Question

$2.18{\text{g}}$ of an organic compound containing sulfur produces $1.02{\text{g}}$ of ${\text{BaS}}{{\text{O}}_4}$. The percentage of sulfur in the compound is:
A. $7.26\%$
B. $8.98\%$
C. $10\%$
D. $6.42\%$

Answer 1

The percentage composition of a component in a compound is the percentage of the total mass of the compound that is due to the component. By finding each element’s percentage composition in a compound, we can calculate the formula mass and empirical mass of the compound.

Complete step by step answer:
Percentage composition is the percentage by mass of each element in a compound.
It is given that amount of organic compound, ${{\text{m}}_{{\text{org}}}} = 2.18{\text{g}}$
Amount of ${\text{BaS}}{{\text{O}}_4}$,${{\text{m}}_{{\text{BaS}}{{\text{O}}_4}}} = 1.02{\text{g}}$
We know that atomic mass of sulfur, ${{\text{M}}_{\text{S}}} = 32{\text{u}}$
Molecular weight of ${\text{BaS}}{{\text{O}}_4}$, ${{\text{M}}_{{\text{BaS}}{{\text{O}}_4}}} = 233{\text{u}}$
Thus the percentage of sulfur can be calculated from these values.
This is obtained by dividing the amount of sulfur in the compound by molar mass.
i.e. $\% {\text{S}} = \dfrac{{{{\text{M}}_{\text{S}}}}}{{{{\text{M}}_{{\text{BaS}}{{\text{O}}_4}}}}} \div \dfrac{{{{\text{m}}_{{\text{org}}}}}}{{{{\text{m}}_{{\text{BaS}}{{\text{O}}_4}}}}}$
Taking reciprocal, we get
The percentage of sulfur, $\% {\text{S = }}\dfrac{{{{\text{M}}_{\text{S}}}}}{{{{\text{M}}_{{\text{BaS}}{{\text{O}}_4}}}}} \times \dfrac{{{{\text{m}}_{{\text{BaS}}{{\text{O}}_4}}}}}{{{{\text{m}}_{{\text{org}}}}}} \times 100$
Substituting the values, we get
$\% {\text{S = }}\dfrac{{32}}{{233}} \times \dfrac{{1.02}}{{2.18}} \times 100$
Simplifying,
$\% {\text{S}} = 0.1373 \times 0.4678 \times 100 = 6.42\%$
Hence the percentage of sulfur in the compound is $6.42\%$
So option D is correct.

Additional information:
Molecular formula tells exactly how many of each atom are in the molecule and empirical formula tells the ratio of atoms in a molecule. Empirical formula is the simplest ratio of elements in a chemical formula. Both of them can be calculated from the percentage composition of elements.

Note:
The steps involved in finding the percentage composition of a component in a compound are:
-Find the molar mass of the compound by adding up the atomic masses of each element.
-Calculate the mass due to the component.
-Divide the mass due to the component by total molar mass of the compound and multiply by $100$.