Core Concept

Percent yield and percent error are two metrics commonly used to evaluate the success of chemical experiments. Percent yield measures the efficiency of a reaction, while percent error assesses the accuracy of experimental results compared to theoretical values.

Key Concepts

1. Theoretical Yield:

   • The maximum amount of product that can be formed in a reaction, based on stoichiometric calculations.

   • Calculated assuming complete reaction with no loss of materials.

2. Actual Yield:

   • The amount of product actually obtained from a reaction.

   • Often less than the theoretical yield due to practical limitations, side reactions, or loss of product.

3. Percent Yield:

   • A measure of the efficiency of a reaction, showing how close the actual yield is to the theoretical yield.

   • Calculated using the formula: Percent Yield=(Actual YieldTheoretical Yield)×100%\text{Percent Yield} = \left( \frac{\text{Actual Yield}}{\text{Theoretical Yield}} \right) \times 100\%Percent Yield=(Theoretical YieldActual Yield​)×100%

   • A percent yield close to 100% indicates an efficient reaction.

4. Percent Error:

   • A measure of the accuracy of an experimental value compared to a theoretical or accepted value.

   • Calculated using the formula: Percent Error=(∣Experimental Value−Theoretical Value∣Theoretical Value)×100%\text{Percent Error} = \left( \frac{|\text{Experimental Value} - \text{Theoretical Value}|}{\text{Theoretical Value}} \right) \times 100\%Percent Error=(Theoretical Value∣Experimental Value−Theoretical Value∣​)×100%

   • A smaller percent error indicates higher accuracy.

Steps to Calculate Percent Yield

1. Determine the Theoretical Yield:

   • Use stoichiometry based on the balanced chemical equation to calculate the theoretical yield of the product.

2. Measure the Actual Yield:

   • Measure the mass or volume of the product obtained from the experiment.

3. Calculate Percent Yield:

   • Plug the actual yield and theoretical yield into the percent yield formula.

Steps to Calculate Percent Error

1. Determine the Theoretical (Accepted) Value:

   • Use stoichiometric calculations or accepted reference values for the expected result.

2. Measure the Experimental Value:

   • Record the value obtained from the experiment.

3. Calculate Percent Error:

   • Substitute the experimental value and theoretical value into the percent error formula.

Example Problem: Percent Yield

Problem: In a reaction, the theoretical yield of NaCl\text{NaCl}NaCl is calculated to be 15.0 g15.0 \, \text{g}15.0g. After the reaction, only 12.5 g12.5 \, \text{g}12.5g of NaCl\text{NaCl}NaCl is actually obtained. Calculate the percent yield.

Solution:

1. Identify Theoretical and Actual Yields:

   • Theoretical Yield = 15.0 g15.0 \, \text{g}15.0g

   • Actual Yield = 12.5 g12.5 \, \text{g}12.5g

2. Use the Percent Yield Formula:

   Percent Yield=(12.5 g15.0 g)×100%=83.3%\text{Percent Yield} = \left( \frac{12.5 \, \text{g}}{15.0 \, \text{g}} \right) \times 100\% = 83.3\%Percent Yield=(15.0g12.5g​)×100%=83.3%

Answer: The percent yield is 83.3%.

Example Problem: Percent Error

Problem: A student measures the density of a metal as 7.85 g/cm37.85 \, \text{g/cm}^37.85g/cm3. The accepted density for this metal is 7.92 g/cm37.92 \, \text{g/cm}^37.92g/cm3. Calculate the percent error.

Solution:

1. Identify Experimental and Theoretical Values:

   • Experimental Value = 7.85 g/cm37.85 \, \text{g/cm}^37.85g/cm3

   • Theoretical Value = 7.92 g/cm37.92 \, \text{g/cm}^37.92g/cm3

2. Use the Percent Error Formula:

   Percent Error=(∣7.85−7.92∣7.92)×100%=(0.077.92)×100%=0.88%\text{Percent Error} = \left( \frac{|7.85 - 7.92|}{7.92} \right) \times 100\% = \left( \frac{0.07}{7.92} \right) \times 100\% = 0.88\%Percent Error=(7.92∣7.85−7.92∣​)×100%=(7.920.07​)×100%=0.88%

Answer: The percent error is 0.88%.

Key Tips for Percent Yield & Percent Error

• Always Start with a Balanced Equation: For percent yield, stoichiometric calculations require a balanced equation to accurately determine the theoretical yield.

• Use Consistent Units: Ensure actual yield and theoretical yield are in the same units for percent yield calculations.

• Interpret Percent Yield:

  • A yield over 100% suggests experimental error, such as contamination.

  • A low percent yield can result from side reactions, incomplete reactions, or losses during product recovery.

• Interpret Percent Error:

  • A lower percent error indicates greater accuracy.

  • High percent error suggests significant deviation from the accepted or theoretical value, potentially due to measurement errors or procedural flaws.