Question

The molecular formula of a gas with vapour density 15 and empirical formula $ \text{C}{{\text{H}}_{3}} $ is:
(A) $ {{\text{C}}_{2}}{{\text{H}}_{6}} $
(B) $ {{\text{C}}_{3}}{{\text{H}}_{8}} $
(C) $ {{\text{C}}_{4}}{{\text{H}}_{10}} $
(D) $ \text{C}{{\text{H}}_{3}} $

Answer 1

Hint: Calculate the empirical formula weight and molecular weight. Using these, find the molecular formula for a given gas. The empirical formula of a compound expresses a ratio between the numbers of atoms of different elements present in a molecule of the compound. This ratio is a mole ratio as well as the ratio between the no of atoms.

Formula Used
Molecular weight $ =2\times $ vapour density
Molecular formula = Empirical formula $ \times $ n
 $ \text{n}=\dfrac{\text{Molecular weight}}{\text{Empirical formula weight}} $ .

Complete Step by Step Answer
Given vapour density= 15
Using, Molecular weight $ =2\times $ vapour density we get, Molecular weight $ =2\times 15=30\text{kg/mol} $ vapour density
Vapour Density: It is the density vapour in relation to that of hydrogen.
Now, finding the value of n we require empirical formula weight.
So, the empirical formula weight for $ \text{C}{{\text{H}}_{3}}= $ atomic weight of carbon(C) $ +3\times $ atomic weight of hydrogen (H)
Therefore, the empirical formula weight
  $ =12+3\times 1 $
 $ \Rightarrow 12+3 $
 $ \Rightarrow 15\text{ amu} $
So, $ \text{n}=\dfrac{\text{Molecular weight}}{\text{Empirical formula weight}}=\dfrac{30}{15}=2 $
Now, for molecular formula we have both ‘n’ and empirical formula.
So,
Molecular formula $ =\text{n}\times $ empirical formula
 $ \Rightarrow 2\times \left( \text{C}{{\text{H}}_{3}} \right) $
 $ \Rightarrow {{\text{C}}_{2}}{{\text{H}}_{6}} $
Therefore, option (A) is correct.

Additional Information
Way to calculate Empirical formula: Convert the mass of each element to mole using the molar mass from the periodic table. Divide each mole value by the smallest no of moles calculated and round off to the nearest whole number. This is the mole ratio of the elements and is represented by subscripts in the empirical formula.

Note
Molecular Formula consists of the chemical symbols for the constituent elements followed by numeric subscripts describing the no of atoms of each element present in the molecule. The Empirical formula represents the simplest whole- integer ratio of atoms in a compound whereas molecular formula shows the number of each type of atom in a molecule. One should know the atomic weights of various elements which can be found using the periodic table. Table the relations between Molecular weight and vapour density.