Question

The empirical formula of the compound is \[{\text{CH}}{{\text{O}}_{\text{2}}}\]. The molecular weight of the compound is 90. Calculate the molecular formula of the compound.
A \[{{\text{C}}_{\text{2}}}{{\text{H}}_{\text{2}}}{\text{0}}\]
B \[{\text{CH0}}\]
C \[{\text{C}}{{\text{H}}_{\text{2}}}{{\text{0}}_4}\]
D \[{{\text{C}}_2}{{\text{H}}_{\text{2}}}{{\text{0}}_4}\]

Answer 1

Hint: Empirical formula gives the lowest value of ration of the elements present in a molecule. But from this formula the actual number of the elements present in the molecule cannot be defined. The molecular formula of a compound is with the actual number of the elements present in a compound .
Formula used:
\[{\text{n = }}\dfrac{{{\text{Molecular weight}}}}{{{\text{Empirical weight}}}}\] , .

Complete step by step answer:
To calculate the molecular formula of that particular molecule, the relation between the molecular formula and empirical formula should be known. The relation is , \[{\text{ molecular formula = }}{\left( {{\text{ empirical formula}}} \right)_{\text{n}}}\]. Now here n is an integer. The value of n can be calculated by the formula, \[{\text{n = }}\dfrac{{{\text{Molecular weight}}}}{{{\text{Empirical weight}}}}\].
Therefore, if the molecular weight and empirical weight is known the value of n can be calculated. Now for the given empirical formula the empirical weight is,
 \[
  \left( {12 + 1 + \left( {16 \times 2} \right)} \right) \\
   = \left( {13 + \left( {32} \right)} \right) \\
   = 45 \\
  \]
The molecular weight is 90 (given).
Therefore, the value of n is ,

Now the relation between the empirical formula and molecular formula for this molecule is,
\[{\text{ molecular formula = }}{\left( {{\text{ empirical formula}}} \right)_2}\]
Now, the empirical formula is , \[{\text{CH}}{{\text{O}}_{\text{2}}}\]
Therefore, the molecular formula is,
\[
  {\text{ molecular formula = }}{\left( {{\text{ CH}}{{\text{O}}_{\text{2}}}} \right)_2} \\
   = {{\text{C}}_2}{{\text{H}}_2}{{\text{O}}_4} \\
  \]

The correct option is D.

Note:
 For acids the number of equivalents is equal to the number of H+ present in one molecule. And for bases the number of HO- groups present in one molecule. The equivalent weight of any substance cannot be greater than its molecular weight. Either the value of equivalent weight is equal or less than the molecular weight of that substance.