To determine the mass of oxygen gas ([tex]\(O_2\)[/tex]) formed from the decomposition of potassium chlorate ([tex]\(KClO_3\)[/tex]), we first need to understand the stoichiometry of the reaction given:
[tex]\[
2 \text{KClO}_3 \rightarrow 2 \text{KCl} + 3 \text{O}_2
\][/tex]
Here’s a step-by-step approach to solve the problem:
1. Calculate the moles of [tex]\(KClO_3\)[/tex]:
- Given mass of [tex]\(KClO_3\)[/tex] = 240 grams
- Molar mass of [tex]\(KClO_3\)[/tex] = 122.5 g/mol
- Moles of [tex]\(KClO_3\)[/tex] = [tex]\(\frac{\text{mass}}{\text{molar mass}}\)[/tex]
[tex]\[
\text{Moles of } KClO_3 = \frac{240 \text{ grams}}{122.5 \text{ g/mol}} = 1.9591836734693877 \text{ moles}
\][/tex]
2. Relate the moles of [tex]\(KClO_3\)[/tex] to the moles of [tex]\(O_2\)[/tex] using the stoichiometry:
- According to the reaction, 2 moles of [tex]\(KClO_3\)[/tex] produce 3 moles of [tex]\(O_2\)[/tex]
- Using the ratio:
[tex]\[
\text{Moles of } O_2 = \text{Moles of } KClO_3 \times \frac{3}{2} = 1.9591836734693877 \times \frac{3}{2} = 2.9387755102040813 \text{ moles}
\][/tex]
3. Convert moles of [tex]\(O_2\)[/tex] to mass:
- Molar mass of [tex]\(O_2\)[/tex] = 31.998 g/mol
- Mass of [tex]\(O_2\)[/tex] = [tex]\(\text{Moles of } O_2 \times \text{Molar mass of } O_2\)[/tex]
[tex]\[
\text{Mass of } O_2 = 2.9387755102040813 \text{ moles} \times 31.998 \text{ g/mol} = 94.0349387755102 \text{ grams}
\][/tex]
From this calculation, we see that the correct choice should compute the mass of [tex]\(O_2\)[/tex]. Checking the formulas provided:
- [tex]\((240 \times 2 \times 31.998) \div(122.5 \times 3)\)[/tex] grams
- [tex]\((240 \times 3 \times 31.998) \div(122.5 \times 2)\)[/tex] grams
- [tex]\((240 \times 2 \times 122.5) \div(31.998 \times 3)\)[/tex] grams
- [tex]\((240 \times 3 \times 122.5) \div(31.998 \times 2)\)[/tex] grams
We find that the correct formula matches the second option:
[tex]\[
(240 \times 3 \times 31.998) \div(122.5 \times 2) \text{ grams}
\][/tex]
Thus, the calculation to determine the mass of oxygen gas formed is correctly given by the formula:
[tex]\[
(240 \times 3 \times 31.998) \div(122.5 \times 2) \text{ grams}
\][/tex]
