Question

The chloride of a metal M contains $65.5\%$ of chlorine, $100{\text{ ml}}$ of the vapour of the chloride of the metal at STP weight $0.72{\text{ gm}}$ . The molecular formula of the metal chloride is:
(A) ${\text{MC}}{{\text{l}}_3}$
(B) ${\text{MCl}}$
(C) ${\text{MC}}{{\text{l}}_{\text{2}}}$
(D) ${\text{MC}}{{\text{l}}_{\text{4}}}$

Answer 1

To answer this question, you should recall the formula for finding the number of moles of a gas when we are given the volume occupied by the gas. The volume occupied by one mole of a substance in the vapour phase is known as the molar volume of the substance and it is equal to $22400{\text{ ml}}$ at STP. We shall calculate the weight of one mole metal chloride and use the percentage of chlorine given to find its mass in one mole and use its molar mass to find the moles of chlorine in one mole metal chloride.

Formula used: $n = \dfrac{w}{M} = \dfrac{V}{{{V_M}}}$
Where, $n$ represents the number of moles of the given substance
$w$ represents the given mass of the substance
$M$ represents the molar mass of the given substance
$V$ represents the volume occupied by the substance in the vapor phase
And ${V_M}$ represents the molar volume of the gas, i.e. the volume which is occupied by one mole of the gas at Standard Temperature and Pressure conditions.

Complete step by step solution
First we have to calculate the mass of the metal chloride. It is given that $100{\text{ ml}}$ vapors of the compound contain $0.72{\text{ gm}}$ of the metal chloride.
So $22400{\text{ ml}}$ of the chloride will contain $\dfrac{{0.72}}{{100}} \times 22400 = 161.28{\text{ g}}$ of the metal chloride.
It is given that $100{\text{ g}}$ of the metal chloride contains $65.5{\text{ g}}$ of chlorine. Thus, $161.28{\text{ g}}$ of the metal chloride will contain $\dfrac{{65.5}}{{100}} \times 161.28 = 105.6{\text{ g}}$ chlorine.
The number of chlorine atoms in the metal chloride will be thus given by $\dfrac{{105.6}}{{35.5}} \approx 3$
The molecular formula of the given metal chloride will be ${\text{MC}}{{\text{l}}_3}$
The correct answer is A.

Note
Mole is the basic unit for the measurement of the amount of a substance in the International System of units, commonly known as the SI Units. One mole of a substance is defined as the amount of the substance that contains particles equal to the Avogadro’s number.