# Percent Yield

Submitted by ChemPRIME Staff on Wed, 12/08/2010 - 23:47

Not all chemical reactions are as simple as the ones we have considered, so far. Quite often a mixtureA combination of two or more substances in which the substances retain their chemical identity. of two or more products containing the same elementA substance containing only one kind of atom and that therefore cannot be broken down into component substances by chemical means. is formed. For example, when octane (or gasoline in general) burns in an excess of air, the reaction is

2C8H18 + 25O2 → 16CO2 + 18H2O

If oxygen is the limiting reagent, however, the reaction does not necessarily stop short of consuming all the octane available. Instead, some carbon monoxide (CO) forms:

2C8H18 + 24O2 → 14CO2 + 2CO + 18H2O

Burning gasoline in an automobile engine, where the supply of oxygen is not always as great as that demanded by the stoichiometric ratio, often produces carbon monoxide, a poisonous substanceA material that is either an element or that has a fixed ratio of elements in its chemical formula. and a major source of air pollutionThe contamination of the air, water, and earth by personal, industrial, and farm waste..

In other cases, even though none of the reactants is completely consumed, no further increase in the amounts of the products occurs. We say that such a reaction does not go to completion. When a mixture of products is produced or a reaction does not go to completion, the effectiveness of the reaction is usually evaluated in terms of percent yield of the desired product. A theoretical yieldThe maximum quantity of a product that could be formed in a chemical reaction if all the limiting reactant reacted to form products (distinguished from actual yield). is calculated by assuming that all the limiting reagent is converted to product. The experimentally determined massA measure of the force required to impart unit acceleration to an object; mass is proportional to chemical amount, which represents the quantity of matter in an object. of product is then compared to the theoretical yield and expressed as a percentage:

$\text{Percent yield}=\frac{\text{actual yield}}{\text{theoretical yield}}\times \text{100 percent}$

EXAMPLE 1 When 100.0 g N2 gas and 25.0 g H2 gas are mixed at 350°C and a high pressureForce per unit area; in gases arising from the force exerted by collisions of gas molecules with the wall of the container., they react to form 28.96 g NH3 (ammonia) gas. Calculate the percent yield.

SolutionA mixture of one or more substances dissolved in a solvent to give a homogeneous mixture. We must calculate the theoretical yield of NH3, and to do this, we must first discover whether N2 or H2 is the limiting reagent. For the balanced equationA representation of a chemical reaction that has values of the stoichiometric coefficients of reactants and products such that the number of atoms of each element is the same before and after the reaction.

N2 + 3H2 → 2NH3

the stoichiometric ratio of the reactants is

$\text{S}\left( \frac{\text{H}_{\text{2}}}{\text{N}_{\text{2}}} \right)=\frac{\text{3 mol H}_{\text{2}}}{\text{1 mol N}_{\text{2}}}$

Now, the initial amounts of the two reagents are

and      \begin{align} & n_{\text{H}_{\text{2}}}\text{(initial)}=\text{25}\text{.0 g H}_{\text{2}}\times \frac{\text{1 mol H}_{\text{2}}}{\text{2}\text{.016 g H}_{\text{2}}}=\text{12}\text{.4 mol H}_{\text{2}} \ & \ & n_{\text{N}_{\text{2}}}\text{(initial)}=\text{100}\text{.0 g N}_{\text{2}}\times \frac{\text{1 mol N}_{\text{2}}}{\text{28}\text{.02 g N}_{\text{2}}}=\text{3}\text{.569 mol N}_{\text{2}} \ \end{align}

The ratio of initial amounts is thus

$\frac{n_{\text{H}_{\text{2}}}\text{(initial)}}{n_{\text{N}_{\text{2}}}\text{(initial)}}=\frac{\text{12}\text{.4 mol H}_{\text{2}}}{\text{3}\text{.569 mol N}_{\text{2}}}=\frac{\text{3}\text{.47 mol H}_{\text{2}}}{\text{1 mol N}_{\text{2}}}$

Since this ratio is greater than $\text{S}\left( \frac{\text{H}_{\text{2}}}{\text{N}_{\text{2}}} \right)$, there is an excess of H2. N2 is the limiting reagent. Accordingly we must use 3.569 mol N2 (rather than 12.4 mol H2) to calculate the theoretical yield of NH3. We then have

$n_{\text{NH}_{\text{3}}}\text{(theoretical)}=\text{3}\text{.569 mol N}_{\text{2}}\times \frac{\text{2 mol NH}_{\text{3}}}{\text{1 mol N}_{\text{2}}}=\text{7}\text{.138 mol NH}_{\text{3}}$

so that

$\text{m}_{\text{NH}_{\text{3}}}\text{(theoretical)}=\text{7}\text{.138 mol NH}_{\text{3}}\times \frac{\text{17}\text{.03 g NH}_{\text{3}}}{\text{1 mol NH}_{\text{3}}}=\text{121}\text{.6 g NH}_{\text{3}}$

The percent yield is then

\begin{align} \text{Percent yield}&=\frac{\text{actual yield}}{\text{theoretical yield}}\times \text{100 percent } \&=\frac{\text{28}\text{.96 g}}{\text{121}\text{.6 g}}\times \text{100 percent} \&=\text{23}\text{.81 percent} \end{align}

Combination of nitrogen and hydrogen to form ammonia is a classic example of a reaction which does not go to completion. Commercial production of ammonia is accomplished using this reaction in what is called the Haber process. Even at the rather unusual temperatures and pressures used for this industrial synthesisFormation of substances with more complicated sturctures than do their precursors., only about one-quarter of the reactants can be converted to the desired product. This is unfortunate because nearly all nitrogen fertilizers are derived from ammonia and the world has come to rely on them in order to produce enough food for its rapidly increasing population. Ammonia ranks third [after sulfuric acidIn Arrhenius theory, a substance that produces hydrogen ions (hydronium ions) in aqueous solution. In Bronsted-Lowry theory, a hydrogen-ion (proton) donor. In Lewis theory, a species that accepts a pair of electrons to form a covalent bond. (H2SO4) and oxygen (O2)] in the list of most-produced chemicals, worldwide. It might rank even higher if the reaction by which it is made went to completion. Certainly ammonia and the food it helps to grow would be less expensive and would require much less energyA system's capacity to do work. to produce if this were the case.