Question

A student added zine metal to a copper nitrate solution to obtain copper metal by a single-displacement reaction. From the known moles of copper nitrate in solution, she calculated the expected mass of copper metal as \(6.7 \mathrm{~g}\). When she weighed the copper on a balance, the mass was \(5.7 \mathrm{~g}\). (a) What is the actual yield of copper metal? (b) What is the theoretical yield of copper metal? (c) Calculate the percent yield.

Short answer

The actual yield of copper is \(5.7 \, g\), the theoretical yield is \(6.7 \, g\), and the percent yield is approximately \(85.07\%.\)

Step-by-step solution

Determining the Actual Yield

The actual yield is the amount of product that is actually formed in a chemical reaction, often less than the theoretical yield due to losses during the reaction. In this experiment, the actual yield of copper is the mass of copper obtained from the reaction, which the student measured as \(5.7 \, \text{g}\).

Determining the Theoretical Yield

The theoretical yield is the amount of product that would be formed in a chemical reaction if everything happened perfectly, often calculated from the balanced chemical equation. In this case, the student calculated the theoretical yield as \(6.7 \, \text{g}\) of copper based on known moles of copper nitrate in solution, assuming there will be no loss during the reaction.

Calculating the Percent Yield

The percent yield is the ratio of the actual yield to the theoretical yield, expressed as a percentage. It is calculated using the formula: \[\text{Percent Yield} = (\frac{\text{Actual Yield}}{\text{Theoretical Yield}}) \times 100\%\] Substituting the given yields into the formula, we get: \[\text{Percent Yield} = (\frac{5.7 \, \text{g}}{6.7 \, \text{g}}) \times 100\% \approx 85.071%.\]

Key concepts

Single-Displacement Reaction

A single-displacement reaction is a type of chemical reaction where one element replaces another in a compound. This usually occurs when a more reactive element displaces a less reactive one. In the context of our experiment, zinc metal is added to a copper nitrate solution. Here, zinc, being more reactive than copper, displaces the copper ions in the solution and forms zinc nitrate, while copper metal is the product that's deposited.

• Zinc metal acts as the displacing agent in this reaction.
• Copper, initially in solution as copper nitrate, is displaced and deposited as metallic copper.

These reactions are helpful in predicting how elements will interact, especially knowing which will displace another. It makes this concept crucial in extracting metals and other practical applications.

Actual Yield

The actual yield is the amount of product truly produced at the end of a chemical experiment. When you perform a reaction in a lab, various factors, such as incomplete reactions, side reactions, or loss of material during processing, can result in less than the expected product. In our experiment with zinc and copper nitrate, the student measured the actual yield of copper metal. Given by the weight on the balance, the actual yield was recorded as 5.7 grams.

• It's vital for realistic success: no experiment is perfect, so knowing actual results is crucial for assessing effectiveness.
• Helps identify issues in the procedure, such as loss of product, which can inform how to improve the experimental setup.

Theoretical Yield

The theoretical yield is the maximum amount of product that could be generated if everything in the reaction went perfectly, without any loss. It's calculated using the balanced chemical equation and the known quantities of reactants. In the case described, the student calculated a theoretical yield of 6.7 grams of copper.

• This amount assumes 100% efficiency, meaning every single molecule of reactant turns into the desired product without any loss.
• It's an essential benchmark that can help compare and evaluate the actual yield.

Understanding theoretical yield provides a basis for gauging the efficiency and viability of chemical processes.

Percent Yield

Percent yield is a ratio expressed as a percentage, demonstrating how efficient a reaction was in producing the desired product compared to its theoretical maximum. The formula for percent yield is:\[\text{Percent Yield} = \left(\frac{\text{Actual Yield}}{\text{Theoretical Yield}} \right) \times 100\%\]In our textbook problem, when substituting the actual yield (5.7 g) and theoretical yield (6.7 g) values into this formula, we get a percent yield of approximately 85.071%.

• This indicates that 85% of the possible product was obtained, revealing both the efficiency and any potential issues in the process.
• A high percent yield suggests a well-conducted experiment, whereas a low percent could show areas for improvement.

Studying percent yield helps chemists optimize reactions for better results in both laboratory and industry settings.