From WolfWikis

Limiting reagents

Stoichiometric ratios

One of the most important things to remember about balanced reaction equations is that the stoichiometric coefficients are essentially ratios. This means we can multiply them all with the same number and the equation still holds. Take the formation of water from the elements:

2H₂ + O₂ ==> 2H₂O

I can read this as two molecules of H₂ plus one molecule of O₂ react to give water (two molecules of it).

However, I could also multiply by, say 17 and get

17*2H₂ + 17O₂ ==> 17*2H₂O

34H₂ + 17O₂ ==> 34H₂O

So 34 hydrogen molecules react with 17 oxygen molecules to give 34 water molecules.

In fact I can even multiply with a huge number like 6.2022 10²³! This is why I can also read the formula in moles rather than in molecules.

Whichever way I read it, the ratio of hydrogen and oxygen should remain 2:1 (which is the same as 34:17, of course). Likewise there are always twice as many water molecules formed as there are oxygen molecules consumed.

So I could simplify the whole equation to its bare essentials and write something like 2:1:2 or better 2:1::2, where I am using :: to separate reactants form products.

Deviating from the ratio

We can put reactants together in the right ratio dictated by the balanced equation, but we do not have to. In fact if you just throw them together without carefully weighing you will seldom hit the right ratio. That is why balances and volumetric containers are so important.

What happens if we deviate from the proper ratio is what happens at a ballroom dance party where the male:female ratio is not quite 1:1. Some people get to watch rather than dance. The minority gets to dance all the time, but their limited numbers limit the fun for the ones in excess.

Chemistry uses exactly those terms. The reactant that is in short supply relative to the proper ratio imposed by the balanced equation is called limiting. The other one(s) is/are in excess. Any surplus of the one(s) in excess will remain unreacted.

In general all of the limiting reactant will disappear, if the reaction goes to completion. The reactions below are all assumed to be of that type. Reactions only involving condensed phases like solids or liquids typically go to completion, just like all ice melts once it really thaws.

However, some reactions do not go to completion, because they go to equilibrium. That can happen if the reaction involves dilute species, e.g. a dilute gas or a dilute solute in solution. In that case you have to worry about concentrations or partial pressures. This is a later topic of CH 101.

Problems related to limiting reagents

When reactants are brought together in a ratio that does not fit the balanced equation, the first order of business is always to find out which one is the limiting reagent. There are various ways of doing that but they all depend on the ratios of the balanced equation.

That does mean you need:

1. a balanced equation
2. all quantities to be (converted) in moles (or mmoles or the like)

Finding the limiting reagent

One strategy is:

1. take a reactant
2. assume it is limiting (i.e. there is enough of the other one(s))
3. calculate how much product that would produce (look at the ratio between product:chosen reactant)
4. do this for all reactants
5. compare the outcomes
6. pick the one that produces the least product: that must be the limiting one.

Another strategy is:

1. take one of the reactants, say you have 6 moles of it available
2. divide or multiply the balanced equation in such a way that the coefficient of that reactant becomes a 6
3. look at the coefficients of the other reactants and see if there is enough available
4. if there is you picked the limiting one, if there is not it is a different one

What to do once you found it

After identifying the limiting reagent you can use the balanced equation to calculate:

1. how much product(s) you can get
2. how much of the excess reactant(s) actually partakes in the dance to produce the product(s)
3. how much of the excess reactant(s) is left after the reaction has run its course

Exercises

Exercise 1

Two moles of hydrogen and two moles of oxygen are brought together in a balloon and ignited.

1. How much water is formed
2. Which reactant is in excess
3. How much of it is left after the reaction has gone to completion

Exercise 2

Consider the reaction Ca + H₂O ==> H₂ + Ca(OH)₂

One gram of calcium is brought into 6 liters of water

1. What is the limiting reactant?
2. What volume of hydrogen is formed (at 1 Atm and 25^oC)

Exercise 3

Gold can react with chlorine to form AuCl₃

1. How much of the excess reactant is left (by weight) if we start with 1 gram of gold and 2 liters of chlorine (at 1 Atm and 25^oC)?

remark: we heat up the mixture to an appropriate temperature of 200^oC to facilitate the reaction.

Exercise 4

Combustion reactions are typically carried out in bomb calorimeters. A pellet of the substance under investigation is brought into a sturdy metal container (the bomb) with an half-inch thick wall and a equally sturdy lid that can be screwed on. The bomb is pressurized with 25 Atm of pure oxygen and a current is yanked through a little fuse wire that rests on top of the pellet. The wire glows red hot and ignites the reaction. The idea is that the oxygen is in excess, that the pellet burns up completely without generating soot. The heat evolved can be measured by putting the bomb in a vat with a lot of water and the temperature change of the water is measured with a good thermometer.

The volume inside the bomb is 500 ml and the oxygen pressure 25 atm and the pellet is 6 grams of solid benzoic acid (C₆H₅COOH)

1. Determine the limiting reactant.
2. How much water is formed?
3. How much benzoic acid must be used for the stoichiometries of the reactants to match?

Exercise 5

CZX1 is a compound^[1] that can be synthesized from zinc chloride ZnCl₂, copper(I)chloride (CuCl) and trimethylammoniumchloride (TMACl) (CH₃)₃NHCl, all anhydrous. Every sixth zinc atom is replaced by the combination of a copper atom plus a TMA moiety, leading to a balanced reaction equation:

5ZnCl₂ + 1CuCl + 1TMACl ==> 1CZX1^[2]

1. Starting with 10g of zinc chloride, 3g of CuCl and 3g of TMACl, what is the limiting reactant
2. How how much CZX1 is formed?

Notes

1. ↑ This compound was the topic of Amanda Josey's recent thesis. Dr. Josey worked under Dr. J. Martin and is now working at BASF.
2. ↑ Actually: Zn₅Cu[(CH₃)₃NH]Cl₁₂. It is not unusual if compounds get this complicated to find a suitable abbreviation for them.