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In the bio-synthesis of shikimic acid, as seen above, how many moles of shikimic acid
(C7H1005) could be synthesized if you had 3.47x1023 molecules of C2H4O2 to start with?
Please give your answer with three digits past the decimal (to the thousandths digit).

Verified Answer :

GinnyAnswer

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:
\(\[ \text{Number of moles} = \frac{\text{Number of molecules}}{\text{Avogadro's number}} \]\)
- Plugging in the given values:
\(\[ \text{Number of moles of C₂H₄O₂} = \frac{3.47 \times 10^{23}}{6.022 \times 10^{23}} \]\)

4. Calculate the Ratio:
- Simplify the expression to get the number of moles:
\(\[ \text{Number of moles of C₂H₄O₂} \approx 0.576 \]\)

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:
\(\[ \text{Moles of shikimic acid} = 0.576 \]\)

So, the answer is 0.576 moles of shikimic acid could be synthesized.

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