Problem 107 - Chemistry The Central Science

Question

Paclitaxel, \(\mathrm{C}_{47} \mathrm{H}_{51} \mathrm{NO}_{14},\) is an anticancer compound that is difficult to make in the lab. One reported synthesis requires 11 steps, and the final yield of paclitaxel is only 5\(\% .\) Assuming all steps have equivalent yields, what is the average percent yield for each step in the synthesis?

Step-by-Step Solution

Answer

The average percent yield for each step in the synthesis of Paclitaxel is approximately 64.2%. This is calculated using the overall percent yield formula, and converting the final yield of paclitaxel to decimal form before taking the 11th root and converting the result back to a percentage.

Step 1: Write the formula

The given formula for overall percent yield is: Final percent yield (in decimal form) = [(Individual percent yield (in decimal form))^Number of steps] Step 2: Convert the final yield of paclitaxel into decimal

Step 2: Convert the final yield

Final yield of paclitaxel = 5% = 0.05 (in decimal form) Step 3: Rewrite the formula with the given values

Step 3: Substitute values into the formula

0.05 = [(Average percent yield (in decimal form))^11] Step 4: Determine the average percent yield in decimal form

Step 4: Find the decimal average percent yield

To find the average percent yield in decimal form, take the 11th root of 0.05: Average percent yield (in decimal form) = (0.05)^(1/11) Step 5: Calculate the value

Step 5: Calculate the decimal average percent yield

Average percent yield (in decimal form) = (0.05)^(1/11) ≈ 0.642 Step 6: Convert the decimal average percent yield to a percentage

Step 6: Convert to percentage

To convert the average percent yield from decimal form to percentage, multiply by 100: Average percent yield (in percentage) = 0.642 * 100 = 64.2% Answer: The average percent yield for each step in the synthesis of Paclitaxel is approximately 64.2%.

Key Concepts

Chemical Synthesis

Chemical synthesis is the process of creating complex chemical compounds from simpler ones through a series of chemical reactions. This process is fundamental to the field of organic chemistry and is widely used in the pharmaceutical industry, materials science, and research.

In chemical synthesis, the objective is to design a sequence of reactions that leads to a desired product with high purity and a high yield. Yields are often a measure of a reaction's efficiency and can vary depending on the complexity of the synthesis and the conditions under which it is carried out. The yield is typically expressed as a percentage of the maximum possible amount of product, which is derived from the stoichiometry of the balanced chemical equation.

Synthesis can involve processes such as functional group transformations, the making and breaking of covalent bonds, and the rearrangement of atoms. Each step requires careful planning and consideration to optimize conditions and select the appropriate reagents and catalysts to drive the reactions toward the desired product with minimal side-product formation.

Paclitaxel Synthesis

The synthesis of Paclitaxel, a complex molecule used as an anticancer drug, is an example of a high-level application of chemical synthesis. Paclitaxel has a complicated molecular structure with numerous chiral centers, making its synthesis a challenging endeavor. This compound is naturally found in the bark of the Pacific yew tree, Taxus brevifolia, but due to sustainability issues and the high demand for this drug, a laboratory synthesis is preferred.

In producing Paclitaxel via chemical synthesis, researchers must replicate a molecule identical to the natural form to ensure efficacy and safety. The synthesis often requires multiple steps - each introducing a new functional group or forming a new bond - and must be designed to protect the integrity of the existing structure. Due to the intricate nature of this molecule, each step must be executed with a high degree of precision to achieve a viable final product.

Even with meticulous planning, the reality of synthesizing such a compound is that yields for each step can be low, and the overall yield after many steps is often much lower than that of the individual steps. This is why understanding and improving the efficiency of each step's yield is critical in pharmaceutical chemistry.

Stoichiometry

Stoichiometry is a quantitative relationship between reactants and products in a chemical reaction. It allows chemists to predict the amounts of substances consumed and produced in a reaction, based on the balanced chemical equation. Understanding stoichiometry is essential for all aspects of chemistry, from preparing reactions in the lab to scaling up for industrial production.

Stoichiometry plays a pivotal role in calculating the percent yield during chemical synthesis. The percent yield indicates the efficiency of a chemical reaction and is calculated by comparing the actual amount of product obtained to the theoretical amount expected from stoichiometry. It's expressed as a percentage, with 100% being the perfect yield, which practically is never achieved due to side reactions and incomplete conversions.

In the context of education, having a firm grasp of stoichiometry is crucial for students to understand and solve problems related to chemical reactions. By breaking down the concepts step by step and providing clear examples, educators can convey the principles of stoichiometry in a way that students can easily relate to their own experiments and observations in the chemistry laboratory.