 # Balancing Chemical Equations

## Introduction

A chemical equation represents the chemical formulas of substances that react and the substances that produce. The number of atoms of the reactants and products supposed to be balanced. Let us discuss balancing chemical equations.

Balancing the chemical equations involves the addition of stoichiometric coefficients to products and reactants. This is necessary because any chemical equation must obey the law of constant proportions and the law of conservation of mass, i.e., the same number of atoms of each element must exist on the product side and reactant side of the equation.

Let us discuss two easy and faster methods of balancing a chemical equation now. The first one is the traditional balancing equations method and the second method is the algebraic balancing method.

### Things to discuss

A few of the things that should be addressed before explaining the two methods are the chemical equation.

### Chemical Equation

• Every chemical equation is a symbolic representation of a chemical reaction where their respective chemical formulae denote the products and reactants.

• Consider an example of a chemical equation, 2H2 + O2 → 2H2O describing the reaction between hydrogen and oxygen to form water

• The reactant side is the chemical equation part to the left of the ‘→’ symbol, and the product side is the part to the right of the ‘→’ symbol.

The first step that needs to be followed while balancing chemical equations is to obtain the complete unbalanced chemical equation. To demonstrate this method, as an example, the combustion reaction between oxygen and propane is taken.

### Step 1

• The unbalanced chemical equation needs to be obtained from the chemical formulae of the reactants and the products if it is not already provided.

• The chemical formula of propane is C3H8. It burns with oxygen (O2) to produce carbon dioxide (CO2) and water (H2O).

• Thus, the unbalanced chemical equation can be represented as C3H8 + O2 → CO2 + H2O.

### Step 2

The total number of atoms contained in each element on the product and reactant side must be compared. For this, as an example, the number of atoms on each side are tabulated below.

## Chemical Equation is - C3H8 + O2 → CO2 + H2O

 Reactant Side Product Side 3 Carbon atoms from C3H8 1 Carbon atom from CO2 8 Hydrogen atoms from C3H8 2 Hydrogen atoms from H2O 2 Oxygen atoms from O2 3 Oxygen atoms, 2 from CO2 and 1 from H2O

Step 3

• Now, the stoichiometric coefficients are added to molecules containing an element that has a different number of atoms in the reactant and the product side.

• Here, the coefficient must balance the number of atoms on each side.

• In general, the stoichiometric coefficients are assigned last to hydrogen and oxygen atoms.

• Now, the number of atoms of the elements on both the reactant and product side must be updated.

• It is necessary to remember that the number of atoms of an element in one species must be determined by multiplying the stoichiometric coefficient with the total number of atoms of that element present in 1 molecule of the species.

• For suppose, when coefficient ‘3’ is assigned to the CO2 molecule, the total number of oxygen atoms in CO2 becomes 6. The coefficient is first assigned to carbon in this example, as listed below.

## Chemical Equation is - C3H8 + O2 → 3CO2 + H2O

 Reactant Side Product Side 3 Carbon atoms from C3H8 3 Carbon atoms from CO2 8 Hydrogen atoms from C3H8 2 Hydrogen atoms from H2O 2 Oxygen atoms from O2 7 Oxygen atoms, 6 from CO2 and 1 from H2O

### Step 4

Step 3 is repeated until the total number of atoms of the reacting elements becomes equal on both the reactant and product side. Hydrogen is balanced next in this example. The chemical equation is transformed as below.

## Chemical Equation is - C3H8 + O2 → 3CO2 + 4H2O

 Reactant Side Product Side 3 Carbon atoms from C3H8 3 Carbon atoms from CO2 8 Hydrogen atoms from C3H8 8 Hydrogen atoms from H2O 2 Oxygen atoms from O2 10 Oxygen atoms, 6 from CO2 and 4 from H2O

As the hydrogen atoms are balanced now, the next balanced element to be is oxygen. There are 10 oxygen atoms on the product side, saying that the reactant side also must contain 10 oxygen atoms.

Each of the O2 molecules contains 2 oxygen atoms. And therefore, the stoichiometric coefficient that must be assigned to the O2 molecule is 5. The updated chemical equation is listed on the below table.

## Chemical Equation is - C3H8 + 5O2 → 3CO2 + 4H2O

 Reactant Side Product Side 3 Carbon atoms from C3H8 3 Carbon atoms from CO2 8 Hydrogen atoms from C3H8 8 Hydrogen atoms from H2O 10 Oxygen atoms from O2 10 Oxygen atoms, 6 from CO2 and 4 from H2O

Step 5

• Once all the individual elements have balanced, the total number of atoms of each element on the product and reactant side are once again compared.

• If there are no inequalities found, the chemical equation is said to be balanced.

• In this example, now every element has an equal number of atoms in both reactant and product sides.

• Therefore, the balanced chemical equation becomes C3H8 + 5O2 → 3CO2 + 4H2O.

