Calculate Percent Yield
Moles and molar mass, the limiting reagent, theoretical and actual yield, and a worked aspirin example.
Chapters
- 0:25 Why reactions fall short
- 1:17 Moles and molar mass
- 2:05 The limiting reagent
- 2:55 Theoretical and actual yield
- 3:25 Worked example with aspirin
- 4:33 Why yields fall below 100 percent
- 5:11 Yields above 100 percent
- 5:35 Yield in protein purification
- 6:55 DNA extraction yield and percent recovery
- 8:06 Troubleshooting low yield
- 8:43 Recap and quiz
Transcript
0:25 Why reactions fall short
Percent yield is the actual amount of product you isolate from a reaction, divided by the maximum amount the reaction could make, multiplied by 100. A reaction written on paper converts all of a reactant into product, and a reaction in a flask never quite does. A recipe written to give 12 cupcakes gives 10, because batter sticks to the bowl and one cupcake falls apart, so 10 of 12 is 83 percent. The same shortfall appears in a synthesis, where some reactant never converts and some product stays behind in the flask. Percent yield measures how close you came to the amount the chemistry allows. Chemists and biochemists use percent yield to report the efficiency of a preparation, and you compare two routes to the same compound by their percent yields.
1:17 Moles and molar mass
A yield compares amounts of two different substances, and a balanced equation counts those substances in moles. A mole is an amount of substance containing 6.022 × 10²³ particles. The molar mass is the mass of one mole of a substance, in grams per mole, and it equals the sum of the atomic masses of the atoms in the formula. A balance reports grams, and the equation needs moles, so you divide the mass by the molar mass. The molar masses are 138.12 g/mol for salicylic acid, 102.09 g/mol for acetic anhydride, which also has a density of about 1.08 g/mL, and 180.16 g/mol for aspirin.
2:05 The limiting reagent
Once you have moles, the balanced equation tells you how the reactants combine. One mole of salicylic acid reacts with one mole of acetic anhydride to give one mole of aspirin and one mole of acetic acid. The limiting reagent is the reactant that runs out first, and it sets the maximum amount of product. To find the limiting reagent, compare the moles you have of each reactant with the ratio in the equation. In the aspirin synthesis, you start from 2.0 g of salicylic acid, which is 0.01448 mol, and 5.0 mL of acetic anhydride, which is 0.0529 mol, about 3.7 times as many. Salicylic acid runs out first, so it is the limiting reagent, and acetic anhydride is in excess.
2:55 Theoretical and actual yield
With the limiting reagent identified, you can state the largest amount of product the reaction could form. The theoretical yield is the amount of product the limiting reagent could form if the reaction went to completion with no losses. The actual yield is the amount of pure, dry product you isolate. Percent yield equals actual yield divided by theoretical yield, multiplied by 100. Weigh the product only after it is dry, because solvent adds mass that the reaction did not make.
3:25 Worked example with aspirin
To apply the formula, take an aspirin synthesis that starts from 2.0 g of salicylic acid, with illustrative numbers. Divide 2.0 g by 138.12 g/mol, and you have 0.01448 mol of salicylic acid. Multiply 5.0 mL of acetic anhydride by its density of 1.08 g/mL, and you have 5.40 g, which divided by 102.09 g/mol is 0.0529 mol. Salicylic acid is the limiting reagent, so the equation gives 0.01448 mol of aspirin at most. Multiply 0.01448 mol by 180.16 g/mol, and the theoretical yield is 2.609 g. You recrystallize the product, dry it, and weigh 2.10 g of aspirin. Divide 2.10 g by 2.609 g and multiply by 100, and the percent yield is 80.5 percent.
4:33 Why yields fall below 100 percent
A yield of 80.5 percent means about a fifth of the possible product was lost or never formed. Some reactions do not reach completion, because the reverse reaction competes with the forward reaction and the mixture settles at an equilibrium. Side reactions consume part of the reactant and give products you discard. Material stays behind on the walls of the flask, on the filter paper and in the mother liquor when you filter crystals. Recrystallization dissolves some of the product and leaves that fraction in the hot solvent you pour away. Each of these losses lowers the actual yield below the theoretical yield.
5:11 Yields above 100 percent
A percentage above 100 looks like a success, yet it always points to an error. A product that still holds water or solvent weighs more than the reaction made. If the damp aspirin weighed 2.75 g, the calculation would give 105.4 percent. Dry the product to constant mass and purify it before you weigh.
5:35 Yield in protein purification
Biochemists use the same idea when they purify an enzyme, with activity in place of moles. Specific activity is enzyme activity per milligram of total protein. In this illustrative purification, the crude lysate holds 1,200 mg of protein and 24,000 units of activity, which is 20 units per milligram. The ammonium sulfate cut leaves 300 mg of protein and 19,200 units, which is 64 units per milligram. The ammonium sulfate step recovers 80 percent of the activity and raises the specific activity 3.2-fold. Ion exchange leaves 40 mg and 14,400 units, which is 360 units per milligram, a yield of 60 percent and an 18-fold purification. The affinity column leaves 6 mg and 10,800 units, which is 1,800 units per milligram, a yield of 45 percent and a 90-fold purification. Yield is the total activity after a step divided by the starting total activity, and the purification fold is the specific activity after a step divided by the starting specific activity. Each step raises purity and loses some enzyme, so the yield falls while the fold purification rises.
6:55 DNA extraction yield and percent recovery
Molecular biology applies the same idea to DNA, but a DNA extraction has no theoretical maximum from an equation, so you report the amount recovered per amount of starting material. You extract DNA from 20 mg of tissue and elute it in 50 µL. A 1 in 50 dilution reads an absorbance at 260 nm of 0.45. For double-stranded DNA, an absorbance of 1.0 corresponds to about 50 µg/mL. Multiply 0.45 by 50 µg/mL and by the dilution factor of 50, and the concentration is 1,125 µg/mL. Multiply by the elution volume of 0.050 mL, and you have 56.25 µg of DNA. Divide by 20 mg of tissue, and the yield is about 2.8 µg per milligram of tissue. Percent recovery compares the amount of a substance you recover with the amount you put in, as in a recrystallization or a spike-recovery test. Percent yield compares the product with the amount the reaction could make in theory.
8:06 Troubleshooting low yield
When the yield is lower than expected, the cause usually lies in a step you can check. Recheck the limiting-reagent calculation and the masses you weighed. Check the reaction time and temperature, and confirm that the reagents were pure and that no moisture reached the flask. Rinse the vessels and scrape the filter to recover material you would otherwise leave behind. In a recrystallization, use the minimum volume of hot solvent and cool the solution slowly. For a biological preparation, add protease inhibitors and keep the sample cold, and load the column within its capacity.
8:43 Recap and quiz
The whole lesson rests on one definition, in which percent yield divides the actual yield by the theoretical yield and multiplies by 100. The limiting reagent sets the theoretical yield, and you find it by comparing moles with the ratio in the balanced equation. A yield below 100 percent comes from incomplete reaction, side reactions and losses in transfer and purification, and a yield above 100 percent comes from solvent or impurity in the product. To check your understanding, consider 3.0 g of salicylic acid reacting with 2.0 mL of acetic anhydride, which has a density of 1.08 g/mL, and 3.05 g of dry aspirin recovered. Find the limiting reagent and the percent yield.