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# Stoichiometry – Limiting and Excess Reagent

Chemical equations are made up of reactants (a substance present at the start of a chemical reaction and appears on the left side of the equation) and products (a substance present at the end of the reaction and appears on the right side of the equation).

A chemical reaction is a formula that denotes how a reaction proceeds from reactants to products via chemical or physical changes.

• Reactants in a chemical formula combine to form the products. The formula’s numerical values to each substance tell us how much of each chemical substance is involved in the reaction.
• This numerical relationship or the relative quantities of reactants and products is referred to as Stoichiometry.
• This term has Ancient Greek origin and comes from Stoicheion (means element) and metron (means measure).
• This numerical relationship or the relative quantities of reactants and products is referred to as Stoichiometry.
• This term has Ancient Greek origin and comes from Stoicheion (means element) and metron (means measure).

As per the law of conservation of mass, matter is neither created nor destroyed but only changes form. Stoichiometry follows the same fundamentals as this law. In simple words, a reaction should be balanced.

It means that the number of atoms of every element in the reaction on the reactant side is equal to that on the product side. A reaction does not create or destroy atoms but only rearranges them.

But in an experiment, the reactants in a chemical reaction are not always a stoichiometric mixture. There could be reactants that are not used up completely at the end of the reaction (called excess reagents) or some reactants that are completely reacted or used up (called limiting reagent). A limiting reagent limits the number of products formed since after the limiting reagent is used up, ultimately, no more products can be formed.

The Limiting Reagent Stoichiometry deals with finding the limiting reactant in a reaction by various methods.

Understanding Balanced Equations

To understand how equations are said to be balanced, we will consider the formation of NaCl (table salt) compound by the reaction between solid sodium (Na) with chlorine gas (Cl)

2Na (solid) + Cl2 (gas) -> 2NaCl (solid)

The above reaction is between a metal (sodium) and a diatomic gas (chlorine). In this balanced reaction, we see that two atoms of Na combine with two Cl atoms (or one CL2 molecule) to give 2 atoms of NaCl. So if there are 6 Na atoms, we would need 3 molecules of Cl2 for the reaction to complete.

If Cl2 atoms are in excess in the reaction, they remain unused even after completion. In other words, we can say 6 moles of Na needs 3 moles of Cl2 gas for this reaction. In this reaction, Na is the limiting reagent as it limits the amount of Sodium chloride formed.

Methods of Determining Limiting Reagents

The theoretical yield in a chemical reaction is the amount of product formed when the limiting reactant is used up fully. To identify the limiting reagent in a reaction, we can follow either of the methods described below:

The first thing we must consider is that the equation has to be balanced, i.e. the quantity of each substance is equal on both sides of the equation.

• Method 1 – By comparing the mole ratio of the number of reactants used –

You can use this method accurately when there are only two reactants in the reaction.

Then you choose one reactant (let us say A) and use the balanced chemical formula to determine how much of the second reactant (let us say B) is necessary to react with the first reactant A. If B present is more than the required amount, B is an excess reagent, and A is the limiting reagent. We will understand this with an example:

Question – If we combine 2.8 grams of Al (aluminium, solid) and 4.15 grams of Cl2 (chlorine gas), find the limiting reagent in this reaction:

2 Al + 3 Cl2 -> 2 AlCl3

Solution –

We will first convert all the mass values into moles by considering the conversion factor as molar masses of each element:

2.8 gm Al * (1 mole)/(26.98 gm) = 0.104 mol of Al

4.15 gm Cl * (1 mol)/(70.90 gm) = 0.0585 mol of Cl2

Now we will compare the mole ratio of Al to Cl2 in the balanced equation to the one which is present in the experiment:

The required mole ratio of Al and Cl2 in the balanced equation

(Required mole of Al)/(Required moles of Cl2) = ⅔ = 0.66

(Actual moles of Al)/(actual mole of CL2) = 0.104/0.0585 = 1.78

The above result shows that the actual mole ratio is greater than the required ratio; there is more Al in the reaction than what is needed to react completely with Cl2. Hence Cl2 is the limiting reagent here. If the actual ratio were less than the required ratio, Cl2 would have been the excess reactant and Al the limiting one.

• Method 2 – Find the limiting reagent by using the mole ratio of Al and Cl2 to figure out how much Cl2 is needed to consume 0.104 moles of Al fully. The steps are as below:

We first get the balanced equation. We will use stoichiometry to find out the mass of product produced by each reactant:

The number of moles of Cl2 needed to react with 0.104 moles of Al =

0.104 mole Al * ((3 moles of Cl2)/(2 moles of Al) = 0.156 moles of Cl2

We know from the earlier method that there are 0.0585 moles of Cl2 in the reaction, less than 0.156 moles. This denotes that Cl2 is the limiting reagent here, as found by the previous method 1 also. We could have also done this calculation for Al and reached the same conclusion.

Conclusion

Chemistry is a fascinating subject if you get your fundamentals cleared. Stoichiometry has many real-life applications in chemical engineering, making it one of the most important topics in Chemistry. Clarifying your basics by referring to well-known academic sites will surely give you a better understanding of this subject to ace your boards and many competitive exams.

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