Question

The empirical formula of a compound is \[C{H_2}\] . One mole of this compound has a mass of \[42g\]. Its molecular formula is:
A. \[C{H_2}\]
B. \[{C_2}{H_2}\]
C. \[{C_3}{H_6}\]
D. \[{C_3}{H_8}\]

Answer 1

Hint: We have to remember that the molecular formula shows the actual number of elements present in an organic compound. Molecular formula may be the same or simple multiple of its empirical formula. If knowing the empirical formula and molecular weight of the compound then the molecular formula of the compound is calculated.

Complete step by step answer:
We must have to know that the empirical formula is the simplest formula of the compound. Empirical formula gives the ratio between the atoms of the various elements present in the compound. Empirical formula may or may not be the equal to the molecular formula of an organic compound.
Molecular weight of the compound is calculated by the known known molecular formula and the empirical formula,
Molecular formula $ = n \times {\text{Empirical formula}}$
(Where \[n\] is simple integer)
\[n\] is calculated by $\dfrac{{{\text{Molecular weight}}}}{{{\text{Empirical formula weight}}}}$
The empirical formula of a compound is \[C{H_2}\].
First, calculate the empirical formula weight.
Empirical formula weight =\[C{H_2}\]= $12 + 2 = 14$
Molecular weight of the compound is \[42{\text{ }}g\].
Now we can substitute the known values we get,
$ \Rightarrow n = \dfrac{{42}}{{14}}$
On simplification we get,
$n = 3$
$\therefore $Molecular formula = $n \times {\text{Empirical formula}}$
Molecular formula = $3 \times (C{H_2})$
Molecular formula = ${C_3}{H_6}$
Molecular formula of the compound is ${C_3}{H_6}$ .
Therefore, option C is correct.

Note:
We must have to know that the empirical formula of the compound \[C{H_2}\] means that compound contains one carbon and two hydrogen. But from the empirical formula of the composed, \[C{H_2}\] , calculated molecular formula is ${C_3}{H_6}$ , suggesting that compound contains three carbons and six hydrogen.
We can also remember that a formula which gives a precise idea about the arrangements of different atoms present in the molecule of a compound is called the structural formula. In structural formula, atoms are connected by short lines – one, two or three lines indicates single, double or triple bond.