Question

The percent free of $S{O_3}$ is an Oleum is $20\%$.Label the sample of Oleum in terms of ${H_2}S{O_4}$.
A)113.5%
B) 104.5%
C)106.75%
D)120%

Answer 1

Hint : The percentage of Oleum should be taken as 100% and oleum is the mixture of diprotic acid and sulphur trioxide. The diprotic acid molecular mass is 98g.

Complete step by step solution :
Oleum is defined as fuming Sulphuric acid . It is a mixture of Sulphuric acid and free Sulphur trioxide.
Oleum chemical formula can be written as ${H_2}S{O_4}.XS{O_3}$. Oleum is used in industrial application and other processes. This is used in the Sulfonation process , Nylon manufacturing , Dye manufacturing and Hydrofluoric acid production.
If oleum is released in the upper atmosphere and exists as sulphuric acid droplets. This sulphuric acid droplet settles in the cloud and Oleum is not biodegradable.
The molecular weight of Sulphur trioxide is 80g
$S{O_3} = 32 + 3 \times 16 = 80g$
The molecular weight of Water is 18g
${H_2}O = 2 + 16 = 18g$
The molecular weight of Sulphuric acid is 98g
${H_2}S{O_4} = 2 + 32 + 4 \times 16 = 98g$
From the question concluded that 20% is free sulphuric acid
In the above stoichiometric balanced equation 1 mole of sulphuric trioxide reacting with 1 mole of Water and gives fuming sulphuric acid nothing but oleum
But as per the question let consider
$\frac{x}{{18}}moles\;of\;water\;\;reacting\;with\;\frac{x}{{18}}moles\;of\;sulphur\;trioxide$
$Number\;of\;moles\;S{O_3} = \frac{{Weight}}{{Gram\;molecular\;weight}}$
So Weight of Sulphur trioxide can be written as $\frac{X}{{18}} \times 80$
$\frac{X}{{18}} \times 80$ $= 20\%$
$\frac{X}{{18}} = \frac{{20}}{{80}} \\\ \frac{X}{{18}} = \frac{1}{4} \\\ X = \frac{{18}}{4} = 4.5\% \\\ \\\$
So total oleum is considered as 100% and but free Sulphur trioxide is 4.5%
So the label of Oleum in the Percent of${H_2}S{O_4}$is $104.5\%$

Hence answer is (B) $104.5\%$

Note : The oleum contains free sulphur trioxide. The given percentage 20% of Sulphur trioxide is equal to 20g of Sulphur trioxide. The sulphur trioxide contains 3 oxygen atoms in its molecular formula.