Question

A salt has the following percentage composition: \[Al = 10.50\% ,K = 15.1\% ,S = 24.8\% \] and the remaining oxygen. The empirical formula of the salt is:
\[({\text{Al}} = 27{\text{g}}/{\text{mol}},{\text{K}} = 39{\text{g}}/{\text{mol}},{\text{S}} = 32{\text{g}}/{\text{mol}},{\text{O}} = 16{\text{g}}/{\text{mol)}}\]
A.\[{\text{A}}{{\text{l}}_2}{\text{K}}{({\text{S}}{{\text{O}}_4})_2}\]
B.\[{\text{Al}}{{\text{K}}_2}{({\text{S}}{{\text{O}}_4})_2}\]
C.\[{\text{AlK}}({\text{S}}{{\text{O}}_4})\]
D.\[{\text{AlK}}{({\text{S}}{{\text{O}}_4})_2}\]

Answer 1

Hint: To answer this question we must need to know the definition for the percentage composition and number of moles. We will get the value of mass and hence number of moles from the percentage composition. We know the total percentage is always 100.

Formula used: \[{\text{number of mole (n) = }}\dfrac{{{\text{mass of substance}}}}{{{\text{Molar mass}}}}\]

Complete step by step solution:
Percentage composition can be defined in two ways percentage by mass and percentage by volume. Since we have not been specified so we will consider it a as percentage by mass. Mass percentage is defined as the mass of substance present in the 100 g of solution.
Since the percentage is always calculated from 100, so we will get the percentage of oxygen as,
\[100 - 10.50 - 15.1 - 24.8 = 49.6\% \]
So this means that \[10.50\% \] \[{\text{Al}}\] by mass means \[10.50\] g of water is present in the 100 g of solution and similarly for others.
Molar mass of each of the elements is given to us and hence we will calculate the number of moles from the above formula:
\[{{\text{n}}_{{\text{Al}}}} = \dfrac{{10.50}}{{27}} = 0.3889\]
\[{{\text{n}}_{\text{K}}} = \dfrac{{15.1}}{{39}} = 0.387\]
\[{{\text{n}}_{\text{S}}} = \dfrac{{24.80}}{{32}} = 0.775\]
\[{{\text{n}}_{\text{O}}} = \dfrac{{49.6}}{{16}} = 3.1\]
Hence the ratio of these elements in the given mixture will be :
\[{\text{Al : K : S : O}} = 0.3889:0.387:0.775:3.1\]
We need to convert this in whole numbers because elements cannot be in fraction in a compound. Hence we will divide all the ratios with \[0.387\], we will get \[{\text{Al : K : S : O}} = 1:1:2:8\]. This means there are 1 atom of aluminum, 1 atom of potassium, 2 atoms of sulphur and 8 atoms of oxygen.
The above criteria fit well in the option D.

Note: Empirical formula represents the small positive integer value in which atoms are present in any compound. It does not mention the arrangement of atoms in any way. The molecular formula exactly depicts the number of atoms as well as their proper arrangements of atoms in a formula. It is possible that two compounds may have similar empirical formula but the molecular formula is unique for each compound.