How many molecules of oxygen are needed to react with [tex]98.6 \, \text{g} \, \text{SO}_2[/tex]?

[tex]2 \, \text{SO}_2 + \text{O}_2 \rightarrow 2 \, \text{SO}_3[/tex]

A. [tex]1.54 \times 10^{23}[/tex] molecules
B. [tex]3.01 \times 10^{23}[/tex] molecules
C. [tex]4.63 \times 10^{23}[/tex] molecules
D. [tex]5.94 \times 10^{25}[/tex] molecules



Answer :

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