How To Calculate Overall Percent Yield

In the world of chemistry, where precision and accuracy are paramount, determining the success of a reaction goes beyond simply observing the formation of a product. It delves into quantifying the efficiency of the process, and that's where percent yield comes into play. Understanding how to calculate overall percent yield is a fundamental skill for any chemist, whether in the lab or in the classroom.

What is Percent Yield?

Percent yield is a measure of the efficiency of a chemical reaction. It represents the ratio of the actual yield (the amount of product obtained in the lab) to the theoretical yield (the amount of product that should be obtained based on stoichiometry), expressed as a percentage. In essence, it tells us how much of the reactants were successfully converted into the desired product. A high percent yield indicates a more efficient reaction, while a low percent yield suggests losses or inefficiencies in the process.

Why is Calculating Percent Yield Important?

Several reasons highlight the importance of calculating percent yield:

• Evaluating Reaction Efficiency: Percent yield provides a quantitative measure of how well a reaction performs. It helps identify potential problems or inefficiencies in the process.
• Optimizing Reaction Conditions: By calculating percent yield under different reaction conditions (temperature, pressure, catalyst, etc.), chemists can optimize the process to maximize product formation.
• Troubleshooting Experimental Errors: A low percent yield can indicate experimental errors, such as incomplete reactions, loss of product during transfer, or side reactions.
• Assessing the Purity of Products: Percent yield, in conjunction with other analytical techniques, can provide insights into the purity of the obtained product. A lower than expected yield may suggest the presence of impurities.
• Economic Considerations: In industrial chemistry, maximizing percent yield is crucial for economic viability. Higher yields translate to less waste and greater profitability.

Understanding the Key Terms

Before diving into the calculation, let's define some key terms:

• Reactants: The starting materials in a chemical reaction.
• Products: The substances formed as a result of a chemical reaction.
• Stoichiometry: The quantitative relationship between reactants and products in a balanced chemical equation.
• Theoretical Yield: The maximum amount of product that can be formed from a given amount of reactant, assuming complete conversion and no losses. It is calculated based on stoichiometry.
• Actual Yield: The amount of product that is actually obtained from a reaction. This is the experimental yield, measured in the lab.
• Limiting Reactant: The reactant that is completely consumed in a reaction. The amount of product formed is limited by the amount of limiting reactant.
• Excess Reactant: The reactant that is present in a greater amount than required for complete reaction with the limiting reactant. Some of this reactant will be left over at the end of the reaction.

The Formula for Percent Yield

The formula for calculating percent yield is straightforward:

Percent Yield = (Actual Yield / Theoretical Yield) x 100%

Where:

• Actual Yield: The experimentally obtained mass (or moles) of the product.
• Theoretical Yield: The mass (or moles) of the product calculated based on the stoichiometry of the reaction and the amount of limiting reactant.

Steps to Calculate Percent Yield

Let's break down the calculation into a step-by-step process:

1. Write the Balanced Chemical Equation:

The first and most crucial step is to write the balanced chemical equation for the reaction. This provides the stoichiometric ratios between reactants and products. For example:

N2(g) + 3H2(g) → 2NH3(g)

This equation tells us that 1 mole of nitrogen gas (N2) reacts with 3 moles of hydrogen gas (H2) to produce 2 moles of ammonia gas (NH3).

2. Determine the Limiting Reactant:

If the amounts of all reactants are given, you need to determine the limiting reactant. This is the reactant that will be completely consumed, and it dictates the maximum amount of product that can be formed. To determine the limiting reactant:

• Convert the mass of each reactant to moles. Use the molar mass of each reactant to perform this conversion.
• Divide the number of moles of each reactant by its stoichiometric coefficient in the balanced equation.
• The reactant with the smallest value is the limiting reactant.

Example:

Suppose you have 10 grams of N2 and 5 grams of H2.

• Molar mass of N2 = 28 g/mol
• Moles of N2 = 10 g / 28 g/mol = 0.357 mol
• Molar mass of H2 = 2 g/mol
• Moles of H2 = 5 g / 2 g/mol = 2.5 mol

Now, divide by the stoichiometric coefficients:

• N2: 0.357 mol / 1 = 0.357
• H2: 2.5 mol / 3 = 0.833

Since 0.357 is smaller than 0.833, N2 is the limiting reactant.

3. Calculate the Theoretical Yield:

Using the balanced equation and the amount of the limiting reactant, calculate the theoretical yield of the product. This involves using the stoichiometric ratios to determine how many moles of product can be formed from the given amount of limiting reactant.

