Question

Two successive reactions, \(\mathrm{A} \rightarrow \mathrm{B}\) and \(\mathrm{B} \rightarrow \mathrm{C}\), have yields of \(90 \%\) and \(80 \%\), respectively. What is the overall percentage yield for conversion of \(\mathrm{A}\) to \(\mathrm{C}\) ? (a) \(90 \%\) (b) \(80 \%\) (c) \(72 \%\) (d) \(85 \%\)

Short answer

72%

Step-by-step solution

Understand the problem

The task is to find the overall percentage yield for the conversion of chemical A to chemical C through an intermediate chemical B. It’s given that the yield of A to B is 90%, and the yield of B to C is 80%.

Calculate the yield from A to B

The yield from A to B is given as 90%. Thus, if you start with 100 units of A, then 90 units of B are formed.

Calculate the yield from B to C

The yield from B to C is given as 80%. Since you have 90 units of B from step 2, 80% of these 90 units will turn into C. Multiply 90 units of B by 0.8 to get the units of C.

Combine the two yields to find the overall yield

To find the overall yield, multiply the individual yields (in their decimal form). The overall yield = yield of A to B × yield of B to C.

Calculate the overall percentage yield

The overall percentage yield is found by multiplying 90% (or 0.9) by 80% (or 0.8). This gives the overall yield in decimal form, which can be converted back into a percentage.

Key concepts

Chemical Reaction Efficiency

Understanding chemical reaction efficiency is critical for students who wish to gauge how well a reaction converts reactants into desired products. Efficiency in this context relates to the 'yield' of a chemical process, which measures the amount of product obtained from a reaction compared to the maximum amount possible, as predicted by stoichiometry.

When a reaction has a high yield, it indicates an efficient conversion of reactants to products, meaning less waste and fewer side reactions. For example, if you start with a 100 grams of a reactant and produce 90 grams of the desired product, the efficiency is fairly high. However, if only 50 grams of product are formed, the reaction is less efficient. This simple notion is vital in research, manufacturing, and even environmental considerations, where maximising efficiency is often economically and ecologically desirable.

Key factors affecting reaction efficiency include reaction conditions like temperature and pressure, catalysts, the purity of reactants, and the reaction mechanism itself. Improving efficiency could involve tweaking these factors and optimizing the reaction conditions.

Sequential Reaction Yields

Sequential reaction yields refer to the individual yields of successive reactions in a multi-step chemical process. Each step has its own efficiency, and the total efficiency of the process is the product of the efficiencies of each step.

To exemplify, consider a two-step reaction where the first step has a yield of 90% and the second has a yield of 80%. The overall yield is not simply the average of these two numbers; it's actually obtained by multiplying the fractional yields of each step. This is because the second step's yield is applied to the product of the first step, thus, its efficiency impacts already reduced quantity of product from the first reaction.

To aid comprehension, imagine the sequential process as a multi-stage manufacturing assembly line where each stage has some defect rate. The overall defect rate of the final product is compounded by the defect rates of each individual stage. Similarly, in chemistry, the final yield is a cumulative product of the individual efficiencies through each reaction stage.

Yield Calculation

Yield calculation is a straightforward yet crucial skill for any chemistry student. It enables the quantification of a reaction's efficiency and can guide decisions in both lab and industry settings. To calculate yield, you typically need two figures: the actual yield (what you obtain in reality) and the theoretical yield (what stoichiometry predicts you should obtain). The percentage yield is then the actual yield divided by the theoretical yield, multiplied by 100%.

In our exercise, we've been discussing percentage yields, which are already provided for each step. To find the overall yield for sequential reactions, the correct approach is to multiply the yields of each step, as illustrated in the given solution. The yields must be used in their decimal forms for this multiplication. It's also important to remember that the overall yield can never be greater than the yield of the least efficient step in the process.

Lastly, for educational purposes, it is beneficial to have students practice these calculations with different initial amounts of reactants and different yields, reinforcing their understanding of yield calculations in various scenarios.