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How can I find the percent composition of ${\text{A}}{{\text{l}}_{\text{2}}}{\left( {{\text{S}}{{\text{O}}_{\text{4}}}} \right)_{\text{3}}}$

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Last updated date: 13th Jul 2024
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Answer
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Hint: We know that, percentage composition of a compound is the relative mass of each of the constituent elements in 100 parts of it by mass. To calculate percentage composition, first we have to calculate the molecular mass of the given compound. Then, we have to calculate the % of each element present in the compound.

Complete step by step answer:
We have to calculate the molecular mass of ${\text{A}}{{\text{l}}_{\text{2}}}{\left( {{\text{S}}{{\text{O}}_{\text{4}}}} \right)_{\text{3}}}$.
We know that the atomic mass of oxygen is 16 g/mol, the atomic mass of sulphur is 32 g/mol and the atomic mass of aluminium is 26.98 g/mol.
Molecular mass of ${\text{A}}{{\text{l}}_{\text{2}}}{\left( {{\text{S}}{{\text{O}}_{\text{4}}}} \right)_{\text{3}}}$=$2 \times $atomic mass of Al+3$ \times $atomic mass of sulphur +12$ \times $atomic mass of oxygen
Molecular mass of ${\text{A}}{{\text{l}}_{\text{2}}}{\left( {{\text{S}}{{\text{O}}_{\text{4}}}} \right)_{\text{3}}}$=$2 \times 26.98 + 3 \times 32.06 + 12 \times 16 = 53.96 + 96.18 + 192 = 342.14\,{\text{g}}\,{\text{mo}}{{\text{l}}^{ - 1}}$
Now, we have to calculate the percentage of each element.
Let’s start with Aluminium.
% of aluminium (Al)$ = \dfrac{{{\text{Mass}}\,{\text{of}}\,{\text{Al}}}}
{{{\text{Molecular}}\,{\text{mass}}\,{\text{of}}\,{\text{A}}{{\text{l}}_{\text{2}}}{{\left( {{\text{S}}{{\text{O}}_{\text{4}}}} \right)}_{\text{3}}}}} \times 100$
$ \Rightarrow $% of aluminium (Al)$ = \dfrac{{53.96}}{{342.14}} \times 100 = 15.77\% $
Then, we calculate % composition of Sulphur.
% of sulphur (S)$ = \dfrac{{{\text{Mass}}\,{\text{of S}}}}
{{{\text{Molecular}}\,{\text{mass}}\,{\text{of}}\,{\text{A}}{{\text{l}}_{\text{2}}}{{\left( {{\text{S}}{{\text{O}}_{\text{4}}}} \right)}_{\text{3}}}}} \times 100$
$ \Rightarrow $% of Sulphur(S)$ = \dfrac{{96.18}}{{342.14}} \times 100 = 28.11\% $
Then, we calculate % composition of oxygen.
% of oxygen (O)$ = \dfrac{{{\text{Mass}}\,{\text{of O}}}}
{{{\text{Molecular}}\,{\text{mass}}\,{\text{of}}\,{\text{A}}{{\text{l}}_{\text{2}}}{{\left( {{\text{S}}{{\text{O}}_{\text{4}}}} \right)}_{\text{3}}}}} \times 100$
$ \Rightarrow $% of oxygen (O)$ = \dfrac{{192}}{{342.14}} \times 100 = 56.11\% $
Hence,
The percentage composition of Al is 15.77%
The percentage composition of S is 28.11%
The percentage composition of Al is 56.11%

Note: It is to be noted that molecular mass of a compound is calculated by adding the atomic masses of all atoms which constitute the molecules of that compound. Also, if we add the percentage of all the elements of a compound, we will get 100. Percentage composition helps us to know about the percentage of each element making the compound.