Percent Yield Formula and Definition

In chemistry, percent yield is a comparison of actual yield to theoretical yield, expressed as a percentage. Here is a look at the percent yield formula, how to calculate it, and why it may be less than or greater than 100%.

Percent Yield Formula

The percent yield formula is actual yield divided by theoretical yield in moles, multiplied by 100%:

Percent Yield = Actual Yield/Theoretical Yield x 100%

It does not matter whether you express actual and theoretical yield in grams or moles, as long as you use the same units for both values.

How to Calculate Percent Yield

Calculating percent yield requires two values: the actual yield and the theoretical yield. Yield depends on the mole ratio between reactants and products. The actual yield is the amount of product obtained from a reaction or experiment. You weigh the product and then convert the mass (usually in grams) to moles.

The theoretical yield comes from stoichiometry. In other words, it comes from the mole ratio between reactants and products in the balanced equation for the chemical reaction. Once you have the balanced equation, the next step is finding the limiting reactant. The limited reactant is the reactant that limits the amount of product because it’s consumed before the other reactant runs out. In a decomposition reaction, there may only be one reactant, which makes it the limiting reactant. In other reactions, you compare the molar masses and mole ratios. Next, use the number of moles of limiting reactant and mole ratio and calculate the theoretical yield. Finally, calculate theoretical yield.

1. Balance the chemical equation for the reaction. Note the number of moles of reactants and products.
2. Identify the limiting reactant. Calculate molar masses of all reactants. Find the number of moles of all species. Use the mole ratio and identify which reactant limits the reaction. Use the number of moles of the limiting reactant and mole ratio and find the theoretical yield.
3. Weigh the product. This is actual yield.
4. Make sure actual yield and theoretical yield have the same units (grams or moles).
5. Calculate percent yield using actual yield and theoretical yield.

Example Percent Yield Calculation (Simple)

First, here is a simple example of the percent yield calculation in action:

The decomposition of magnesium carbonate forms 15 grams of magnesium oxide in an experiment. The theoretical yield is 19 grams. What is the percent yield of magnesium oxide?

Here, you know the actual yield (15 grams) and the theoretical yield (19 grams), so just plug the values into the formula:

Percent Yield = Actual Yield/Theoretical Yield x 100%
Percent Yield = 15 g/19 g x 100%
Percent Yield = 79%

Example Percent Yield Calculation (With Limiting Reactant)

Find the percent yield of a reaction when you obtain 4.88 g of AlCl₃(s) from a reaction between 2.80 g Al(s) and 4.15 g Cl₂(g).

First, write out the balanced equation for the reaction:

Next, find the limiting reactant. Start with the molar masses of the reactants and products:

2.80 g Al x (1 mol Al/26.98 g Al) = 0.104 mol Al
4.15 g Cl₂ x (1 mol Cl₂/70.90 g Cl₂) = 0.0585 mol Cl₂

Compare the mole ratio to the actual number of moles present in the reaction. From the balanced equation, you see 2 moles of Al reacts with 3 moles of Cl₂.

Mole ratio: moles Al/moles Cl₂ = 2/3 = 0.6667
Actual ratio moles Al/moles Cl₂= 0.104/0.0585 = 1.78

The actual ratio is larger than the mole ratio, so there is excess Al and Cl₂ is the limiting reactant. (If the actual ratio is smaller than the mole ratio, it means there is excess Cl₂ and Al is the limiting reactant.)

Use the actual number of moles of Cl₂ and the mole ratio and find the maximum amount of AlCl₃.

0.00585 mol Cl₂ x (2 mol AlCl₃/3 mol Cl₂) = 0.00390 mol AlCl₃

Convert the number of moles of product into grams so the units of actual and theoretical yield are the same. Get this from the molar mass.

0.00390 mol AlCl₃ x (133.33 g AlCl₃/1 mol AlCl₃) = 5.20 g AlCl₃

Finally, calculate percent yield. Actual yield is 4.88 g of AlCl₃ (given in the problem) and theoretical yield is 5.20 g AlCl₃.

Percent Yield = Actual Yield/Theoretical Yield x 100%
Percent Yield = 4.88 g AlCl₃ / 5.20 g AlCl₃ x 100%
Percent Yield = 93.8%

Is Percent Yield Always Less Than 100%

Percent yield is always less than 100% (often by a lot), yet it’s possible to calculate a value greater than 100%.

There are a few reasons why percent yield always falls short.

• Not all reactions proceed to completion.
• Sometimes reactants and products exist in equilibrium, so the reverse reaction also occurs.
• Two or more reactions occur simultaneously, converting some reactant to one or more side products.
• There may be other species or impurities that interfere with the reaction.
• Product gets lost during transfer.
• Product gets lost during purification.

And yet, sometimes you get more product than predicted. Occasionally, an impurity contributes to product formation. But, usually there’s less product than the theoretical yield. Yet, if you collect an impure product, the mass exceeds the theoretical yield. The most common situation is weighing product that isn’t completely dry. Part of the mass is solvent, so it appears you got more product than predicted.

References

• Cornforth, J. W. (1993). “The Trouble With Synthesis”. Australian Journal of Chemistry. 46 (2): 157–170. doi:10.1071/ch9930157
• Petrucci, Ralph H.; Herring, F. Geoffrey; Madura, Jeffry; Bissonnette, Carey; Pearson (2017). General Chemistry: Principles and Modern Applications. Toronto: Pearson. ISBN 978-0-13-293128-1.
• Whitten, Kenneth W.; Davis, Raymond E; Peck, M. Larry (2002). General Chemistry. Fort Worth: Thomson Learning. ISBN 978-0-03-021017-4.
• Vogel, Arthur Israel; Furniss, B. S; Tatchell, Austin Robert (1978). Vogel’s Textbook of Practical Organic Chemistry. New York: Longman. ISBN 978-0-582-44250-4.