Question

Naphthalene balls contain \[93.71\% \] carbon and \[6.29\% \] hydrogen. If its molar mass is\[128{\text{ }}gmo{l^{ - 1}}\], calculate its molecular formula.

Answer 1

Hint:Molecular formulas give the exact number of atoms of each element present in the molecular compound whereas Empirical formula gives the simplest whole-number ratio of atoms in a compound.
If the empirical formula and molecular mass of the compound is known we can calculate the Molecular formulas of the compound.

Complete answer:
The molecular formula is the formula derived from molecules and is representative of the total number of individual atoms present in a molecule of a compound. The molecular formula and the empirical formula expressed as,
\[Molecular{\text{ }}formula{\text{ }} = {\text{ }}n{\text{ }} \times {\text{ }}empirical{\text{ }}formula\]
First we find the empirical formula.
Step 1: If percentages are given, assume that the total mass is \[100{\text{ }}grams\]
Then the mass of each element = the percent given.
Now, the Mass of carbon = \[93.71\]
Mass of hydrogen = \[6.29\]
Step 2: Convert the mass of each element to moles
Number of moles (carbon) = Mass of carbon / atomic weight of carbon = \[\dfrac{{93.71}}{{12{\text{ }}}} = 7.8\]
Number of moles (hydrogen) = Mass of hydrogen / atomic weight of hydrogen = \[{\text{ }}\dfrac{{6.29}}{1} = 6.29\]
Step 3: Divide each mole value by the smallest number of moles calculated.
Hence, most simple ratio for carbon \[ = {\text{ }}\dfrac{{7.8}}{{6.29{\text{ }}}} = 1.25\;\]
Most simple ratio for hydrogen \[ = \dfrac{{6.29}}{{6.29}} = 1\]
Step 4: Round to the nearest whole number.
(it is not a whole number we multiply the ratio by \[4\] to get a whole number ratio.
Now, Lowest whole number ratio for carbon = \[5\]
Lowest whole number ratio for hydrogen = \[4\]
Empirical formula = \[{C_5}{H_4}\]
Step 5: Now, we can find the molecular formula by finding the mass of the empirical formula.
 \[\Rightarrow M_{C_5}{H_4} = \;\left( {5{\text{ }} \times 12} \right) + \left( {4 \times 1} \right) = 64\,g\]
\[\Rightarrow n = \dfrac{{{\text{ }}Molar{\text{ }}mass{\text{ }}}}{{empirical{\text{ }}formula}}\] \[ = \dfrac{{128\,g}}{{64\,g}} = {\text{ }}2\]
 Putting value of \[n = 2\] in the empirical formula we get molecular formula as

Molecular formula of Naphthalene balls \[ = 2{\text{ }} \times {\text{ }}{C_5}{H_{4}} = {C_{10}}{H_{8}}\]

Note:
Divide the molar mass of the compound by the empirical formula mass. The result should be a whole number or very close to a whole number. Sometimes, the empirical formula and molecular formula both can be the same.