Question

(a) A metal M forms a volatile chloride containing 65.5% chlorine. If the density of the chloride relative to hydrogen is 162.5, find the molecular formula of the chloride.
(M = 56; Cl = 35.5)

Answer 1

Percentage of Cl in the metal chloride = 65.5
Percentage of M in the metal chloride = (100 − 65.5) = 34.5

Elements	Percentage	Atomic mass	Relative Number of Moles	Simplest Ratio
M	34.5	56	$\left(\frac{34.5}{56}\right)=0.62$	$\left(\frac{0.62}{0.62}\right)=1$
Cl	65.5	35.5	$\left(\frac{65.5}{35.5}\right)=1.84$	$\left(\frac{1.84}{0.62}\right)=2.97\approx 3$

Empirical formula of chloride = MCl₃
Empirical formula mass = {56 + (35.5 $\times$ 3)} = 162.5 u
Vapour Density = 162.5
Molecular mass of chloride = Vapour Density $\times$ 2 = (162.5$\times$2) u = 325 u
Molecular formula = (Empirical formula)_n
$$\begin{gathered} n=\frac{\text{Molecular mass}}{\text{Emiprical Formula Mass}} \\ n=\frac{325}{162.5}=2 \end{gathered}$$

∴ Molecular formula of chloride = (MCl₃)₂ = M₂Cl₆