Question

Calculate the indicated quantity for each of the various chemical reactions given: a. theoretical yield \(=20.0 \mathrm{g},\) actual yield \(=15.0 \mathrm{g}\) percentage yield \(=?\) b. theoretical yield \(=1.0 \mathrm{g},\) percentage yield \(=90.0 \%\) actual yield \(=?\) c. theoretical yield \(=5.00 \mathrm{g},\) actual yield \(=4.75 \mathrm{g}\) percentage yield \(=?\) d. theoretical yield \(=3.45 \mathrm{g}\) , percentage yield = 48.0\(\%\) , actual yield =?

Short answer

a) 75.0%, b) 0.90 g, c) 95.0%, d) 1.66 g

Step-by-step solution

- Percentage Yield Equation

The percentage yield can be calculated using the formula: \[ \text{Percentage Yield} = \left( \frac{\text{Actual Yield}}{\text{Theoretical Yield}} \right) \times 100 \]

- Calculate Percentage Yield for (a)

Using the provided values, calculate percentage yield: \[ \text{Percentage Yield} = \left( \frac{15.0 \, \text{g}}{20.0 \, \text{g}} \right) \times 100 = 75.0\% \]

- Rearrange Formula for Actual Yield

To find the actual yield, rearrange the percentage yield formula as follows: \[ \text{Actual Yield} = \left( \frac{\text{Percentage Yield}}{100} \right) \times \text{Theoretical Yield} \]

- Calculate Actual Yield for (b)

Using the rearranged formula, solve for the actual yield: \[ \text{Actual Yield} = \left( \frac{90.0}{100} \right) \times 1.0 \text{g} = 0.90 \text{g} \]

- Calculate Percentage Yield for (c)

Again, use the percentage yield formula with provided values: \[ \text{Percentage Yield} = \left( \frac{4.75 \, \text{g}}{5.00 \, \text{g}} \right) \times 100 = 95.0\% \]

- Calculate Actual Yield for (d)

Using the actual yield formula, calculate: \[ \text{Actual Yield} = \left( \frac{48.0}{100} \right) \times 3.45 \, \text{g} = 1.66 \, \text{g} \]

Key concepts

theoretical yield

Theoretical yield is a core concept in chemistry that refers to the maximum amount of product that can be formed in a chemical reaction, based on the amount of limiting reactant. It's calculated using stoichiometry—a method that relies on the balanced chemical equation of the reaction. Think of theoretical yield as the perfect scenario where everything reacts perfectly without any losses or side reactions.

For instance, if you start with a certain amount of reactants, the theoretical yield tells you how much of the product you could ideally produce. This yield is measured in grams or moles, depending on the problem.

Understanding theoretical yield is crucial because it sets the stage for comparing the actual yield, helping to determine how efficient a reaction is.

actual yield

While theoretical yield is a 'perfect world' scenario, the actual yield is the amount of product you actually obtain from a reaction. Real-world factors like incomplete reactions, side reactions, and loss of product during handling mean that the actual yield is usually less than the theoretical yield.

To find the actual yield, you can either measure it directly from an experiment or calculate it if you have the percentage yield and the theoretical yield. For example, given a percentage yield and theoretical yield, you can use the formula:
Actual Yield = (Percentage Yield / 100) × Theoretical Yield.

This relationship makes it handy to cross-check your experiment's accuracy and understand where improvements might be made. Knowing the actual yield helps you to evaluate the efficiency of your chemical processes.

yield calculation

Yield calculation is the process of comparing the actual yield to the theoretical yield by finding the percentage yield. The percentage yield helps chemists determine the efficiency and success of their reactions. The fundamental formula for percentage yield is:
Percentage Yield = (Actual Yield / Theoretical Yield) × 100.

This straightforward formula yields a percentage that tells you how close your actual yield is to the theoretical maximum. For example, if your actual yield is 15.0g and your theoretical yield is 20.0g, your percentage yield would be:
Percentage Yield = (15.0g / 20.0g) × 100 = 75.0%.

This tells you that your reaction was 75% efficient. Understanding this calculation helps you identify how changes in your process can improve yields. Moreover, yield calculation is a staple in both academic and industrial settings, making it an essential skill for anyone involved in chemistry.