Limiting Reagent

A chemical reaction occurs when one or more reactants undergo some chemical changes to form new products. If the reaction involves two or more reactants, one of the reactants becomes the limiting reactant, when the reaction occurs practically. As, theoretically, a chemical reaction occurs in a stoichiometric proportion of the number of moles of reactants and products, but when a chemical reaction is carried out practically, it is impossible to have exact proportions of reactant moles due to limitations in the measuring instruments. Thus, the reactant which gets exhausted first and stops the reaction from proceeding further is termed a limiting reagent. 

In this article, we will explore the definition, examples, formula, and some examples of limiting reactants.

Definition of Limiting Reagent

The reactant in a chemical reaction that gets consumed wholly or used up first, and thus, stops the reaction from proceeding further, and limits the amount of product formed is called limiting reactant of that particular reaction.

The reaction is stopped when the limiting reactant is consumed wholly, even if the other reactants are present in excess. Also, the quantity of limiting reactant limits the amount of product formed, so it becomes quite important to study about limiting reactant of any chemical reaction. By determining the limiting reactant, we can optimize the yield of the reaction accordingly. 

The concept of limiting reactant can be learnt with the help of the image discussed below,

Limiting Reagent Formula

Basically, there are two methods to determine the limiting reactant for a chemical reaction. Both are explained as follows:

Method 1: Reaction Stoichiometry Method

In this method, we compare the mole ratios of reactants to determine the limiting reactant. The basic steps involved are as follows:

• To begin with, we need to write the balanced chemical equation for the reaction.
• Then, we determine the amount (in moles or mass) of each reactant involved in the reaction.
• Then, we calculate the mole ratio of each reactant by dividing the amount of each reactant by its respective stoichiometric coefficient in the balanced chemical equation.
• Next, we compare the mole ratios of the reactants. 
• The reactant with the smaller mole ratio is the limiting reactant.

Let’s look at an example to illustrate these steps.

Example: Consider the reaction between hydrogen gas (H₂) and oxygen gas (O₂) to form water (H₂O). Suppose that we have 10.0 grams of H₂ and 20.0 grams of O₂.

Solution:

Here are the steps to determine the limiting reactant:

First, we write the balanced chemical equation:

   2H₂ + O₂  → 2H₂O

Now, we determine the amount of each reactant involved: Moles of H₂=10/1=10 and Moles of O₂=20/16=1.25.

Next, we determine the mole ratio as discussed above.

Mole ratio for H₂=10/2=5

Mole ratio for O₂=1.25/1=1.25

As O₂ has a lesser mole ratio, O₂ is the limiting reactant in this case.

Method 2: Product Yield Method

In this method, we determine the limiting reactant by comparing the amount of product each reactant would produce. The basic steps involved in this method are as follows:

• First of all, we need to write a balanced chemical equation for the chemical reaction.
• Then, we need to convert the amount of each reactant into the number of moles.
• Now, we calculate the moles of products that can be produced from each reactant, assuming other reactants to be present in excess.
• The reactant that will produce the least amount of product would be the limiting reactant.

The above steps will be clear with help of an example below:

Example: Consider the reaction of hydrogen and oxygen to produce water. The first step is to write the balanced chemical equation for the reaction, i.e.

2H₂ + O₂  → 2H₂O

Solution:

The balanced chemical equation involves 2 moles of hydrogen gas and 1 mole of oxygen gas to produce 1 mole of water. Let’s assume that, we have 4 moles of H₂ and 3 moles of O₂. 

Now, as 2 moles of H₂ can produce 2 moles of H₂O, 4 moles will produce 4 moles of H₂O. And similarly, 3 moles of O₂ can produce 6 moles of H₂O. 

As H₂ produces the least amount of product, H₂ will be the limiting reactant in this case.

Read More,

• How to Calculate Percentage Yield?
• Characteristics of Chemical Reactions
• Rate of a Reaction

Solved Examples on Limiting Reagent Formula

Question 1: If you have 6 moles of iron (Fe) and 4 moles of sulfur (S), which one is the limiting reactant in the following reaction:

Fe + S → FeS

Determine the limiting reactant for this reaction.

Solution:

The balanced chemical equation is already given as:

Fe + S → FeS

Using Reaction Stoichiometry Method,

We determine the mole ratio for each reactant:

Mole ratio of Fe = 6/1 = 6

Mole ratio of S = 4/1 =4

As the mole ratio of S is lesser in this case, S is the limiting reactant in this case.

Question 2: Consider the reaction of the formation of ammonia from nitrogen and hydrogen. We have 14 grams of Nitrogen gas and 12 grams of Hydrogen gas. Determine the limiting reactant for this case.

