Limiting and Excess Reagents

Let’s consider the reaction between hydrogen gas and nitrogen gas to form ammonia gas: \[
3\ce{H}_{2}\left(g\right)+\ce{N}_{2}\left(g\right)\rightarrow2\ce{NH}_{3}\left(g\right)
\]

Based on stoichiometry, we know that if we mix three moles of  [latex]\ce{H}_{2}[/latex] with one mole of [latex]\ce{N}_{2}[/latex] we can obtain two moles of  [latex]\ce{NH}_{3}[/latex]. In other words, [latex]\ce{H}_{2}[/latex] reacts with [latex]\ce{N}_{2}[/latex] in a molar ratio of  [latex]3:1[/latex]. If we mix three moles of hydrogen gas and two moles of nitrogen gas, what will happen? Similarly, three moles of  [latex]\ce{H}_{2}[/latex] will react with one mole of [latex]\ce{N}_{2}[/latex] and produce two moles of  [latex]\ce{NH}_{3}[/latex]. However, the entire quantity of [latex]\ce{H}_{2}[/latex] will be used before the [latex]\ce{N}_{2}[/latex] as we start with the exact amount of [latex]\ce{H}_{2}[/latex] required for the reaction. The product mixture will contain one unreacted mole of [latex]\ce{N}_{2}[/latex] as we only required one mole of [latex]\ce{N}_{2}[/latex] for the reaction. If we had more [latex]\ce{H}_{2}[/latex] we could have produced more [latex]\ce{NH}_{3}[/latex] as we already have excess [latex]\ce{N}_{2}[/latex]. Therefore, in this reaction, we call [latex]\ce{H_{2}}[/latex] the limiting reagent since it limits the production of [latex]\ce{NH}_{3}[/latex].

The limiting reagent is the reactant that runs out first, limiting the formation of products. In the above example, nitrogen gas is called the excess reagent because we have a greater amount than required for the reaction.

One of the fundamental principles in chemistry and physics is the law of conservation of energy and mass. This famous rule explains that we cannot create nor destroy matter, only transform it. Just like baking a cake, you can only get as much as you put it! The amont of reactants present is our core limitation of how much a reaction can produce – which will form a foundational concept within the topic of yields.

Yields

As we have just seen, stoichiometry allows us to determine the maximum mass or amount of a product a reaction can generate for a given quantity of reactants. In reality, chemists never extract the full 100% of a generated product in a reaction.

Consider a mug of coffee. Once you have ingested the liquid, there is often a visible brown stain in the mug due to the adhesive forces of the liquid (see Figure 5.4.1). There is likely to be trace amounts of caffeine that you have yet to digest. While you could fill the cup with water and attempt to recover the caffeine, eliminating the visible colour, on the molecular scale with sextillions of molecules, it is impossible to capture every compound. Even in perfect reactions that go to completion with many repetitive washes to gather all of a produced product, we are unable to confidently have recovered everything.

From a more chemical perspective, however, side reactions are a common occurrence in many processes. For example, in the combustion of some carbon-containing compounds, such as methane, there are 2 potential reactions that can occur depending on the available levels of oxygen. They are:

\[\ce{CH}_{4}\left(g\right)+\ce2{O}_{2}\left(g\right)\rightarrow\ce{CO}_{2}\left(g\right)\ce2{H}_{2}{O}\left(g\right)\] \[\ce2{CH}_{4}\left(g\right)+\ce3{O}_{2}\left(g\right)\rightarrow\ce2{CO}\left(g\right)\ce4{H}_{2}{O}\left(g\right)\]

Complete combustion (with oxygen excess) generates [latex]\ce{CO}_{2}[/latex] (carbon dioxide), whereas incomplete combustion produces [latex]\ce{CO}[/latex] (carbon monoxide) – a more toxic greenhouse gas responsible for smog! Car manufacturers attempt to design engines with sufficient airflow to allow for excess oxygen in the environment. However, as they might, some CO is always produced. This, alongside every other chemical reaction, is inefficient to some degree. It is impossible to recover 100% of a reaction.

Finally, we can address our first assumption, that all reactions go to completion. This is not true. While most reactions will undergo enough conversion that we can realistically say they have completed fully, some reactions instead exist in equilibrium, where only a certain amount of potential product is produced. The equation we looked at the beginning of this chapter, the production of ammonia, is one of the most famous equilibrium reactions, known as the Haber process:

[latex]\ce{3H2(g) + N2(g) <=> 2NH3(g)}[/latex]

In the Haber process, reactants and products exist in equilibrium with each other (denoted by the two-way arrow in the equation). This equilibrium can be influenced by air pressure and temperature – which, if carefully managed, allows for the extraction of ammonia. However, this system will never allow for the full 100% extraction of the gas.

This is all to say that in chemical processes, we must consider our percentage yield. Percentage yield indicates the success of the reaction. If the value is closer to 100%, that means losses are minor, and most reactants have converted to products. This is calculated by considering the theoretical yield. as previously demonstrated, and the actual yield, measured in a laboratory, in the following formula:

\[
\frac{\textrm{Actual yield}}{\textrm{Theoretical yield}}\times100
\]

The theoretical yield is the maximum amount of the product that can form under the given reaction conditions. The available amount of limiting reagent determines the maximum amount of the product that can be formed. As demonstrated previously, theoretical yield can be calculated using the stoichiometric coefficients (or molar ratios) displayed in the balanced chemical equation. We calculate theoretical yield assuming that no losses occur during the reaction and all the reactants convert to products. However, in reality, losses and inefficiencies often occur during chemical reactions. Therefore, the actual amount that you isolate and measure from a chemical reaction is less than the theoretically expected amount.

The actual yield of a product is the amount of the product you isolate from the chemical reaction. You cannot calculate the actual yield. It is required to be determined experimentally, generally through weighing the product produced.

From these two values, the percentage yield can be calculated. As a general rule of thumb, yield decreases with the number of steps needed to complete a chemical reaction but can be increased through repeat filtrations and extractions within an experiment. In chemistry and especially industrial applications, bolstering percentage yield is essential to cost-effective operations and the adoption of processes.