# Yield (chemistry)

In chemistry, yield, also referred to as reaction yield, is the amount of product obtained in a chemical reaction.[1] The absolute yield can be given as the weight in grams or in moles (molar yield). The percentage yield (or fractional yield or relative yield), which serves to measure the effectiveness of a synthetic procedure, is calculated by dividing the amount of the obtained desired product by the theoretical yield (the unit of measure for both must be the same):

${\displaystyle {\mbox{percent yield}}={\frac {\mbox{actual yield}}{\mbox{theoretical yield}}}\times 100}$

The theoretical yield is the amount predicted by a stoichiometric calculation based on the number of moles of all reactants present. This calculation assumes that only one reaction occurs and that the limiting reactant reacts completely. However, the actual yield is always smaller (the percent yield is less than 100%), often very much so, for several reasons:[2][3]

• Many reactions are incomplete and the reactants are not completely converted to products. If a reverse reaction occurs, the final state contains both reactants and products in a state of chemical equilibrium.
• Two or more reactions may occur simultaneously, so that some reactant is converted to undesired side products.
• Losses occur in the separation and purification of the desired product from the reaction mixture.
• Impurities are present in the starting material which do not react to give desired product

The ideal or theoretical yield of a chemical reaction would be 100%, an ideal that is never reached. According to Vogel's Textbook of Practical Organic Chemistry,[4] yields close to 100% are called quantitative, yields above 90% are called excellent, yields above 80% are very good, yields above 70% are good, yields above 50% are fair, and yields below 40% are called poor.[1] These names are arbitrary and not universally accepted, and depending on the nature of the reaction in question, these expectations may be unrealistically high. Yields may appear to be 100% or above when products are impure, as the measured weight of the product will include the weight of any impurities.[5]

Purification steps always lower the yield, through losses incurred during the transfer of material between reaction vessels and purification apparatus or imperfect separation of the product from impurities, which may necessitate the discarding of fractions deemed insufficiently pure. The yield of the product measured after purification (typically to >95% spectroscopic purity, or to sufficient purity to pass combustion analysis) is called the isolated yield of the reaction. Yields can also be calculated by measuring the amount of product formed (typically in the crude, unpurified reaction mixture) relative to a known amount of an added internal standard, using techniques like gas / liquid chromatography, or NMR spectroscopy. A yield determined using this approach is known as an internal standard yield. Yields are typically obtained in this manner to accurately determine the quantity of product produced by a reaction, irrespective of potential isolation problems. Additionally, they can be useful when isolation of the product is challenging or tedious, or when the rapid determination of an approximate yield is desired. Unless otherwise indicated, yields reported in the synthetic organic and inorganic chemistry literature refer to isolated yields, which better reflect the amount of pure product one is likely to obtain under the reported conditions, upon repeating the experimental procedure.

Organic chemist Tomas Hudlicky and coworkers have noted the phenomenon of "yield inflation", in which reported yields in the chemistry literature has gradually crept upward in recent decades, a phenomenon attributed to careless measurement of yield on reactions conducted on small scale, wishful thinking and a desire to report higher numbers for publication purposes, or scientific fraud. After performing careful control experiments, they note that each physical manipulation (including extraction/washing, drying over desiccant, filtration, and column chromatography) results in a loss of yield of about 2%. Thus, isolated yields measured after standard aqueous workup and chromatographic purification should seldom exceed 94%.[6]

When more than one reactant participates in a reaction, the yield is usually calculated based on the amount of the limiting reactant, whose amount is less than stoichiometrically equivalent (or just equivalent) to the amounts of all other reactants present. Other reagents present in amounts greater than required to react with all the limiting reagent present are considered excess. As a result, the yield should not be automatically taken as a measure for reaction efficiency.

## Example

This is an example of an esterification reaction where one molecule acetic acid (also called ethanoic acid) reacts with one molecule ethanol, yielding one molecule ethyl acetate (a bimolecular second-order reaction of the type A + B C):

120 g acetic acid (60 g/mol, 2.0 mol) was reacted with 230 g ethanol (46 g/mol, 5.0 mol), yielding 132 g ethyl acetate (88 g/mol, 1.5 mol). The yield was 75%.
1. The molar amount of the reactants is calculated from the weights (acetic acid: 120 g ÷ 60 g/mol = 2.0 mol; ethanol: 230 g ÷ 46 g/mol = 5.0 mol).
2. Ethanol is used in a 2.5-fold excess (5.0 mol ÷ 2.0 mol).
3. The theoretical molar yield is 2.0 mol (the molar amount of the limiting compound, acetic acid).
4. The molar yield of the product is calculated from its weight (132 g ÷ 88 g/mol = 1.5 mol).
5. The % yield is calculated from the actual molar yield and the theoretical molar yield (1.5 mol ÷ 2.0 mol × 100% = 75%).