Question

A chemistry student prepared lead(II) iodide from \(10.0 \mathrm{~g}\) of lead(II) nitrate and aqueous potassium iodide. If the student collected \(12.5 \mathrm{~g}\) of \(\mathrm{PbI}_{2}\) and the theoretical yield is \(13.9 \mathrm{~g},\) what is the percent yield?

Short answer

The percent yield is approximately 89.93%.

Step-by-step solution

Understand the Percent Yield Formula

The percent yield formula is given by \( \text{Percent Yield} = \left( \frac{\text{Actual Yield}}{\text{Theoretical Yield}} \right) \times 100 \% \). Here, the actual yield is the amount of product collected, and the theoretical yield is the amount of product expected based on calculations.

Identify the Actual and Theoretical Yield

From the problem, the actual yield of \( \text{PbI}_2 \) is \( 12.5 \text{ g} \), and the theoretical yield is \( 13.9 \text{ g} \). These values will be used in the percent yield formula.

Calculate Percent Yield

Substitute the actual and theoretical yield values into the percent yield formula: \[\text{Percent Yield} = \left( \frac{12.5}{13.9} \right) \times 100 \%\]Calculate the percent yield: \[\text{Percent Yield} = \left( \frac{12.5}{13.9} \right) \times 100 \% \approx 89.93\%\]

Interpret the Result

The percent yield of the experiment is approximately \(89.93\%\). This means that the student collected 89.93% of the lead(II) iodide that was theoretically possible to produce.

Key concepts

Chemical Reactions

When we talk about chemical reactions, we refer to the fascinating process where substances, called reactants, are transformed into different substances, known as products. These fundamental processes are what drive chemistry and explain many phenomena in our world.
A classic example is the reaction between lead(II) nitrate (\( ext{Pb(NO}_3 ext{)}_2\)) and potassium iodide (KI), which forms lead(II) iodide (\( ext{PbI}_2\)) and potassium nitrate (\( ext{KNO}_3\)). This reaction can be summarized by the balanced chemical equation: \[\text{Pb(NO}_3\text{)}_2 + 2\text{KI} \rightarrow \text{PbI}_2 + 2\text{KNO}_3\]
The balanced equation tells us the proportion in which substances react, giving insight into the reaction's stoichiometry. It's like a recipe, ensuring the right amounts of reactants combine to form the desired products.

• Reactants: Lead(II) nitrate and potassium iodide
• Products: Lead(II) iodide and potassium nitrate

Understanding these fundamental concepts helps us predict the outcomes of reactions and calculate important values such as percent yield, by relating the experimental results to what was expected under ideal conditions.

Stoichiometry

In the realm of chemistry, stoichiometry is the method that ensures the proper balance in chemical equations and calculates reactants and products in a chemical reaction. It is fundamentally the study of relationships between the amounts of reactants used and products formed in a chemical reaction.
This "chemical bookkeeping" provides chemists the tools needed to predict the amounts of substances consumed and produced, ensuring reactions go off without a hitch.

• Ensures mass is conserved through the reaction
• Aids in determining how much of each reactant is needed
• Predicts the yield of the products

Using stoichiometry, we can determine the theoretical yield from a given amount of reactants by applying the balanced chemical equation. Theoretical yield is essential for calculating the percent yield, which compares the actual output of the reaction with what was theoretically possible.
In our example, stoichiometry was used to say that starting with 10.0 g of lead(II) nitrate and potassium iodide should theoretically produce 13.9 g of lead(II) iodide.

Theoretical Yield

The theoretical yield is a calculated value that represents the maximum amount of product that can be generated from a given amount of reactants in a chemical reaction, assuming complete conversion and no losses. Achieving the theoretical yield is often not feasible due to imperfections in the reaction process and practical limitations.
To calculate the theoretical yield:

• Use the balanced chemical equation to understand the stoichiometric ratios.
• Calculate the moles of each reactant.
• Determine which reactant is the limiting reactant, as it dictates the maximum product that can form.
• Convert the moles of the product formed to grams.

In the scenario provided, stoichiometry helps chemists understand that from the quantities given, the reaction could ideally produce 13.9 g of lead(II) iodide. It acts as a reference point for percent yield calculations, where the actual yield is typically less due to various factors like incomplete reactions, impure reactants, or side reactions.
This value, though theoretical, is essential for evaluating efficiency and effectiveness in chemical manufacturing and laboratory experiments.