Solution: 

The balanced chemical equation for the reaction:

N₂ + 3H₂ → 2NH₃

Find the moles of the reactant,

n(N₂) = 14/14 = 1 mole

n(H₂) = 12/2 = 6 moles

Using the Product Yield Method,

We observe that 1 mole of Nitrogen is required to form 2 moles of Ammonia and 3 moles of Hydrogen gas are required for the same.

In the given problem, we have 1 mole of Nitrogen which can produce 2 moles of ammonia.

6 moles of hydrogen which can produce 4 moles of ammonia.

Thus, in this case, the reaction would stop when 1 mole of Nitrogen and 3 moles from the available 6 moles of hydrogen would react completely. Thus, Nitrogen(N₂) becomes the limiting reactant in this case. The other reactant H₂, which would remain after the reaction will be called an excess reactant.

Question 3: Determine the limiting reagent if 32 grams of methane reacts with 32 grams of oxygen gas.

Solution:

The balanced chemical equation for the above reaction is as follows:

CH₄ + 2O₂ →  CO₂ + 2H₂O

We have, 

n(CH₄) = 32/16 = 2 moles

n(O₂) = 32/16 = 2 moles

Using Product Yield Method,

2 moles of methane(CH₄) can produce 2 moles of carbon dioxide(CO₂).

2 moles of oxygen(O₂) can produce 1 mole of carbon dioxide(CO₂).

We know that the reactant which produces the least amount of product is the limiting reactant. Thus, in this case, oxygen(O₂) gas will be the limiting reactant.

Question 4: Consider the chemical reaction that produces silver chloride from silver nitrate and hydrochloric acid. If you have 2 moles of silver nitrate and 1 mole of hydrochloric acid, determine the limiting reactant by the Mole-Ratio method.

Solution:

The balanced chemical equation for the reaction is as follows,

AgNO₃ + HCl → AgCl + HNO₃

Using Reaction Stoichiometry Method,

Mole ratio of AgNO₃ = 2/1 = 2

Mole ratio of HCl = 1/1 = 1

As the mole ratio of HCl is less in this case, HCl is the limiting reactant in this case.

Question 5: Consider the chemical reaction between magnesium metal and oxygen gas to form magnesium oxide. If you have 4 moles of magnesium and 3 moles of oxygen gas, determine the limiting reactant by the Product Yield method.

Solution:

The balanced chemical equation for the reaction is as follows:  

2Mg + O₂ -> 2MgO

Using Product Yield Method,

We observe that 2 moles of Mg produces 2 moles of MgO and 1 Mole of O₂ produces 2 moles of MgO. 

We have 4 moles of Mg, so 4 moles of MgO can be produced from them. And, we have 3 moles of oxygen gas, which can produce 6 moles of MgO. As Mg produces the least amount of product in this case, Mg becomes the limiting reactant for this reaction.

FAQs on Limiting Reagent

Q1: What is the limiting reagent of a reaction?

Answer:

The reactant that determines the amount of product produced and causes the reaction to cease upon its depletion is known as the limiting reactant for that reaction. In other words, the reactant that is completely consumed in a chemical reaction and thereby limits the amount of product that can be formed is referred to as the limiting reactant.

Q2: What is the importance of limiting reagents in a chemical reaction?

Answer:

The progress of a chemical reaction depends on the amount of limiting reactant because the reaction gets stopped when the limiting reactant is consumed wholly. Thus, to know how much time would the reaction take to complete, one needs to know about the limiting reactant. Along with that, the amount of product formed also varies in a fixed stoichiometric proportion with the amount of limiting reactant. So, the reaction yield can be optimized accordingly, once the limiting reactant is known. Thus, it is quite important to identify the limiting reactant in a chemical reaction.

Q3: What is the theoretical yield of a chemical reaction?

Answer:

The maximum amount of product that can be produced from a chemical reaction provided that the reaction proceeds to completion and the limiting reactant gets consumed completely is referred to as the theoretical yield of any chemical reaction. It can be calculated using stoichiometric ratios in the balanced chemical equation of the reaction.

Q4: What is the actual yield of a chemical reaction? How does it differ from the theoretical yield?

Answer:

The amount of product that is actually obtained from a chemical reaction is known as the actual yield of the chemical reaction. Usually, the actual yield is lesser than the theoretical yield due to factors such as side reactions, incomplete reactions, experimental errors, etc. These factors cause the reaction to be inefficient and thus should be avoided as much as possible.

Q5: Does the temperature or pressure of a chemical reaction affects the limiting reactant?

Answer:

The temperature and pressure of a chemical reaction affect the kinetics of the reaction, but they do not affect which reactant is the limiting reactant. The limiting reactant is determined by the stoichiometric ratios of the reactants, which are independent of temperature and pressure.