To determine how many moles of trifluoromethanoic acid (CHF₃O₃S) are present in \( 9.0345 \times 10^{24} \) molecules of CHF₃O₃S, we can use Avogadro's number. Avogadro's number tells us that one mole of a substance contains \( 6.022 \times 10^{23} \) molecules.
Here is how we can calculate the number of moles step by step:
1. Identify the number of molecules given:
[tex]\[ 9.0345 \times 10^{24} \text{ molecules} \][/tex]
2. Identify Avogadro's number:
[tex]\[ 6.022 \times 10^{23} \text{ molecules per mole} \][/tex]
3. Use the formula to convert molecules to moles:
[tex]\[ \text{Number of moles} = \frac{\text{Number of molecules}}{\text{Avogadro's number}} \][/tex]
4. Substitute the given values:
[tex]\[
\text{Number of moles} = \frac{9.0345 \times 10^{24} \text{ molecules}}{6.022 \times 10^{23} \text{ molecules per mole}}
\][/tex]
5. Perform the division to find the number of moles:
[tex]\[
\text{Number of moles} \approx 15.002490866821654
\][/tex]
The result of our calculation is approximately \( 15.002490866821654 \) moles. When we look at the provided answer options:
- A. \( 1.5 \times 10^{23} \text{ mol} \)
- B. \( 1.5 \text{ mol} \)
- C. \( 15 \text{ mol} \)
- D. \( 1.5 \times 10^{24} \text{ mol} \)
- E. \( 0.15 \text{ mol} \)
It is clear that the closest answer to our calculated result of 15.002490866821654 moles is option C. \( 15 \text{ mol} \).
Therefore, the correct answer is:
C. [tex]\( 15 \text{ mol} \)[/tex]
