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Chapter 3: Problem 107

Viridicatumtoxin B, \(\mathrm{C}_{30} \mathrm{H}_{31} \mathrm{NO}_{10},\) is a natural antibiotic compound. It requires a synthesis of 12 steps in the laboratory. Assuming all steps have equivalent yields of \(85 \%\), which is the final percent yield of the total synthesis?

Short Answer

Expert verified
The final percent yield of the total synthesis of Viridicatumtoxin B can be found by converting the 85% yield to a fraction (0.85), raising it to the 12th power (representing the 12 steps), and then converting it back to a percentage. The calculation is as follows: \((0.85^{12}) \times 100 \approx 21.32 \% \). Thus, the final percent yield is approximately 21.32%.

Step by step solution

01

Convert the percentage yield to fractional form

To obtain the yield in fractional form, divide the percent yield (85%) by 100. \(\frac{85}{100}\) = 0.85. Now we have the yield for a single step in fractional form.
02

Calculate the total yield for all 12 steps

Since there are 12 steps, we will multiply the fractional yield from step 1 by itself 12 times: \(0.85^{12}\).
03

Convert the total fractional yield back to percentage

Multiply the result from step 2 by 100 to convert it back to percentage form: \(0.85^{12} \times 100\).
04

Evaluate the expression for the final percent yield

Calculation: \((0.85^{12}) \times 100 = 21.32 \% \) (rounded to two decimal places). The final percent yield of the total synthesis of Viridicatumtoxin B is about 21.32%.

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Most popular questions from this chapter

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