# All you need to know about stoichiometry

Stoichiometry- a complex term, stems from two Greek words; stoikhein which means element
and metron which stands for measuring. So, stoichiometry literally means measuring elements.
But that doesn’t explain the actual concept behind it so let’s delve into it further with an example.
If I say that water is made up by the combination of hydrogen with oxygen. Is this information
correct? Absolutely. But is this information enough? Well, not from a chemist’s point of view. The
chemist would be more satisfied if you tell him/her that one mole of water consists of a combination of two moles of hydrogen atoms and one mole oxygen atoms.
The particularity in terms of giving minute details about a specific amount of reactant A reacting
with a specific amount of reactant B to give a compound C using a balanced chemical equation is
an art. The toolkit that a chemist uses for exhibiting this art is called ‘’Stoichiometry’’.

## Stoichiometry Definition

Stoichiometry is the chemical arithmetic that is used to relate the amounts of reactants and products to each other. It describes the quantitative relationship, in terms of relative ratios of mass and/or volume, between the reactants and products of a given chemical reaction.

## What is meant by a balanced chemical equation

Chemical equations are a concise way of representing chemical reactions. The reactants appear on the left side of a chemical equation while products appear on the right side of it. The physical states (solid, liquid, gas, aqueous) of the reactants as well as the products are written in parentheses right next to each compound. Both sides of the reaction are separated by a single or a double arrow that is used to signify the direction of the chemical reaction. Stoichiometric coefficients are then inserted to balance the chemical equation. A balanced chemical equation thus consists of equal number of atoms of each element on the reactant and the product sides.

## Stoichiometric Coefficients

A stoichiometric coefficient is the numerical value inserted in front of the atoms, ions and/or
molecules in a chemical equation to balance their numbers on each side of the equation.
Stoichiometric coefficients are important to establish the mole ratio between reactants and
products involved in the chemical reaction. Stoichiometric coefficients are ideally integers i.e.,
whole numbers. In case of a fraction, every stoichiometric coefficient in the equation should be
multiplied by the denominator of that fraction to create whole numbers while maintaining the
mole ratio.

## How to write a balanced chemical equation

To write a balanced chemical equation, sequence wise follow all the steps given below:
Step I: Determine the molecular formulae of each of the reactants employed and the products
formed in the chemical reaction.
For example: A reaction involving the following compounds

Step II: Write a word equation for the chemical reaction.

Magnesium hydroxide +Hydrochloric acid →Magnesium chloride+ Water

(Reactants on L.H.S)                                           (Products on R.H.S)

Step III: Write the chemical equation from this word equation.

$Mg(OH)_{2}+HCl\rightarrow&space;MgCl_{2}+H_{2}O$

Step IV: Add physical state symbols right next to each compound.

$Mg(OH)_{2}(aq)+HCl(aq)\rightarrow&space;MgCl_{2}(s)+H_{2}O(l)$

Step V: Add stoichiometric coefficients to balance the atoms of each element on the reactant and the product sides.

1. 1 magnesium (Mg) atom on each side
2. 2 chlorine (Cl) atoms on product side so insert 2 next to HCl on reactant side
3. 2 oxygen (O) atoms on reactant side so insert 2 next to H2O on product side
4. This automatically balances 4 hydrogen (H) atoms on both reactant and product sides

$Mg(OH)_{2}(aq)+2HCl(aq)\rightarrow&space;MgCl_{2}(s)+2H_{2}O(l)$

As a general rule of thumb in stoichiometric principles, balance a chemical equation by adding
stoichiometric coefficients to balance different atoms in the following order:

### Significance of a balanced chemical equation in stoichiometry

A balanced chemical equation represents how all chemical reactions follow the Law of
Conservation of mass. The law of conservation of mass states that matter is neither created nor
destroyed in a chemical reaction, it can be converted from one form to another. Therefore, the
number of atoms of each element reacting on the reactant side will always be equal to the
number of atoms of each element formed on the product side. In case of chemical reactions
involving charged species, total charge on the reactant side must be equal to the total charge on
the product side.

Solved Examples
Write balanced chemical equations for the following chemical reactions.
Hint: Follow all the steps discussed above, one at a time.

