Absolutely! Let's solve the problem step-by-step.
Given the decomposition reaction of potassium chlorate ([tex]\(KClO_3\)[/tex]):
[tex]\[
2 KClO_3(s) \rightarrow 2 KCl(s) + 3 O_2(g)
\][/tex]
To find out how many moles of [tex]\(O_2\)[/tex] are formed from a 3.8-mol sample of [tex]\(KClO_3\)[/tex], we need to analyze the molar relationship from the balanced chemical equation.
1. Identify the molar ratio: According to the balanced chemical equation, 2 moles of [tex]\(KClO_3\)[/tex] decompose to produce 3 moles of [tex]\(O_2\)[/tex].
[tex]\[
2 \text{ moles } KClO_3 \rightarrow 3 \text{ moles } O_2
\][/tex]
2. Calculate the molar ratio: For 1 mole of [tex]\(KClO_3\)[/tex]:
[tex]\[
\text{Moles of } O_2 = 1 \times \frac{3}{2} = 1.5 \text{ moles of } O_2
\][/tex]
3. Apply the molar ratio to the given sample: Now, we need to determine how many moles of [tex]\(O_2\)[/tex] are produced from a 3.8-mol sample of [tex]\(KClO_3\)[/tex]:
[tex]\[
\text{Moles of } O_2 = 3.8 \text{ moles of } KClO_3 \times \frac{3}{2} = 3.8 \times 1.5
\][/tex]
4. Perform the multiplication:
[tex]\[
3.8 \times 1.5 = 5.7 \text{ moles of } O_2
\][/tex]
Hence, the number of moles of [tex]\(O_2\)[/tex] formed from a 3.8-mol sample of [tex]\(KClO_3\)[/tex] is [tex]\(5.7\)[/tex] moles.
Therefore, the correct answer is:
[tex]\[ \boxed{5.7 \text{ mol}} \][/tex]
