Question

A 1.00-g sample of potassium bicarbonate is decomposed by heating. If the resulting potassium carbonate weighs $0.725\mathrm{g}$ and the calculated yield is $0.690\mathrm{g}$, what is the percent yield?

Short answer

The percent yield is approximately 105.07%.

Step-by-step solution

Understand Percent Yield Formula

Percent yield is calculated using the formula $\text{Percent Yield}=\left(\frac{\text{Actual Yield}}{\text{Theoretical Yield}}\right)\times 100\mathrm{\%}$. The actual yield is the experimental amount you obtain, while the theoretical yield is the amount calculated from stoichiometry or given in the problem.

Identify Actual Yield

In this exercise, the actual yield refers to the mass of potassium carbonate obtained, which is given as $0.725\mathrm{g}$.

Identify Theoretical Yield

The theoretical yield is provided as $0.690\mathrm{g}$ of potassium carbonate, which is the amount expected based on complete decomposition.

Apply Formula for Percent Yield

Substitute the actual yield and theoretical yield into the percent yield formula: $$\text{Percent Yield}=\left(\frac{0.725\mathrm{g}}{0.690\mathrm{g}}\right)\times 100\mathrm{\%}$$.

Calculate Percent Yield

Complete the division and multiplication: $\frac{0.725}{0.690}\approx 1.0507$. Multiply by 100 to get the percent yield: $1.0507\times 100\mathrm{\%}=105.07\mathrm{\%}$. Round if necessary for significant figures.

Key concepts

Stoichiometry

Stoichiometry is a science that deals with the quantitative aspects of chemical reactions. It allows us to predict the amounts of products produced from reactants in a chemical reaction. This is accomplished through balanced chemical equations, which act like recipes for molecules. In these equations, the coefficients show the ratio in which substances react and form new substances.
For example, in a decomposition reaction like the one involving potassium bicarbonate, stoichiometry helps determine the amount of each product formed. Potassium bicarbonate decomposes into potassium carbonate, water, and carbon dioxide when heated. By using stoichiometric coefficients from the balanced equation, chemists can calculate the theoretical amount of potassium carbonate expected if the reaction proceeds completely.

• This calculated amount is key to determining theoretical yield, which is explained further in our next section.
• Understanding stoichiometry is essential for predicting outcomes and confirming the accuracy of experimental results.

Theoretical Yield

Theoretical yield refers to the maximum amount of product that can be formed from a given amount of reactant, assuming complete reaction efficiency. It is calculated using stoichiometry based on the balanced chemical equation. But it's vital to remember that real-world reactions are not always as efficient as theoretical predictions.
In the potassium bicarbonate decomposition exercise, the theoretical yield of potassium carbonate is given as 0.690 g. This value stems from stoichiometry calculations and assumes every molecule of reactant fully converts to product without any side reactions or loss.

• It's vital to compare this to the actual yield to assess reaction efficiency.
• Understanding the theoretical yield helps in identifying potential losses during the reaction process.

Theoretical yield guides chemists in evaluating the practical limitations and efficiencies in lab settings and industrial applications.

Actual Yield

Actual yield is the measured amount of a product obtained from a chemical reaction in a laboratory. It more often than not differs from the theoretical yield because of various factors such as impure reactants, incomplete reactions, or experimental errors.
In the provided exercise, the actual yield is the mass of potassium carbonate obtained after the decomposition reaction, which is 0.725 g. This is the tangible output from the experiment that helps chemists gauge how a "perfect world" stoichiometric calculation holds up in practice.

• Discrepancies between actual and theoretical yield can indicate practical challenges in the experimental setup.
• Knowing the actual yield is integral to calculating the percent yield, giving insight into the reaction’s efficiency.

Monitoring actual yield also aids in improving experimental techniques for better yield outcomes.