Question

# The empirical formula of a compound is CH. Its molecular weight is 78. The molecular formula of the compound will be:   (A) - C$_2$H$_2$   (B) - C$_3$H$_3$   (C) - C$_4$H$_4$   (D) - C$_6$H$_6$

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Hint: Empirical formula is the simplest whole-number ratio of atoms in any compound whereas molecular formula is exactly the number of each atom present in any compound. The empirical weight of CH can be calculated and then divided with the molecular weight. The number, thus, obtained would be the exact number of carbon and hydrogen atoms in the compound.

According to the question, the empirical formula of a compound is CH, i.e. it is the lowest whole number ratio of that particular compound.
-> Now, we will calculate the empirical weight of CH.
Empirical weight = atomic mass of C + atomic mass of H = 12+1 = 13 g/mol.
->The molecular weight of the compound is given, i.e. 78 g/mol.
-> Now, we have to calculate the molecular formula;
Molecular weight = n $\times$ empirical weight, n represents the no. of atoms.
n = Molecular weight / empirical weight = 78 /13 = 6, or
n = $\dfrac{molecular weight}{empirical weight}$ = $\dfrac{78}{13}$ = 6
->So, molecular formula = (CH)$_n$ = (CH)$_6$ =C$_6$H$_6$; in this case we substituted the calculated value of n.
->Therefore, the molecular formula of the compound having the molecular weight 78 g/mol is (D) - C$_6$H$_6$.

Hence option ‘D’ is the correct answer.

Note:: The significance of empirical formula in chemistry is that it makes the stoichiometry calculations very easy and handy, especially when it comes in organic chemistry where a long chain of carbohydrates and proteins is there. Also, it could provide an avenue to find the molecular formula of any unknown compound by finding empirical formula experimentally and using other tools.