To determine how many molecules of oxygen ([tex]\(O_2\)[/tex]) are needed to react with [tex]\(98.6 \, \text{g}\)[/tex] of sulfur dioxide ([tex]\(SO_2\)[/tex]), we need to follow these steps:
1. Calculate the molar mass of [tex]\(SO_2\)[/tex]:
- The atomic mass of sulfur (S) is [tex]\(32\, \text{g/mol}\)[/tex].
- The atomic mass of oxygen (O) is [tex]\(16\, \text{g/mol}\)[/tex].
- Since [tex]\(SO_2\)[/tex] consists of one sulfur atom and two oxygen atoms, its molar mass is:
[tex]\[
\text{Molar mass of } SO_2 = 32\, \text{g/mol (S)} + 2 \times 16\, \text{g/mol (O)} = 64\, \text{g/mol}
\][/tex]
2. Calculate the number of moles of [tex]\(SO_2\)[/tex]:
- Given mass of [tex]\(SO_2 = 98.6\, \text{g}\)[/tex].
- Using the formula:
[tex]\[
\text{Number of moles} = \frac{\text{given mass}}{\text{molar mass}}
\][/tex]
- We get:
[tex]\[
\text{Number of moles of } SO_2 = \frac{98.6\, \text{g}}{64\, \text{g/mol}} = 1.541 \text{ mol} (approximately)
\][/tex]
3. Determine the moles of [tex]\(O_2\)[/tex] required using the balanced chemical equation:
- The balanced chemical equation is:
[tex]\[
2 SO_2 + O_2 \rightarrow 2 SO_3
\][/tex]
- According to the equation, [tex]\(2\)[/tex] moles of [tex]\(SO_2\)[/tex] react with [tex]\(1\)[/tex] mole of [tex]\(O_2\)[/tex].
- Therefore, the moles of [tex]\(O_2\)[/tex] required are half the moles of [tex]\(SO_2\)[/tex]:
[tex]\[
\text{Moles of } O_2 \text{ needed} = \frac{1.541}{2} = 0.7705 \text{ mol} (approximately)
\][/tex]
4. Convert moles of [tex]\(O_2\)[/tex] to molecules:
- Using Avogadro's number ([tex]\(6.022 \times 10^{23}\)[/tex] molecules per mole), we convert the moles of [tex]\(O_2\)[/tex] to molecules:
[tex]\[
\text{Number of molecules} = \text{moles} \times \text{Avogadro's number}
\][/tex]
- Therefore:
[tex]\[
\text{Number of molecules of } O_2 \text{ needed} = 0.7705 \text{ mol} \times 6.022 \times 10^{23} \frac{\text{molecules}}{\text{mol}} = 4.638821875 \times 10^{23} \text{ molecules}
\][/tex]
Based on these calculations, the correct answer is:
C. [tex]\(4.63 \times 10^{23}\)[/tex] molecules
