Problem 107 - Chemistry: The Central Science in SI Units, Global Edition

Question

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?

Step-by-Step Solution

Answer

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 1: 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.

Step 2: 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: \(0.85^{12}\).

Step 3: Convert the total fractional yield back to percentage

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

Step 4: 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%.

Key Concepts

Synthesis

In organic chemistry, synthesis is the process by which complex chemical compounds are constructed from simpler ones. This is often achieved through a series of chemical reactions.
This process is crucial for developing complex organic molecules, such as antibiotic compounds, which are often found in nature.
In the laboratory, synthesizing such compounds can involve numerous steps. Each step has specific reagents and conditions required to convert one molecule to another. The synthesis of Viridicatumtoxin B, for example, involves 12 specific steps. Each step must proceed with precision to ultimately create the desired compound. This labor-intensive process helps chemists not only prove the structure of natural products but also create them in sufficient quantity for further testing or use.

Percent Yield

Percent yield is a measure of the efficiency of a chemical synthesis, telling us how much product we actually obtain compared to the maximum possible amount.
It can often be much lower than expected due to various factors like incomplete reactions or losses during processing.
To calculate percent yield, we compare the actual yield (from the experiment) with the theoretical yield (the calculated maximum amount of product possible). In the case of Viridicatumtoxin B's synthesis, each of the 12 steps has an individual yield of 85%. This means each individual transformation from reactants to products successfully produces 85% of what is theoretically possible.
However, when considering the entire multi-step synthesis, the final percent yield can be dramatically reduced, resulting in an overall yield of just over 21%.

Antibiotic Compounds

Antibiotic compounds are a class of substances that target and kill bacterial cells, helping to combat bacterial infections. These compounds can be derived from natural sources or synthesized in the lab.
Viridicatumtoxin B is one such antibiotic compound, known for its complex structure and potent antibacterial properties. Understanding the synthesis of an antibiotic compound like Viridicatumtoxin B is vital to producing them in large numbers outside of natural sources.
This allows scientists to explore modifications to enhance effectiveness or improve safety. Studying these compounds not only aids in developing new drugs but also in understanding the underlying structures that make them effective against bacteria.

Chemical Reactions

Chemical reactions are the foundational processes in chemistry that involve the transformation of substances. During a reaction, reactants are converted into products through rearrangements of atoms and changes in bonding.
Each reaction step in a synthesis pathway has specific reaction mechanisms and requirements, such as catalysts, specific temperatures, and pressures. For a compound like Viridicatumtoxin B, a series of chemical reactions are meticulously planned and executed to achieve the desired product through 12 individual steps.
These steps involve various types of reactions, such as oxidation, reduction, and condensation, each contributing to building the complex molecular structure.
Understanding each reaction's role in the synthesis helps ensure that the final compound is produced accurately and efficiently.