Question

A metal, M, of atomic mass 56 amu reacts with chlorine to form a salt that can be represented as MClx. A boiling point elevation experiment is performed to determine the subscript x, and therefore, the formula of the salt. A 29.2 g sample of the salt is dissolved in 100.0 g of water and the boiling point of the solution is found to be 377 K. Find the formula of the salt. Assume complete dissociation of the salt in solution.

formula:

Answer 1

The molecular weight of the salt MCl_x can be calculated by the elevation in boiling point using the formula

T_b = ( K_b x W₂ ) / ( M₂ x W₁ )

Where

T_b is the elevation in boiling point = 377-373.15 = 3.85 K

K_b is the ebullioscopic constant for solvent ( water ) = 0.52 Kg K mol^-1

W₂ = wt of the solute in g = 29.2 g

M₂ = M.Wt of the solute in g = ?

W₁ = wt of the solvent in Kg = 100/1000 = 0.1 Kg

Substituting the values we get M₂ = ( K_b x W₂ ) / ( T_b x W1 ) = 39.44 g mol^-1

Since the compound is an electrolyte, this molecular mass must be multiplied by vant hoff factor i because the electrolyte dissociates into ions showing increased colligative property ( in denominator) which reduces the molecular mass.

Vant hoff factor is related to dissociation constant by the relation, i-1/n-1 = where alpha is the dissociation constant .

Since it is assumed complete dissociation, alpha = 1, therefore i-1 = n-1 or i = n.

where n is the total number of ions on dissociation.

MCl_x M ^x+ + x Cl^- therefore n = 1 + x = i

Therefore the molecular mass of the sample = 39.44 (1+x)

Also the molecular mass from the formula MCl_x = 56 + 35.44x

Equating the above two molecular masses as they represents the same,

39.44 + 39.44x = 56 + 35.44x

(39.44 - 35.44)x = 56 - 39.44

4x = 16.56

or x = 16.56/4 = 4

Therefore the formula of the salt is MCl₄