Question

Vapor density of a metal chloride is$66$. Its oxide contains $53\% $ metal. The atomic weight of the metal is.
A) $21$
B) $54$
C) $27.06$
D) $2.086$

Answer 1

Hint: We know that, the ratio of the mass of a volume of a gas, to the mass of an equal volume of hydrogen, calculated under the typical conditions of temperature and pressure is defined as vapor density.
${\text{Vapour density}} = \dfrac{{{\text{Mass of volume of gas}}}}{{{\text{Mass of equal volume of hydrogen}}}}$

Complete step by step answer:
We know that, the relationship between the molar mass of a gas and the vapor density of the gas. The molar mass of a gas is twice the vapor density of the gas.
${\text{Molar mass}} = 2 \times {\text{Vapour density}}$
Given,
The vapor density of a metal chloride $ = 66$
Now we assume that the weight of the metal chloride is $100g$.
${\text{Mass of oxygen}} = {\text{Mass of metal chloride}} - {\text{Mass of metal}}$
${\text{Mass of oxygen}} = 100 - 53 = 47g$
We can calculate the equivalent weight of the metal by using the given formula as,
${\text{Equivalent weight}} = \dfrac{{{\text{Weight of metal}}}}{{{\text{Weight of oxygen}}}} \times 8$
Now substitute the known values we get,
\[{\text{Equivalent weight}} = \dfrac{{53}}{{47}} \times 8 = 9.02\]
We know that the valence of the substance is equal to twice the vapor density divided by the molecular weight of the substance.
${\text{Valency}} = \dfrac{{2 \times {\text{Vapour density}}}}{{{\text{Equivalent weight}} + {\text{Molar mass}}}}$
Now we can substitute the values we get,
\[{\text{Valency of C}}{{\text{l}}^ - } = \dfrac{{2 \times \,66}}{{\left( {9.02 + 35.5} \right)}} = 2.96 \simeq 3\]
Now, calculate the atomic weight of the compound,
${\text{Atomic weight}} = {\text{Equivalent weight}} \times {\text{Valency}}$
Now substitute the values of equivalent weight and valency we get,
${\text{Atomic weight}} = 9.02 \times 3 = 27.06$

Therefore, the option C is correct.

Note:
We define the equivalent weight of the substance as the ratio of the molecular weight or mass of the compound to the n-factor or the acidity or basicity. We can calculate the n- factor by determining the change in oxidation state. We know that the 'n' factor of an acidic substance is equal as the number of ions removed by one mole of an acid. The n-factor for an acidic substance wasn’t equal as the number of moles of usable Hydrogen atoms present in one mole of acid. The oxidation state of the single element is zero but if it has any charge present on it then it is considered as n-factor while basicity for the acidic substance and the acidity is defined for the basic substance.