Concept:Using the law of definite proportions, the mass of an individual element within a compound sample can be calculated by applying its mass percentage to the total sample mass.
Formula:$$ \text{Mass of Sulphur} = \left( \frac{\text{Molar mass of S}}{\text{Molar mass of H}_2\text{SO}_4} \right) \times \text{Given mass of compound} $$
Solution:- Calculate total molar mass of Sulfuric Acid (\( \text{H}_2\text{SO}_4 \)):
- \( (2 \times 1) + 32 + (4 \times 16) = 2 + 32 + 64 = 98 \text{ g/mol} \).
- In exactly 98g of \( \text{H}_2\text{SO}_4 \), there are 32g of Sulphur.
- Set up the ratio for the 24.5g sample: \( \left( \frac{32}{98} \right) \times 24.5 \).
- Notice that \( 24.5 \times 4 = 98 \). Therefore, 24.5 is exactly one-fourth (\( 1/4 \)) of 98.
- \( 32 \times (1/4) = 8 \text{ grams} \).
Why other options are incorrect:- 32 g: This is the mass of sulphur in a full 98g mole, impossible to exist in a 24.5g sample.
- 24 g & 16 g: Incorrect arithmetic outputs that do not align with the strict \( 32/98 \) mass fraction.
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