1. Zinc + Nitric acid →Zinc Nitrate +Hydrogen

2. Methane+Oxygen →Carbon dioxide+Water

1. Step I: Writing the molecular formulae
Zinc: Zn
Nitric acid: HNO3
Zinc nitrate: Zn (NO3)2
Hydrogen: H2
Step II: Write chemical equation with state symbols

$Zn(s)+HNO_{3}(aq)\rightarrow&space;Zn(NO_{3})_{2}(aq)+H_{2}(g)$

Step III: Balance the equation by adding stoichiometric coefficients

$Zn(s)+2HNO_{3}(aq)\rightarrow&space;Zn(NO_{3})_{2}(aq)+H_{2}(g)$

2. $CH_{4}(g)+2O_{2}(g)\rightarrow&space;CO_{2}(g)+2H_{2}O(g)$

3. $Pb(OH)_{_{4}}(s)+2H_{2}SO_{4}(aq)\rightarrow&space;Pb(SO_{4})_{2}(s)+4H_{2}O(l)$

### General types of chemical reactions

In order to write a balanced chemical equation, one must be aware of the different types that
chemical reactions can be categorized into. There are six main types of chemical reactions that
can take place:
Combination Reaction

A combination reaction involves the addition of two or more simple substances to form a single, complex compound. It is also known as a synthesis reaction.

$2Na(s)+Cl_{2}(g)\rightarrow&space;2NaCl(s)$

$N_{2}(g)+3H_{2}(g)\rightarrow&space;2NH_{3}(g)$

Decomposition Reaction

$2Ca(NO_{3})_{2}(s)\rightarrow&space;2CaO(s)+4NO_{2}(g)+O_{2}(g)$

Combustion Reaction

Combustion represents burning of a substance in the presence of oxygen. Hydrocarbons are
organic compounds made up of hydrogen and oxygen. Complete combustion of hydrocarbons
produces carbon dioxide and water.

$C_{12}H_{24}(l)+18O_{2}(g)\rightarrow&space;12CO_{2}(g)+12H_{2}O(g)$

Neutralization Reaction
Neutralization is a reaction of an acid with a base to produce salt and water.

$NaOH(aq)+HCl(aq)\rightarrow&space;NaCl(s)+H_{2}O(l)$

Single Displacement Reaction

$Zn(s)+2HCl(aq)\rightarrow&space;ZnCl_{2}(aq)+H_{2}(g)$

Double Displacement Reaction

A double displacement reaction is also called a salt metathesis reaction. It is a chemical reaction
involving exchange of atoms and/or ions between two chemical entities to form two new
chemical compounds at the product side.

$AgNO_{3}(aq)+HCl(aq)\rightarrow&space;AgCl(s)+HNO_{3}(aq)$

## What factors control the stoichiometry of a reaction

To find the stoichiometry of a reaction, one must know the ‘amount’ of each reactant that reacts
exactly to form particular amounts of products. Let’s discuss the different terms that a chemist
uses in determining the amount of a chemical entity.

### Molar Mass

One mole of a substance is defined as the amount of substance consisting of an Avogadro number
of particles i.e., 6.02×1023 atoms, molecules or ions. Molar mass relates the mass of a substance
(in grams) with the number of moles present in it. It is a useful chemical ratio to develop a
stoichiometric relationship. Molar mass of atoms or ions can be determined from their atomic
masses in accordance with their arrangement in the periodic table. On the other hand, the molar
mass of molecules and/or compounds can be calculated by taking sum of the atomic mass of
each element multiplied by the number of atoms of that element. For instance, molar mass of
butane C4H10 is:
4 (atomic mass of carbon) + 10 (atomic mass of hydrogen) = 4(12.01) + 10 (1.01) = 58.1 g/mol

### Determining the stoichiometry of a chemical reaction using molar mass

Problem: In a chemical reaction ,200 grams of butane burnt in a sufficient supply of oxygen. Using this information and the concept of molar mass, calculate the amounts (in grams) of carbon dioxide and water expected to be produced in this reaction.

Step I: From the knowledge we acquired in the preceding sections, write a balanced chemical equation for the above reaction.

