

[tex]0.4^0C=1\times (5.35K.kg/mole)\times \frac{19g}{\text{Molar mass of X}\times 0.2kg}[/tex]

[tex]\text{Molar mass of X}=1271g/mol[/tex]

Thus molar mass of X is 1271 grams