To determine how many moles of shikimic acid (C₇H₁₀O₅) can be synthesized given 3.47 × 10²³ molecules of C₂H₄O₂, we should proceed through the following steps:
1. Understand Avogadro's Number: Avogadro's number is 6.022 × 10²³, which is the number of molecules in one mole of any substance.
2. Given Data:
- Number of molecules of C₂H₄O₂: 3.47 × 10²³
3. Convert Molecules to Moles:
- The number of moles of a substance can be calculated using the formula:
[tex]\[
\text{Number of moles} = \frac{\text{Number of molecules}}{\text{Avogadro's number}}
\][/tex]
- Plugging in the given values:
[tex]\[
\text{Number of moles of C₂H₄O₂} = \frac{3.47 \times 10^{23}}{6.022 \times 10^{23}}
\][/tex]
4. Calculate the Ratio:
- Simplify the expression to get the number of moles:
[tex]\[
\text{Number of moles of C₂H₄O₂} \approx 0.576
\][/tex]
5. Moles of C₂H₄O₂ to Moles of Shikimic Acid:
- Assuming that each molecule of C₂H₄O₂ contributes to the synthesis of one molecule of shikimic acid and given the ratio is 1:1, the moles of shikimic acid synthesized will be the same as the moles of C₂H₄O₂.
6. Final Answer:
- Therefore, the number of moles of shikimic acid that could be synthesized is:
[tex]\[
\text{Moles of shikimic acid} = 0.576
\][/tex]
So, the answer is 0.576 moles of shikimic acid could be synthesized.
