From ChemPRIME

Limiting reactant: Purifying Silica

Figure 1: Solar Panel

Solar cells trap energy, which excites electrons of silicon metal present in them. These electrons flow in the wires of the electric circuit generating electrical current. Silicon is a very vital metal for an electronic industry. It is used to manufacture Light Emitting Diodes, (LED), liquid crystal display (LCD) screens, transistors and almost all semiconductor devices. For some of these devices, we require pure silicon. To obtain pure silicon, the mineral has to go through several chemical and physical changes. To understand these reactions, it is important that one have knowledge of limiting reactant. Here we try to understand the concept of limiting reactant in the reaction of silica and carbon.

Concept analogy:

In a chemical reaction, one reactant is consumed fully and therefore it is known as limiting reagent. This reactant therefore is responsible for the reaction regulation, as it limits or decides the amount of product in the reaction. For example,

X + 2Y -------> XY2
1mole 2 moles 1 mole of XY2 formed
Equation 1: Balanced Chemical Reaction

In equation 1, one mole of X reacts with 2 moles of Y to give 1 mole of XY2 molecule. In this particular reaction for every mole of X, 2 moles of Y is required. One cannot tell the limiting reagent just by looking at the balanced equation. It depends entirely on the amounts of each reactant, not their reaction coefficients.

Let’s assume we have 1 mole of X and 1 mole of Y available to react. Can you determine how moles of XY2 are produced?

2 moles of Y reacts with 1 mole of X
1 mole of Y would react with 1/2 moles of X
When 1 mole of Y reacts with 1/2 mole of X, all of the Y is used up and only 1/2 of the X is used up
Therefore, Y is the limiting reagent

Next step is to determine -How much product would be formed?

2 moles of Y produces 1 mole XY2
1 mole of Y would produce 1/2 moles of XY2

Let’s understand this with a real-life example. We have two glass frames and six glass lenses to be fitted in those two frames. What would be the limiting reagent?

6 glass lens two glass frames two lens remain un-used four lenses f fitted in two glass frames.
We have enough lenses to make 3 pairs of glasses. But we only have enough frames to make 2 pairs of glasses. Therefore, frames are the limiting reagent. Two frames would need just four lenses (two lenses per frame) and two glass lenses remain unused. [2]

We can apply what we just learned in the following reaction: Silicon oxide is reacted with carbon at around 2000 degree Celsius to extract pure silicon. In this reaction, carbon monoxide is released. Electronic grade (EG) - purified silicon is used in the manufacture the products in electronic industry. Carbon in the reaction is obtained from the coke, while silica is in the form of quartz or sand. The reaction goes like this:

SiO2(s) + 2C(s) ---------------------> Si (l) + 2CO

In the above reaction, we assume that either of the reactants (SiO2 and C) can be a limiting reagent and any one of these can be in excess. Firstly, we need to find the reactant that is completely consumed in the reaction like in the case of eyeglasses.

1 glass frame + 2 glasses --->one glass with frame.
SiO2 +2C------> Si +2CO

Formation of silicon with the fusion of SiO2 and carbon takes place in the following way. We would first look at how much silicon would be formed by each reactant present in this reaction. The reactant that would form less of the product would act as the limiting reagent.

Example:

What if 500 moles of silica is heated with 800 moles of carbon? We need to calculate maximum number of moles of silicon formed in the reaction. This is just like the earlier example where one glass frame would need 2 glasses to make a complete glass and frame set. We would start with balancing the equation. From these coefficients, one can find the molar ratio for the moles of products and reactants.

Number of mol of Si produced = 800 mol C ( 1 mol Si/2 mol C)=400 mol Si
Number of mol Si produced= 500 mol SiO2 ( 1 mol Si/1 mol SiO2)= 500 mol Si

400 mol Si will be produced with 800 moles of C, while 500 mol Si would be produced with 500 mole of SiO2. By this relation we can determine that all carbon (800 moles) is used in producing 400 mole of Silicon. On the other hand, SiO2 won’t be used up until 500 moles of silicon are produced. Silicon is produced in minimal quantities by carbon. Thus, carbon is the reactant that will be consumed first in the reaction. Therefore, carbon is a limiting reagent, and 400 moles of Silicon are produced. [1]

Here is an example you can try yourself:

The Thermite process was accidentally developed by Hans Goldschmidt while investigating the reaction of aluminum and metal oxides. Later this process was developed to weld railroad tracks, instead of putting them together with nuts and bolts. This revolutionary change made the rail track safer and less noisy. The thermite reaction is written as: Fe2O3 + Al ----> Al2O3 + Fe. If you start with 100 moles of Fe2O3 and 75 moles of Al, can you find the reactant that is a limiting reagent, and also determine the number of moles of the reactant in excess?

We would try to follow some simple steps to solve this problem.
Step1. Balance the chemical equation.
Step2. Calculate moles of reactants involved in the reaction. You can form the ratio between reactant & another reactant, also you can take into consideration one reactant and one product (Depends upon the product/reactant quantities mentioned in the reaction).
Step 3. Assess the molar ratio of the reactants considering the balanced equation.
Step 4. Compare any pair of reactant and product - for their available and the required moles (consider molar ratio again!).
Step 5. Determine the reactant in access and the one present in limited quantity.(This would determine the amount of products formed!)

The key is here

1. Balanced reaction:
Fe2O3 + 2Al ------> Al2O3 + 2 Fe
2. We have 100 moles of Fe2O3 and 75 moles of Al.
3. Molar ratio for Fe2O3 and Al is = 1:2
4. That means for every 1 moles of Fe2O3 we need 2 mole of Al. (As per the balanced equation)
Therefore for 100 mole of Fe2O3 we would require 200 moles of Al. (But only 75 moles of Al are available for the reaction). Thus Aluminum would limit the reaction.
5. To calculate the amount how many moles of Fe2O3 would be used up in the reaction, one need to find how many moles would remain unused?
2 moles of Al would require 1 moles Fe2O3 in this reaction.
Therefore 1 Al would require 1/2 moles of Fe2O3
(as per the available moles in the reaction) 75 Al would need 75 (1/2) = 37.5 Fe2O3 in this reaction.

100(initial moles of Fe2O3) - 37.5(Fe2O3 moles used up in this reaction) =62.5 moles of Fe2O3 would be left after the complete reaction.