• Use the stoichiometric ratio between the limiting reactant and the product to determine the moles of product that can be formed.
• Convert the moles of product to grams using the molar mass of the product.

Example (Continuing from above):

Since N2 is the limiting reactant, we use it to calculate the theoretical yield of NH3. The balanced equation shows that 1 mole of N2 produces 2 moles of NH3.

• Moles of NH3 = 0.357 mol N2 * (2 mol NH3 / 1 mol N2) = 0.714 mol NH3
• Molar mass of NH3 = 17 g/mol
• Theoretical yield of NH3 = 0.714 mol * 17 g/mol = 12.14 g

4. Determine the Actual Yield:

The actual yield is the amount of product that you actually obtained in the experiment. This value will be given to you, or you will have measured it in the lab.

Example:

Suppose you obtained 9 grams of NH3 in the experiment. This is your actual yield.

5. Calculate the Percent Yield:

Now, plug the actual yield and theoretical yield into the percent yield formula:

Percent Yield = (Actual Yield / Theoretical Yield) x 100%

Example:

• Percent Yield = (9 g / 12.14 g) x 100% = 74.1%

Therefore, the percent yield of the reaction is 74.1%.

Calculating Overall Percent Yield in Multi-Step Reactions

Many chemical syntheses involve multiple steps, where the product of one reaction becomes the reactant for the next. In such cases, we need to calculate the overall percent yield for the entire process. There are two primary methods for doing this:

Method 1: Multiplying Individual Percent Yields:

This method involves calculating the percent yield for each individual step and then multiplying them together to obtain the overall percent yield.

• Calculate the percent yield for each step in the reaction sequence.
• Multiply the percent yields of all the steps together.

Overall Percent Yield = (% Yield Step 1) x (% Yield Step 2) x (% Yield Step 3) x ...

Example:

Consider a three-step synthesis:

• Step 1: A → B, Percent Yield = 80%
• Step 2: B → C, Percent Yield = 90%
• Step 3: C → D, Percent Yield = 70%

Overall Percent Yield = (0.80) x (0.90) x (0.70) = 0.504 = 50.4%

This means that for every 100 molecules of A you start with, you will only obtain approximately 50 molecules of D.

Method 2: Using Initial Reactant and Final Product:

This method focuses on the overall transformation from the initial reactant to the final product, ignoring the individual steps in between.

• Determine the theoretical yield of the final product based on the initial reactant. Consider the stoichiometry of the entire reaction sequence.
• Determine the actual yield of the final product obtained experimentally.
• Calculate the overall percent yield using the standard formula: (Actual Yield / Theoretical Yield) x 100%.

Example:

Let's revisit the three-step synthesis: A → B → C → D

Assume the following:

• You start with 100 grams of A (initial reactant).
• After the three steps, you obtain 40 grams of D (final product).
• Based on the stoichiometry of the entire process (A → D), 100 grams of A should theoretically produce 80 grams of D.

Overall Percent Yield = (40 g / 80 g) x 100% = 50%

Which Method is Better?

• Multiplying Individual Percent Yields: This method is useful when you want to assess the efficiency of each individual step in the synthesis. It helps identify which steps are contributing the most to the overall yield loss. However, it requires knowing the percent yield of each step.

• Using Initial Reactant and Final Product: This method is simpler when you only care about the overall efficiency of the process and don't need to analyze the individual steps. It only requires knowing the amount of initial reactant and the amount of final product.

Important Considerations for Multi-Step Reactions:

• Purification Losses: Each step in a multi-step synthesis typically involves purification of the intermediate product. Purification processes (e.g., recrystallization, chromatography) can lead to losses of the product, which contribute to the overall yield reduction.
• Side Reactions: Side reactions can occur in any step, consuming reactants and forming unwanted byproducts. This reduces the amount of desired product that can be formed, lowering the percent yield.
• Stoichiometry: It is crucial to carefully consider the stoichiometry of each step in the reaction sequence when calculating the theoretical yield of the final product.

Factors Affecting Percent Yield

Several factors can influence the percent yield of a chemical reaction:

• Incomplete Reactions: Reactions may not proceed to completion, meaning that some of the reactants remain unreacted. This can be due to factors such as slow reaction rates, unfavorable equilibrium constants, or steric hindrance.
• Side Reactions: Reactants may participate in side reactions, forming unwanted byproducts instead of the desired product.
• Loss of Product During Transfer: Product can be lost during transfer between containers, filtration, or purification steps.
• Impurities in Reactants: Impurities in the starting materials can interfere with the reaction or consume reactants, leading to lower yields.
• Experimental Errors: Errors in weighing, measuring volumes, or controlling reaction conditions can affect the yield.
• Reversibility of Reaction: If the reaction is reversible, it may reach an equilibrium state where both reactants and products are present. The yield will be less than 100% unless the equilibrium is shifted towards product formation.
• Volatility of Reactants or Products: Volatile reactants or products can be lost through evaporation, especially at elevated temperatures.

