If a pure sample of an oxide of sulfur contains 40. percent sulfur and 60. percent oxygen by mass, t — Stoichiometry Chemistry Question

STEPS:

1. Understand the definition of an empirical formula: An empirical formula represents the simplest, lowest whole-number ratio of the elements present in a chemical compound.
2. Assume a convenient sample size: To easily convert the given mass percentages into tangible masses, assume a 100.0 g sample of the sulfur oxide. Under this assumption:
* The mass of sulfur ($\text{S}$) is exactly $40.0\text{ g}$.
* The mass of oxygen ($\text{O}$) is exactly $60.0\text{ g}$.
3. Convert the mass of each element to moles: Use the average atomic molar masses from the periodic table:
* For Sulfur ($\text{Molar Mass} \approx 32.06\text{ g/mol}$):
$$\text{Moles of S} = \frac{40.0\text{ g}}{32.06\text{ g/mol}} \approx \mathbf{1.25\text{ mol S}}$$
* For Oxygen ($\text{Molar Mass} \approx 16.00\text{ g/mol}$):
$$\text{Moles of O} = \frac{60.0\text{ g}}{16.00\text{ g/mol}} = \mathbf{3.75\text{ mol O}}$$
4. Determine the simplest molar ratio: Divide the number of moles of each element by the smallest number of moles calculated ($1.25\text{ mol}$):
* Ratio for S: $\frac{1.25}{1.25} = \mathbf{1}$
* Ratio for O: $\frac{3.75}{1.25} = \mathbf{3}$
5. Write the empirical formula: Because the molar ratio of $\text{S}$ to $\text{O}$ is exactly $1:3$, the empirical formula of the sulfur oxide is $\text{SO}_3$, which identifies Option A as the correct answer.

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WHY_OTHERS_WRONG:

• Option B is incorrect ($\text{SO}_4$): If the compound were sulfur tetroxide ($\text{SO}_4$), the molar ratio of sulfur to oxygen would be $1:4$. This corresponds to a mass composition of approximately $33.4\%$ sulfur and $66.6\%$ oxygen, which is inconsistent with the given data.
• Option C is incorrect ($\text{S}_2\text{O}_6$): Although the ratio of atoms in $\text{S}_2\text{O}_6$ is chemically equivalent to the correct mass percentage, an empirical formula must show the lowest whole-number ratio of atoms. $\text{S}_2\text{O}_6$ is a molecular formula because it can be mathematically simplified down to $\text{SO}_3$.
• Option D is incorrect ($\text{S}_2\text{O}_8$): This represents a molecular formula that simplifies to the empirical formula $\text{SO}_4$ (representing $25.0\%$ sulfur and $75.0\%$ oxygen by mass). It is neither the lowest whole-number ratio nor does it match the specified mass percentage composition of the sample.