What's the difference between reactant, excess reactant and limited reactant in a balanced equation?

Question

In some reactions, the reactant is mentioned as being "excess". For example, "phosphorus pentoxide forms in excess oxygen" or "pentahalides form with excess halogen".

But since the balanced equation shows exactly how many moles of a reactant are necessary, what is "excess" about the reactant? And how does it contrast with "limited reactant" and just "reactant"? (Ie: What's the difference in a balanced equation between oxygen, limited oxygen and excess oxygen?)

Does each balanced equation need to explicitly say somewhere that this is specifically an excess/limited reactant, or can this be inferred from the stoichiometric coefficients of the balanced equation? Do you need at least two equations side by side to see that one is excess and the other isn't?

Additionally, taking for example the following two reactions

$$\ce{P4 + 3O2 -> P4O6}\\[1em] \ce{P4 + 5O2 -> P4O10}$$

it seems to me that mathematically on a mole basis, sure we can say that tetraphosphorus hexoxide will form with 3 moles of O₂ available (per mole of P₄), but tetraphosphorus decoxide needs 5 moles of O₂, however, given the huge amount of actual molecules in the reaction, how do the molecules know when there's excess? I mean, why doesn't the phosphorus just form a lot of P₄O₁₀ and then just a few molecules of P₄O₆ with the few leftover O₂ molecules, or would this be some kind of unstable situation and the phosphorus molecules are pretty considerate and don't start forming P₄O₁₀ until every P₄ has at least 3 O₂ attached to it?

To sum up, my questions are:

1. What's the difference between "reactant", "limited reactant" and "excess reactant" in a balanced equation?

2. Can the fact that the reactant is excess/limited be inferred from the balanced equation?

3. Why is it that the same reactant (such as P₄) proceeds in two different ways depending on whether the second reactant is excess/limited?

Answer 1

Suppose that you want to make a cake. You would first need to go your fridge to check whether you have the necessary ingredients to make one. So you go to your fridge. Luckily, you have all the ingredients: milk, eggs, flour, and frosting. So you decide to make one. You also decide to make the cake as big as possible to avoid the hassle of cleaning/preparing again. Now, what determines how big you can make the cake?

It is the quantity of ingredients of course. But what happens if you have enough milk to make a 10 cm cake, enough eggs to make a 1000 cm cake, enough flour to make a 1000 cm cake, and enough frosting to make a 10000 cm cake? How big can you make the cake?

You would only be able to make a 10 cm cake. Because you would run out of milk. And since you no longer have milk, you cannot make anymore cake.

Lets go back to your question of excess reagents and limiting reagents. The limiting reagent is the milk in the example above. It is what determines how much of a product you will obtain. It is what limits the amount of product you get (hence the apt name limiting reagent). Everything else are excess reagents: the eggs, the flour, the frosting. They are leftovers; they are in excess.

Now question 2. You cannot tell which reactant will be in excess by just looking at the balanced equation. Going back to the cake example, the balanced equation is sort of like a recipe for the cake. You cannot tell whether you will have eggs, flour, and frosting left over by just looking at the recipe. You also have to check your fridge. In other words, you have to know what you are starting with.

Now question 3. I think question 3 will be answered in more detail as you study more chemistry. A complete answer involves thermodynamics and statistical mechanics. Nevertheless, going back to the example of the cake: Whether or not you can make cake depends on whether you have all four ingredients. It also depends on how much of each ingredient you have. If you have no milk, you won't be able to make any cake.

But say that you want to make boiled eggs as well. You only need eggs to make boiled eggs so you would could turn all eggs leftover eggs from the cake into boiled eggs. The fact that you can make boiled eggs with the leftover eggs does not change the fact that you can make a 10 cm cake.

This is what the two equations are trying to get at. The major product, will be determined by how much of a certain reactant you have. It doesn't mean that the reaction is solely determined by what it is in excess or not.

Answer 2

Reagent is an overarching word and it covers everything that is added to a chemical reaction.^[1] So all we need to define are limiting and excess reagents.

A limiting reagent is one that limits the maximum outcome of a reaction. Remember that a reaction needs all reagents to proceed from starting material to product, and that it will consume them in the ratios given in the balanced equation. On paper, we can write a fully balanced equation and know exactly how much we have. In the real world, we will not have added exactly the same amount of everything so some reagents will remain unreacting. Those reagents that can be used up completely — the scarcest ones — limit the maximum output, therefore they are limiting.

In a real world example, consider burning petrol (approximated as hexane, $\ce{C6H14}$). The full reaction equation will be: $$\ce{2 C6H14 + 19 O2 -> 12 CO2 + 14 H2O}\tag{1}$$ Of course, the reaction will consume the hexane from the jar you have it in and oxygen from the surrounding air. After some time, the fire will go out. The petrol will have been completely consumed — but the air of course stil contains oxygen. Petrol was the limiting reagent.

If you do the same experiment but in a closed, transparent container, you will notice that the flame is extinguished before all the petrol was burnt. Here, there was only a limited supply of oxygen in the sealed container. After it was used up, the combustion cannot continue. Oxygen was the limiting reagent.

An excess reagent, on the other hand, will be present in excess, i.e. more than is needed to drive the reaction to completion. In the above examples, the reagent that was not limiting was automatically present in excess (oxygen in the first, petrol in the second example).

In examples actually performed in the chemistry lab, one defines one reagent as the ‘standard’ and its amount as ‘1 equivalent’ or $\pu{1eq}$. A limiting reagent would be one that is present in less than $\pu{1eq}$ (assuming equal stoichiometries; otherwise balanced accordingly)^[2] while an excess reagent means that it is present in (significantly) more than $\pu{1eq}$ (same stoichiometry caveat).

In the examples I have shown you, both reagents can be limiting or excess, depending on the actual reaction conditions. Thus, you cannot infer which is which by looking at a balanced equation. If you read the experimental sections of journal articles, these will make it quite clear because rather than listing fully balanced equations they list methods and (in organic chemistry typically) always refer to equivalents used.

Now how do we explain different reaction products depending on how much in excess a certain reagent is? It is not always trivial but you can always consider it some sort of a stepwise process. In the phosphorus example you gave, you might consider a first reaction step (very rapid) that forms phosphorus trioxide from white phosphorus.

$$\ce{P4 + 3O2 -> P4O6}\tag{2}$$

After this reaction has run to completion, phosphorus turns out to be the limiting reagent so a second subsequent oxidation step is added to finally generate phosphorus pentoxide.

$$\ce{P4O6 + 2 O2 -> P4O10}\tag{3}$$

This may noy be a correct mechanism on microscopic scale but it does help explain how excess of one reagent can lead to different products.

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Notes:

[1]: Unless you also count reactant as something different. I never understood the true difference between the two, as far as I can tell, they are synonyms.

[2]: Beneath a certain threshold, however, the term will be catalytic rather than limiting. The difference is that, in theory, one molecule of the catalytic reagent will be enough to forward the reaction while the limiting reagent will be used up and end the reaction.