Butane+ Oxygen →Carbon dioxide+ Water

$C_{4}H_{10}(g)+\frac{13}{2}O_{2}(g)\rightarrow&space;4CO_{2}(g)+5H_{2}O(g)$

The equation written above is balanced but since 13/2 is a fraction so we ideally convert it into an integer by multiplying the whole equation with the denominator of this fraction.

$2C_{4}H_{10}(g)+13O_{2}(g)\rightarrow&space;8CO_{2}(g)+10H_{2}O(g)$

Step II: Find the number of moles of butane reacted by using the equation 1 given below:

$moles&space;=\frac{mass}{molar&space;mass}$                             Equation 1

$=&space;\frac{200}{58.1}=3.44$ moles of butane

Step III: Find the mole ratio from the balanced chemical equation: x number of moles of reactant
that reacted to produce y number of moles of product.

Step IV: Find the number of moles of each product formed using the mole ratio determined from the balanced chemical equation.

C4H10: CO2

2        :    8

3.44     :    x1

C4H10: H2O

2        :    10

3.44     :    x2

Step V: Use some basic mathematics to find the values of x1 and x2

x1 = 8/2 (3.44) = 13.76 moles of  CO2

x2 = 10/2 (3.44) = 17.2 moles of H2O

Step VI: Use molar masses and equation 1 to find the amounts of both products formed

Molar mass of CO2 = Atomic mass of carbon + 2 (atomic mass of oxygen)

= 12.01 + 2 (16.0) = 44.01

Mass of CO2 produced = no of moles x molar mass

= 13.76 x 44.01 = 605.6 grams

Molar mass of H2O = 2(Atomic mass of hydrogen) + atomic mass of oxygen

= 2(1.01) + 16.0 = 18.02

Mass of H2O produced = no of moles x molar mass

= 17.2 x 18.02 = 309.9 grams

Result: The stoichiometric calculations performed for the given chemical reaction reveal that
200 grams of butane burns in an excess of oxygen to yield 605.6 grams of carbon dioxide and
309.9 grams of water.
You must have noticed that we only considered the amount of butane that reacted to produce
both the products of the reaction. Why no attention paid to the amount of oxygen used? This
question introduces us to another interesting concept related to stoichiometry.

### Limiting Reagent

In a chemical reaction involving two or more reactants, the reactant that gets consumed first is
called a limiting reagent or a limiting reactant. In other words, this reactant ‘limits’ the rate of
reaction by controlling the amount of product formed. The reactants other than the limiting
reagent are then automatically perceived to be present in excess amount.
Thus, in the example given above, butane is the limiting reagent while oxygen is present in excess.
We always use the number of moles of the limiting reagent present to calculate the no of moles
and hence the amount of product formed. Therefore, the stoichiometry of the above chemical
reaction was calculated with reference to butane only.
Limiting reagent paves way for the calculation of some other informative entities about a
chemical reaction called ‘reaction yields’’.

### Theoretical Yield

Theoretical yield of a chemical reaction is defined as the maximum amount of product expected
to form when the limiting reagent of the reaction is fully consumed. In accordance with this
definition, can we say that 605.6 grams was the theoretical yield of carbon dioxide produced
from the combustion of butane in the above example? Yes, you guessed it right.
practice further on how to calculate theoretical yield.

### Percentage Yield

Percentage yield can be calculated from theoretical yield by using the formula given in equation
2 below.

$%&space;yield&space;=&space;\frac{Actual&space;yield&space;}{Theoretical&space;yield}&space;\times&space;100%$                         Equation 2

We should keep in mind that the actual yield of a reaction is generally smaller than the theoretical
yield expected from the reaction’s stoichiometry. None of the real-world chemical reactions hold
100% efficiency. Not all the reactants are fully converted to products, some matter is lost in the
form of energy to the surroundings as the reaction proceeds.

Say for instance, If the actual yield of carbon dioxide collected from the combustion of butane is
402.6 grams, then the percentage yield of the reaction can be calculated as:

$%&space;age&space;yield&space;=\frac{402.6}{605.6}&space;\times&space;100%$

= 66.5%