Question

A sulphide of iron contains 46.5% of iron by weight. The empirical formula of the sulphide is:
(A)- FeS
(B)- $F{{e}_{2}}S$
(C)- $Fe{{S}_{2}}$
(D)- $F{{e}_{2}}{{S}_{3}}$

Answer 1

Hint: Empirical formula of a compound represents the simplest whole number ratio of atoms present in the compound. To find the empirical formula, first determine the number of moles of each element present in the compound and then convert them to obtain the simplest whole number ratio.

Complete step by step answer:
Percentage of a substance by weight means the mass of the substance (in grams) present in 100 grams of the solution.
46.5% of iron by weight simply means that 46.5 g of iron is present in 100 g of the compound, i.e. sulphide of iron.
Thus, we can say that (100 - 46.5) g is the mass of sulphur present in the 100 g of the given compound.
Now, we have mass of iron = 46.5 g
Mass of sulphur = 53.5 g
First let us calculate the number of moles of Fe.
We know that number of moles is calculated as
     \[n=\dfrac{\text{mass of substance}}{\text{mass of one mole of substance}}\]
Mass one mole of iron = 55.8 g/mol.
Given mass of iron is 46.5g, therefore, the moles of moles of iron will be equal to
     \[\begin{align}
  & {{n}_{Fe}}=\dfrac{\text{mass of Fe}}{\text{molar mass of Fe}} \\
 & {{n}_{Fe}}=\dfrac{46.5g}{55.8g/mol}=0.833mol \\
 & \\
\end{align}\]

Similarly, we can calculate the number of moles of sulphur as
     \[{{n}_{S}}=\dfrac{\text{mass of S}}{\text{molar mass of S}}\]
Substituting given mass of sulphur = 53.5 g and molar mass of sulphur = 32.1 g/mol in the above equation, we get
     \[\begin{align}
  & {{n}_{S}}=\dfrac{53.5g}{32.1g/mol}=1.667mol \\
 & \\
\end{align}\]
Therefore, the number of moles of iron and sulphur present in the one mole sulphide of iron is 0.833 mol and 1.667 mol, respectively.
To convert them into a simple whole number ratio. Multiply the number of moles by 2. Thus, we get

Element	%	Mole	Simple ratio
Fe	46.5	0.833	1
S	53.5	1.667	2

Therefore, the empirical formula of the sulphide of iron is $Fe{{S}_{2}}$.
So, the correct answer is “Option C”.
Note: Note that the empirical formula of a compound only gives the relative number of atoms or the number of moles in one mole of the compound whereas molecular formula gives the actual number of atoms or moles in the compound. Multiply the number of moles with the smallest whole number that can convert the decimal numbers into whole numbers.