Question

Given,10g of hydrofluoric acid occupies 5.6 litre of volume at NTP. If the empirical formula of the gas is HF, then its molecular formula will be: (At. Mass of F = 9).
(A)HF
(B)${{\text{H}}_{\text{3}}}{{\text{F}}_{\text{3}}}$
(C)${{\text{H}}_{\text{2}}}{{\text{F}}_{\text{2}}}$
(D) ${{\text{H}}_{\text{4}}}{{\text{F}}_{\text{4}}}$

Answer 1

Empirical formula is the simple formula of any compound whose constituent atoms are in the simplest possible ratio of whole numbers. Knowing empirical formula, molecular formula of any compound can be known by the number of moles of each atom present in it.

Complete answer:
In the question it is given that 10g of hydrofluoric acid occupies 5.6 litre at NTP. But we know that one mole of a compound occupies 22.4 litre volume at NTP. The mass of one mole of a compound is the molecular mass of that compound. Therefore, the molar mass of hydrofluoric acid is known by crisscross method, let the unknown mass be denoted by M,
$M=\dfrac{10\times 22.4}{5.6}$
M=40g
Now we have the data of both the masses, so let us find out n and then molecular formula. We know that empirical formula is HF, since one atom of each element is present, its mass is sum of atomic mass of H and F. Therefore mass of HF is 1+9= 10 g, since the atomic mass of hydrogen is 1.008g and fluorine is already given as 9g.
So, $n=\dfrac{40}{10}=4$ and the molecular mass is 4(HF) that equals to ${{\text{H}}_{\text{4}}}{{\text{F}}_{\text{4}}}$

So the answer for the above question is option (D).

Additional information:
Empirical formula and molecular formula of any given compound are related to each by the relation that is molecular formula equals to ‘n’ times the empirical formula. Where n is the whole number which is multiplied with the number of constituent atoms present in the empirical formula. ‘n’ can be otherwise found by knowing the masses of both empirical formula and molecular formula of a compound. The formula for finding n using formula masses is n= molecular mass/empirical formula mass.

Note:
Empirical formula mass can be found by knowing the empirical formula and molecular mass from the molecular formula. But when a molecular formula is not known to calculate the molecular mass or molar mass, knowing its volume at NTP or STP conditions gives the molecular mass of a compound.