Question

A reaction having a 90 percent yield may be considered a successful experiment. However, in the synthesis of complex molecules such as chlorophyll and many anticancer drugs, a chemist often has to carry out multiple-step syntheses. What is the overall percent yield for such a synthesis, assuming it is a 30 -step reaction with a 90 percent yield at each step?

Short answer

The overall percent yield is approximately 4.24%.

Step-by-step solution

Understanding Percent Yield Per Step

Each step in this synthesis has a percent yield of 90%. This means that after each reaction step, only 90% of the substance is successfully converted into the desired product.

Overall Yield Calculation Formula

The overall yield for a multi-step synthesis can be calculated by multiplying the yield of each individual step. If each of the 30 steps has a 90% yield, the overall yield formula is: \( (0.9)^{30} \), where 0.9 represents the 90% yield expressed as a decimal.

Calculating Overall Yield

Now we compute \( 0.9^{30} \). It simplifies to approximately 0.0424, or 4.24%.

Interpretation of Results

The overall yield for this multi-step synthesis reaction is approximately 4.24%, indicating that only around 4.24% of the starting material is converted into the desired final product after 30 reaction steps.

Key concepts

Multi-Step Synthesis

In chemistry, multi-step synthesis refers to a series of chemical reactions where the product of one reaction becomes the reactant for the next. This process is crucial when synthesizing complex molecules that cannot be formed through a single reaction.
This method involves several stages, each responsible for adding, removing, or modifying a part of the molecule to gradually build up to the target compound. During a multi-step synthesis, chemists carefully plan each step to optimize yields and minimize byproducts. The success of a multi-step synthesis largely depends on the efficiency of each individual reaction. Such syntheses are common in developing pharmaceuticals, agricultural chemicals, and materials science, where precision and complexity are key. It's similar to assembling a puzzle, where each piece must fit perfectly to form the complete picture.

Complex Molecules

Complex molecules are the target of many multi-step syntheses. These molecules have intricate structures and often exhibit significant biological activity.
- Examples include **antibiotics**, **hormones**, and **proteins**. - Due to their complexity, these molecules cannot be synthesized through a single-stage reaction. Chemists use multi-step synthesis to delicately build these large, intricate structures, one small logical step at a time. Each reaction step might introduce a new functional group or modify an existing one, contributing to the growing complexity and specific function of the molecule. Synthesizing complex molecules requires careful planning to ensure that each reaction step is successful and that the pathways chosen maximize the yield of the final product. Even slight errors can drastically affect the final product's structure and activity, emphasizing the need for precision.

Reaction Steps

Each reaction step in a multi-step synthesis aims to achieve a specific transformation. These steps are carefully designed and sequenced to build the target molecule efficiently.
- **Planning**: Chemists must meticulously plan these steps to ensure each one aligns with the overall synthetic goal. - **Conditions**: Each reaction step may require different conditions, such as temperature, solvent, and catalysts, to proceed efficiently. Reactions can include simple transformations, like oxidation or reduction, or more complex processes, like forming a new carbon-carbon bond. Each reaction step is a small, controlled change that steers the progress toward the final, desired complex molecule. With each step, the substance progresses closer to becoming the desired product. However, losses are inevitable, which is why each step's percent yield is a consideration for the overall success of the synthesis.

Overall Yield

The overall yield in a multi-step synthesis is the cumulative product of the yields of each reaction step. It is a critical metric for evaluating the success and efficiency of the synthesis.
- **Calculation**: To calculate the overall yield of a process, multiply the yield of each individual step. If a reaction step has a 90% yield, multiplying this step by 30 leads to the formula: - \( \text{Overall Yield} = (0.9)^{30} \) - This results in approximately 4.24% overall yield for the entire synthesis.Such a low overall yield, as seen in a 30-step process, underscores the challenge chemists face. A high yield for each step is crucial, as even small losses accumulate dramatically.In practical terms, an overall yield of 4.24% means that only a small fraction of the starting materials end up as the final desired product after all steps. It highlights the need for optimization in each reaction step to improve the final yield.