Percent Yield & Percent Error
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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.
$\text{Percent Error} = \left( \frac{|\text{Experimental Value} - \text{Theoretical Value}|}{\text{Theoretical Value}} \right) \times 100\%$
$\text{Percent Yield} = \left( \frac{\text{Actual Yield}}{\text{Theoretical Yield}} \right) \times 100\%$
Practice Tips
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.
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Steps to Calculate Percent Yield
STEP 1: Determine the Theoretical Yield
Use stoichiometry based on the balanced chemical equation to calculate the theoretical yield of the product.
STEP 2: Measure the Actual Yield
Measure the mass or volume of the product obtained from the experiment. This is usually given to you in a word problem.
STEP 3: Calculate Percent Yield
Plug the actual yield and theoretical yield into the percent yield formula.
Steps to Calculate Percent Error
STEP 1: Determine the Theoretical (Accepted) Value
Use stoichiometric calculations or accepted reference values for the expected result.
STEP 2: Measure the Experimental Value
Record the value obtained from the experiment.
STEP 3: Calculate Percent Error
Substitute the experimental value and theoretical value into the percent error formula.
Key Terms
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.
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.
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: $\text{Percent Yield} = \left( \frac{\text{Actual Yield}}{\text{Theoretical Yield}} \right) \times 100\%$
A percent yield close to 100% indicates an efficient reaction.
Percent Error:
A measure of the accuracy of an experimental value compared to a theoretical or accepted value.
Calculated using the formula: $\text{Percent Error} = \left( \frac{|\text{Experimental Value} - \text{Theoretical Value}|}{\text{Theoretical Value}} \right) \times 100\%$
A smaller percent error indicates higher accuracy.
$\boxed{\text{EXAMPLE PROBLEM}}$ Percent Yield
The following reaction has a 68% yield.
$$\text{AlCl}_3(\text{aq}) + 4\text{NaOH}(\text{aq}) \longrightarrow \text{NaAlO}_2(\text{aq}) + 3\text{NaCl}(\text{aq}) + 2\text{H}_2\text{O}(\ell)$$
Calculate the actual mass of sodium chloride that is recovered if $18.2 \, \text{g}$ of aluminum chloride, $\text{AlCl}_3(\text{aq})$, reacts with $16.00 \, \text{g}$ of sodium hydroxide.
Determine the Theoretical Yield
FIND LIMITING REACTANT
Calculate the moles of the product ($\text{NaCl}$) that can be formed from each reactant (aka determine the limiting reactant). The smaller amount is the theoretical yield (in moles).
A. Calculate Moles NaCl from 18.2 g of $\text{AlCl}_3$
$ = 18.2 \, \text{g } \text{AlCl}_3 \times \frac{1 \, \text{mol } \text{AlCl}_3}{133.33 \, \text{g } \text{AlCl}_3} \times \frac{3 \, \text{mol } \text{NaCl}}{1 \, \text{mol } \text{AlCl}_3} \approx \mathbf{0.4093 \, \text{mol } \text{NaCl}}$
B. Calculate moles of NaCl from 16.00 g of NaOH
$ = 16.00 \, \text{g } \text{NaOH} \times \frac{1 \, \text{mol } \text{NaOH}}{40.00 \, \text{g } \text{NaOH}} \times \frac{3 \, \text{mol } \text{NaCl}}{4 \, \text{mol } \text{NaOH}} \approx \mathbf{0.3000 \, \text{mol } \text{NaCl}}$
Comparing the results: $0.3000 \, \text{mol } \text{NaCl}$ is less than $0.4093 \, \text{mol } \text{NaCl}$. Therefore, NaOH is the limiting reactant.
CONVERT TO MASS (GRAMS)
The theoretical yield is based on the limiting reactant (which produced $0.3000 \, \text{mol } \text{NaCl}$). Convert these moles to mass using the molar mass of $\text{NaCl}$.
$$\text{Theoretical Yield} (\text{NaCl}) = 0.3000 \, \text{mol } \text{NaCl} \times \frac{58.44 \, \text{g } \text{NaCl}}{1 \, \text{mol } \text{NaCl}}$$
Theoretical Yield = 17.53 g NaCl
Calculate the Actual Mass of NaCl Recovered
Use the percent yield formula to find the actual yield:
$\text{Percent Yield} = \left( \frac{\text{Actual Yield}}{\text{Theoretical Yield}} \right) \times 100\%$
Rearrange the formula to solve for Actual Yield:
$\text{Actual Yield} = \text{Theoretical Yield} \times \left( \frac{\text{Percent Yield}}{100\%} \right)$
Plugging in the values:
$\text{Actual Yield} = 17.53 \, \text{g} \times \left( \frac{68}{100} \right)$
Actual Yield = 11.92 g
