Question

What is the formula of a substance with mass percentage is of 35.79% for S, 62.92% for O and 1.13% for H?​
(A) ${{H}_{2}}S{{O}_{3}}$
(B) ${{H}_{2}}S{{O}_{4}}$
(C) ${{H}_{2}}{{S}_{2}}{{O}_{7}}$
(D) ${{H}_{2}}{{S}_{2}}{{O}_{8}}$

Answer 1

Hint: If we first find the number of moles of each atom, then we can find the molecular formula by dividing them with the lowest number of moles. We can find the number of moles of an atom in the compound by following equation:
     \[\text{Number of moles of atom=}\dfrac{\text{Weight}}{\text{Atomic weight}}\]

Complete step by step answer:
- Mass percentage is a way of representing the concentration of an element or a compound in a mixture. So, we can compare it with a total of 100 gram of compound.
So, by using the above concept we will calculate the mass of elements present.
- Now, suppose that the weight of the substance is 100 gram. So, we can say that it will have 35.79gm of S, 62.92 gram O and 1.13 gram of H in that compound.
- Now, we will calculate the number of moles of each element by dividing it by their molecular mass and then find the empirical formula of the compound. And from the empirical formula, we will find its molecular formula.
We know that Atomic mass of Sulphur = 32$gmmo{{l}^{-1}}$
So, $\text{Number of moles of S = }\dfrac{Weight}{\text{Atomic mass}}$
$\text{Number of moles of S = }\dfrac{35.79}{3}=1.11$ moles

In the same manner, we will calculate moles of other elements.
We know that Atomic mass of Oxygen = 16$gmmo{{l}^{-1}}$
$\text{Number of moles of O = }\dfrac{\text{Weight}}{\text{Atomic mass}}$
$\text{Number of moles of O = }\dfrac{\text{62}\text{.92}}{16}=3.9$ moles
We also know that Atomic mass of Hydrogen is 1$gmmo{{l}^{-1}}$
So, $\text{Number of moles of H = }\dfrac{Weight}{\text{Atomic mass}}$
$\text{Number of moles of H = }\dfrac{1.13}{1}=1.13$ moles

Now, we will find the ratio of number moles of element by lowest number of moles of the element present in order to assign it an empirical formula. Sulphur has the lowest number of moles. We will divide each by moles of sulphur to calculate this ratio.
     \[\text{Ratio for sulfur = }\dfrac{\text{Total moles of sulfur}}{\text{Lowest number moles}}=\dfrac{1.11}{1.11}=1\]
     \[\text{Ratio for Oxygen = }\dfrac{\text{Total moles of oxygen}}{\text{Lowest number moles}}=\dfrac{3.9}{1.11}=3.5\]
     \[\text{Ratio for Hydrogen = }\dfrac{\text{Total moles of hydrogen}}{\text{Lowest number moles}}=\dfrac{1.13}{1.11}\sim 1\]

So, we have found the empirical formula of the compound which is $H{{S}_{3.5}}O$. We have obtained the number of atoms in the empirical formula from the ratio. Now, we will have to multiply the atoms present in the empirical formula by a smallest number in a way that we do not get a fractional number.
So, we will multiply the ratio by 2.

For Sulphur, it will be 2$\times $1=2
For, Oxygen it will be 2$\times $3.5=7
For Hydrogen, it will be 2$\times $1=2
Thus, we can assign the formula of the compound as ${{H}_{2}}{{S}_{2}}{{O}_{7}}$.
So, the correct answer is “OptionC”.

Note: We can also match the percent composition of elements in the compounds given in the options by following formula. We can simply find the % weight of an element in the given compound by given formula:
     \[\text{ }\!\!%\!\!\text{ mass of an element = }\dfrac{\text{100}\times \text{Total mass of element in given compound}}{\text{Molecular weight of the compound}}\]