1. The Algebraic Balancing Equations Method

This balancing method of chemical equations includes assigning algebraic variables as stoichiometric coefficients to every species in the unbalanced chemical equation. And, these variables are used in mathematical equations and solved to obtain the values of each stoichiometric coefficient. In order to explain this method better, as an example, the balancing reactions between oxygen and glucose, which yields the carbon dioxide and water, have been considered.

### Step 1

• The unbalanced equation must be achieved by writing the reactants and products’ chemical formulae.

• The reactants are glucose (C6H12O6), oxygen (O2), and the products are carbon dioxide (CO2), and water (H2O) in this example.

• An unbalanced chemical equation is C6H12O6 + O2 → CO2 + H2O

### Step 2

Now, the algebraic variables are assigned to each species, as stoichiometric coefficients in the unbalanced chemical equation. In this example, the equation can be written as below.

aC6H12O6 + bO2 → cCO2 + dH2O

Now, a set of equations must be formulated between the reactant side and the product side in order to balance a chemical equation of each element in the balancing reactions. The following equations can be formed in this example.

### Equation for Carbon

• On the reactant side, ‘a’ molecules of C6H12O6 will contain ‘6a’ carbon atoms.

• On the product side, ‘c’ molecules of CO2 will contain ‘c’ carbon atoms.

• In this equation, only the species containing carbon are C6H12O6 and CO2.

Therefore, the equation can be formulated for carbon is - 6a = c

### Equation for Hydrogen

• Species containing hydrogen in this equation are C6H12O6 and H2

• 'a' molecules of C6H12O6 contain '12a' hydrogen atoms, whereas 'd' H2O molecules contain '2d' hydrogen atoms.

• Thus, the equation for hydrogen results as 12a=2d.

Now, simplifying this equation, dividing both sides by 2, the equation transforms, 6a = d.

### Equation for Oxygen

There is Oxygen on every species in this chemical equation. Therefore, the below relations can be formed to obtain the Oxygen equation.

• 'a' molecules of C6H12O6, there exist '6a' oxygen atoms.

• For 'b' molecules of O2 contain a total of '2b' oxygens.

• For 'c' molecules of CO2 contain '2c' number of oxygen atoms.

• Finally, for 'd' molecules of H2O hold oxygen atoms of 'd'.

Thus, the equation for oxygen can be given as, 6a + 2b = 2c+ d

### Step 3

The equations for each element are together listed to form an equation system. For this example, the system of equations is written below.

For carbon, 6a = c, for hydrogen, 6a = d, and for oxygen, 6a + 2b = 2c + d.

This equation system can have multiple solutions, but the solution with minimal values of the variables is required. Obtaining this solution, a value is assigned to one of the coefficients. In this case, the value of 'a' is assumed to be 1. Thereby, the system of equations is converted, as explained below.

a = 1,

c = 6a = 6*1 = 6,

d = 6a = 6

Substituting a, c, and d values in the equation 6a + 2b = 2c + d, we get the value of 'b,' and the same can be obtained as below.

6*1 + 2b = 2*6 + 6

2b = 12; b = 6

It is necessary to note that these equations must be solved in a way that each variable is a positive integer. If the fractional values are obtained, the lowest common denominator between all the variables must be multiplied with each and every variable. This is important because the variables hold the values of the stoichiometric coefficients, which must be a positive integer.

### Step 4

• Now when the smallest value of each variable is obtained, their values can be substituted into the chemical equation obtained in step 2.

• Thus, the equation aC6H12O6 + bO2 → cCO2 + dH2O becomes as C6H12O6 + 6O2 → 6CO2 + 6H2O

• The balanced chemical equation is obtained, therefore.

Balancing chemical equations using algebraic balancing equations method is considered to be more effective than the traditional method. However, it may yield fractional values for the stoichiometric coefficients, which must be converted into integers then.

1. Explain the balanced chemical equation for the reaction between ferric chloride and sodium hydroxide?

The chemical formula of ferric chloride is FeCl3, and that of sodium hydroxide is NaOH. The unbalanced chemical equation is written as,

FeCl3 + NaOH → Fe(OH)3 + NaCl

Balancing the number of oxygen atoms and hydrogen atoms first and then balancing the number of sodium atoms, the balanced chemical equation is formed to be,

FeCl3 + 3NaOH → Fe(OH)3 + 3NaCl

2. Why should chemical equations be balanced?

Before knowing why the chemical equations should be balanced and balancing chemical equations practice, let us look at the example to know what law of conservation of mass is.

Suppose we are making biscuits. Let the mass of the batter be 250 g. After we bake the biscuits, the mass of all the biscuits + evaporated water will be equal to 250g.

mass of reactants = sum of the mass of products (s).

This is called the law of conservation of mass. In large factories producing chemicals, the amount of the reactants needed should be accurately known to produce profitably. That's why chemical equations are to be balanced.