Question

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

Let the molecular formula of metal chloride be M_xCl_y.
It is given that metal chloride contains 65.5% of chlorine.
Chlorine present in 100 g of metal chloride = $\frac{100(35.5y)}{56x+35.5y}=65.5$
On rearranging the above equation, we get:
=> x = 0.33y ..........(i)

$$\begin{gathered} \mathrm{Vapour}\mathrm{density}=\frac{\mathrm{Molecular}\mathrm{mass}}{2} \\ \mathrm{Molecular}\mathrm{mass}=162.5\times 2=325\mathrm{g} \end{gathered}$$
Molecular mass of metal chloride can also be calculated as:
Molecular mass = 56x + 35.5y = 325 ...........(ii)
Solve equations (i) and (ii) for x and y.
325 = 56 (0.33y) + 35.5y
y = 6
Putting the value of y in equation (ii), we get:
56x + 35.5(6) = 325
x = 2
Hence, the molecular formula of metal chloride is M₂Cl₆.