Question

Nitrobenzene is formed as the major product along with a minor product in the reaction of benzene with a hot mixture of nitric acid and sulphuric acid. The minor product consists of carbon 42.86 %, hydrogen 2.40 % , nitrogen 16.67 %, and oxygen 38.07 %.
(i) Calculate the empirical formula of the minor product.
(ii) When 5.5 gm of the minor product is dissolved in 45 gm of benzene, the boiling point of the solution is 1.84 C higher than that of pure benzene. Calculate the molar mass of the minor product and determine its molecular and structural formulae.

Answer 1

Hint: The empirical formulae is the ratio between the numbers of atoms of different elements which is present in the molecule of the given compound. To calculate empirical formula from molecular formula we have to divide all the subscripts in the empirical formulae by the simplest whole number. Molecular formula is the actual whole number ratio of the elements present in the molecule of the compound.

Complete Solution :
(i) Empirical formulas usually give the proportion of the elements present in the molecule of the given compound but nor the actual number of the atoms or how the atoms are arranged.

element	percentage	Atomic weight	Relative number	ratio
C	42.86	12	$\dfrac{42.86}{12}$ =3.57	$\dfrac{3.57}{1.19}$ =3.00
H	2.40	1	$\dfrac{2.40}{1}$=2.40	$\dfrac{2.40}{1.19}$=2.00
N	16.67	14	$\dfrac{16.67}{14}$=1.19	$\dfrac{1.19}{1.19}$=1.00
O	38.07	16	$\dfrac{38.07}{16}$=2.37	$\dfrac{2.37}{1.19}$=1.99=2.0

Hence, the empirical formulae of the compound is:${{C}_{3}}{{H}_{2}}N{{O}_{2}}$ .
(ii) given = 5.5 g of minor product is dissolve in 45g of benzene
Molecular weight of the minor compound is calculated using the formulae
\[MW=\dfrac{100\times {{K}_{b}}}{\Delta {{T}_{b}}}\times \dfrac{w}{W}\]
Substituting all the given value in the question we get:
\[MW=\dfrac{100\times 2.53}{1.84}\times \dfrac{5.5}{45}=168\]
The smallest whole number n =
\[\begin{align}
& n=\dfrac{MW}{weight\text{ of EF}} \\
& n=\dfrac{168}{36+2+14+32} \\
& n=2 \\
\end{align}\]
The molecular formulae of product is:
\[n\times {{C}_{3}}{{H}_{2}}N{{O}_{2}}=2\times {{C}_{3}}{{H}_{2}}N{{O}_{2}}={{C}_{6}}{{H}_{4}}{{N}_{2}}{{O}_{4}}\]
According to the question the product formed is m-Dinitrobenzene and the structural formulae is:

Additional information:
Empirical formula is calculated from the molecular formula using the given steps:
Step 1 – write down the molecular formulae of the given compound.
Step 2- find the simplest whole number by which the compound must be divided to convert the molecular formulae into its simplest form.

Note: If mass of compound is given then empirical formula is calculated by changing the mass of every element to moles and then by dividing every mole value by the lowest value of mole computed and then the value of mole is rounded off to the closest whole number.