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 $\mathrm{Pb}{\mathrm{I}}_2$ 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 Formula for Percent Yield

The percent yield is calculated using the formula:$$\text{Percent Yield}=\left(\frac{\text{Actual Yield}}{\text{Theoretical Yield}}\right)\times 100\mathrm{\%}$$Where the actual yield is the amount of product actually collected, and the theoretical yield is the amount of product that should have been collected under perfect conditions.

Identify the Given Values

In this problem, the actual yield of lead(II) iodide (${\mathrm{PbI}}_2$) is given as $12.5\mathrm{g}$. The theoretical yield is given as $13.9\mathrm{g}$.

Apply the Formula

Substitute the given values into the percent yield formula:$$\text{Percent Yield}=\left(\frac{12.5\mathrm{g}}{13.9\mathrm{g}}\right)\times 100\mathrm{\%}$$

Calculate the Percent Yield

Divide the actual yield by the theoretical yield:$$\frac{12.5}{13.9}\approx 0.8993$$Then multiply by 100 to convert it to a percentage:$$0.8993\times 100\approx 89.93\mathrm{\%}$$

Final Result

Round the result to a reasonable number of significant figures (2 decimal places, since the precision of the measurements is up to one decimal place). The percent yield is therefore approximately $89.93\mathrm{\%}$.

Key concepts

Stoichiometry

In chemistry, stoichiometry is a crucial concept that helps us understand the relationships between reactants and products in a chemical reaction. It involves using balanced chemical equations to calculate the quantities of substances involved. In simpler terms, stoichiometry is like a recipe for chemical reactions, ensuring that you have just the right amount of each ingredient to create your desired product.

When dealing with stoichiometry, you follow these key steps:

• Write a balanced chemical equation for the reaction.
• Use the molar ratios from the balanced equation to link amounts between reactants and products.
• Convert the given quantities (usually mass or volume) to moles, because stoichiometric coefficients refer to moles.
• Calculate the theoretical yield, which is the maximum amount of product that can be generated under perfect conditions.

For our example, if we know the starting amount of lead(II) nitrate, stoichiometry allows us to predict how much lead(II) iodide can be produced, assuming nothing is lost in the process.

Chemical Reactions

Chemical reactions are processes where substances, known as reactants, are transformed into different substances called products. In every reaction, bonds between the elements in the reactants are broken and new bonds form to create the products.

A typical chemical reaction can be represented by a chemical equation, where the reactants are written on the left and products on the right, separated by an arrow indicating the direction of the reaction. For example, in the reaction between lead(II) nitrate and potassium iodide to form lead(II) iodide and potassium nitrate, the equation can be written as:$${\text{Pb(NO}}_3{\text{)}}_2(aq)+2\text{KI}(aq)\to {\text{PbI}}_2(s)+2{\text{KNO}}_3(aq)$$In this equation:

• ${\text{Pb(NO}}_3{\text{)}}_2$ is lead(II) nitrate.
• $\text{KI}$ is potassium iodide.
• ${\text{PbI}}_2$ is lead(II) iodide.
• ${\text{KNO}}_3$ is potassium nitrate.

Balancing a chemical equation like this ensures the conservation of mass, meaning the same number of each type of atom appears on both sides of the equation.

Lead(II) Iodide

Lead(II) iodide, denoted by the chemical formula ${\text{PbI}}_2$, is a bright yellow compound that precipitates out of solution, making it easy to observe in reactions. It's an interesting compound not only because of its vibrant color but also due to its significant role in educational and industrial chemical reactions.

Here are some important aspects of lead(II) iodide:

• It is formed by combining a solution containing lead ions with one containing iodide ions.
• In reactions, it's often used to demonstrate the concept of precipitation, where an insoluble solid forms from mixing two solutions.
• Although useful in certain contexts, lead(II) iodide is toxic due to its lead content, requiring careful handling and disposal.

In the context of percent yield calculations, lead(II) iodide acts as the product whose mass is measured to determine how efficient a reaction has been, compared to the theoretical yield calculated through stoichiometry.