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]

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Solution

## Let the molecular formula of metal chloride be MxCly. It is given that metal chloride contains 65.5% of chlorine. Chlorine present in 100 g of metal chloride = $\frac{100\left(35.5y\right)}{56x+35.5y}=65.5$ On rearranging the above equation, we get: => x = 0.33y ..........(i) $\mathrm{Vapour}\mathrm{density}=\frac{\mathrm{Molecular}\mathrm{mass}}{2}\phantom{\rule{0ex}{0ex}}\mathrm{Molecular}\mathrm{mass}=162.5×2=325\mathrm{g}$ 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.

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