Tips for Improving Percent Yield

Here are some tips to help improve the percent yield of your reactions:

• Use High-Quality Reagents: Ensure that your starting materials are pure and free from contaminants.
• Optimize Reaction Conditions: Carefully optimize reaction conditions such as temperature, pressure, solvent, and reaction time.
• Use a Catalyst: If applicable, use a catalyst to speed up the reaction rate and promote complete conversion.
• Minimize Product Loss: Use careful techniques to minimize product loss during transfer, filtration, and purification.
• Control Temperature: Maintain the correct temperature throughout the reaction to avoid side reactions or decomposition.
• Work Under Inert Atmosphere: For air-sensitive reactions, perform the reaction under an inert atmosphere (e.g., nitrogen or argon) to prevent oxidation or hydrolysis.
• Purify Intermediates: In multi-step syntheses, purify intermediate products to remove impurities that could interfere with subsequent steps.
• Dry Solvents and Reagents: Ensure that solvents and reagents are dry, especially for reactions that are sensitive to water.
• Use Proper Stoichiometry: Use the correct stoichiometric ratios of reactants to ensure that the limiting reactant is completely consumed.

Examples of Percent Yield Calculations

Let's work through some additional examples to solidify your understanding:

Example 1: Simple Reaction

Reaction: 2Mg(s) + O2(g) → 2MgO(s)

• You react 4.86 g of magnesium (Mg) with excess oxygen.
• You obtain 7.25 g of magnesium oxide (MgO).
• What is the percent yield?

Solution:

1. Balanced Equation: Already given.
2. Limiting Reactant: Mg is the limiting reactant (oxygen is in excess).
3. Theoretical Yield:
   • Moles of Mg = 4.86 g / 24.3 g/mol = 0.2 mol
   • From the balanced equation, 2 moles of Mg produce 2 moles of MgO. Therefore, 0.2 mol Mg will produce 0.2 mol MgO.
   • Molar mass of MgO = 40.3 g/mol
   • Theoretical yield of MgO = 0.2 mol * 40.3 g/mol = 8.06 g
4. Actual Yield: 7.25 g
5. Percent Yield: (7.25 g / 8.06 g) x 100% = 90%

Example 2: Reaction with Limiting Reactant

Reaction: Cu(s) + 2AgNO3(aq) → 2Ag(s) + Cu(NO3)2(aq)

• You react 3.17 g of copper (Cu) with 20.0 g of silver nitrate (AgNO3).
• You obtain 6.0 g of silver (Ag).
• What is the percent yield?

Solution:

1. Balanced Equation: Already given.
2. Limiting Reactant:
   • Moles of Cu = 3.17 g / 63.5 g/mol = 0.05 mol
   • Moles of AgNO3 = 20.0 g / 169.9 g/mol = 0.118 mol
   • Divide by stoichiometric coefficients:
     • Cu: 0.05 mol / 1 = 0.05
     • AgNO3: 0.118 mol / 2 = 0.059
   • Cu is the limiting reactant.
3. Theoretical Yield:
   • From the balanced equation, 1 mole of Cu produces 2 moles of Ag. Therefore, 0.05 mol Cu will produce 0.1 mol Ag.
   • Molar mass of Ag = 107.9 g/mol
   • Theoretical yield of Ag = 0.1 mol * 107.9 g/mol = 10.79 g
4. Actual Yield: 6.0 g
5. Percent Yield: (6.0 g / 10.79 g) x 100% = 55.6%

Conclusion

Calculating percent yield is a crucial aspect of chemistry, allowing us to quantify the efficiency of chemical reactions. By carefully following the steps outlined above, you can accurately determine the percent yield of a reaction, identify potential problems, and optimize reaction conditions. Whether you are a student learning the fundamentals or a seasoned chemist working in the lab, mastering the concept of percent yield is essential for success in the field. Remember to always pay attention to stoichiometry, limiting reactants, and potential sources of error to ensure accurate and meaningful results. Strive for continuous improvement in your experimental techniques to maximize your yields and achieve your desired outcomes.