Question

Two successive reactions, \(\mathrm{D} \longrightarrow \mathrm{E}\) and \(\mathrm{E} \longrightarrow \mathrm{F},\) have yields of \(48 \%\) and \(73 \%\), respectively. What is the overall percent yield for conversion of \(\mathrm{D}\) to \(\mathrm{F} ?\)

Short answer

35.04%

Step-by-step solution

Understand the Reaction Yields

Identify the yield of each individual reaction. The yield for the reaction \(\text{D} \longrightarrow \text{E}\) is 48%, and the yield for the reaction \(\text{E} \longrightarrow \text{F}\) is 73%.

Convert Percentages to Decimals

Convert the given percentage yields to decimal form. For the first reaction: \(\frac{48}{100} = 0.48\). For the second reaction: \(\frac{73}{100} = 0.73\).

Calculate Overall Yield

Multiply the decimal yields of the two reactions to find the overall yield: \(\text{Overall yield} = 0.48 \times 0.73\).

Convert Back to Percentage

Convert the product from the previous step back to a percentage. Thus, the overall percent yield is \(0.48 \times 0.73 \times 100\).

Perform the Calculation

Calculate the result: \0.48 \times 0.73 = 0.3504\. Converting to a percentage: \(0.3504 \times 100 = 35.04\text{\text{\footnotesize \text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\footnotesize}}}}}}}}}})))))).//}}}}])))]))]} )))): \)}.\}\}\}

Key concepts

reaction yields

In chemistry, reaction yield refers to how much product is obtained from a chemical reaction. It is usually expressed as a percentage, indicating how close the actual yield comes to the theoretical yield. Theoretical yield is the maximum amount of product expected based on the reactants used, assuming perfect conditions without any losses.
Reaction yields can vary due to several factors, such as reaction efficiency, side reactions, or incomplete reactions. Understanding reaction yields helps to assess the efficiency of chemical processes and optimize them for better productivity. Measuring reaction yields is crucial in both academic settings and industrial applications to ensure the best possible outcomes.
When dealing with multiple reactions, each step's yield affects the overall result. Whether in laboratory experiments or large-scale manufacturing, knowing how to calculate overall yield is vital for achieving desired results efficiently and cost-effectively.

step-by-step calculation

Calculating overall yields involves a series of steps, making it essential to approach each systematically. Below, we detail a clear process to ensure accurate computations:

Identify individual yields: Start by noting the percentage yield of each reaction in a sequence. For example, in the given exercise, the yield for the first reaction (D to E) is 48%, and the yield for the second reaction (E to F) is 73%.

Convert percentages to decimals: To facilitate multiplication, convert each percentage yield to a decimal. Simply divide by 100. Therefore, 48% becomes 0.48 and 73% becomes 0.73.

Multiply the decimal yields: The overall yield is found by multiplying the individual decimal yields of each step. In our exercise, multiply 0.48 by 0.73.

Convert the result back to a percentage: Finally, convert the decimal product back to a percentage by multiplying by 100. This gives the overall percent yield for the multi-step reaction.
Through these simple steps, calculating overall yield becomes manageable and straightforward, even for complex multi-step reactions.

percentage to decimal conversion

Percentage to decimal conversion is a fundamental skill in calculating yields and various other chemistry problems. Conversion is simple and involves a basic division:
To convert a percentage to a decimal, divide by 100. This shifts the decimal point two places to the left. For example, 48% becomes 0.48 and 73% becomes 0.73.

Here's a quick guide to illustrate:

• 48%: 48 ÷ 100 = 0.48
• 73%: 73 ÷ 100 = 0.73

Conversely, to convert a decimal back to a percentage, multiply by 100, which shifts the decimal point two places to the right. Thus, 0.35 becomes 35%. Managing these conversions accurately is crucial for correct calculations in all chemistry-related percentage problems, ensuring you achieve reliable and precise results.

successive reactions

In chemistry, successive reactions involve a series of steps where the product of one reaction becomes the reactant for the next. Each step has its own yield, and the overall yield depends on the yields of all the individual steps.
For example, consider the reactions D to E and E to F. If D converts to E with a 48% yield and E converts to F with a 73% yield, the combined effect of these reactions must be calculated:

• Convert yields to decimals: 48% becomes 0.48, and 73% becomes 0.73.
• Multiply these decimals: 0.48 × 0.73 = 0.3504.
• Convert the result back to a percentage: 0.3504 × 100 = 35.04%.

The overall yield for converting D to F is 35.04%. This method ensures you account for losses at each step, giving a realistic assessment of the entire process.
Understanding successive reactions helps in designing and optimizing chemical processes, whether in research or industrial applications, where achieving high-efficiency results is critical.