Before we can balance a chemical equation, we have to recall and understand the law of conservation of mass.

According to the law of conservation of mass, mass can neither be created nor destroy but can change from one form to another

Therefore, in a chemical equation, the mass of the reactants must be equal to the mass of the products. For this to happen, the number of atoms of each element in the reactants must be equal to the number of atoms of those same elements in the products. Some examples are shown below:

**Example 1**:

**Fe + S → FeS**

Reactants

Atomic mass of reactants = 55.8 u + 32.1 u = 87.9 u Number of atoms of each element in the reactants: (1 × Fe) and (1 × S)

Products

Atomic mass of product = 55.8 u + 32.1 u = 87.9 u

Number of atoms of each element in the products: (1 × Fe) and (1 × S)

Since the number of atoms of each element is the same in the reactants and in the products, we say that the equation is balanced.

**Example 2**:

NaOH + HCl → NaCl + H2O

Reactants

Atomic mass of reactants = (23 + 16 + 1) + (1 + 35.4) = 76.4 u Number of atoms of each element in the reactants: (1 × Na) + (1 × O) + (2 × H) + (1 × Cl)

Products

Atomic mass of products = (23 + 35.4) + (1 + 1 + 16) = 76.4 u

Number of atoms of each element in the products: (1 × Na) + (1 × O) + (2 × H) + (1 × Cl)

Since the number of atoms of each element is the same in the reactants and in the products, we say that the equation is balanced.

**Example 3:**

**H2 + O2 → H2O**

Reactants

Atomic mass of reactants = (1 + 1) + (16 + 16) = 34 u

Number of atoms of each element in the reactants: (2 × H) and (2 × O)

Product

Atomic mass of product = (1 + 1 + 16) = 18 u Number of atoms of each element in the products: (2 × H) and (1 × O)

Since the total atomic mass of the reactants and the products is not the same, and since there are more oxygen atoms in the reactants than there are in the product, the equation is not balanced.

We now need to ﬁnd a way to balance those equations that are not balanced so that the number of atoms of each element in the reactants is the same as that for the products.

This can be done by changing the coeﬃcients of the molecules until the atoms on each side of the arrow are balanced. You will see later in chapter 13 that these coeﬃcients tell us something about the mole ratio in which

**Steps to balance a chemical equation**

When balancing a chemical equation, there are a number of steps that need to be followed.

**STEP 1:** Identify the reactants and the products in the reaction, and write their chemical formulae.

**STEP 2:** Write the equation by putting the reactants on the left of the arrow, and the products on the right.

**STEP 3:** Count the number of atoms of each element in the reactants and the number of atoms of each element in the products.

**STEP 4:** If the equation is not balanced, change the coeﬃcients of the molecules until the number of atoms of each element on either side of the equation balance.

**STEP 5:** Check that the atoms are in fact balanced.

**STEP 6:** (we will look at this a little later): Add any extra details to the equation e.g. phase. substances react.

**Note** that if you put a number in front of a molecule, that number applies to the whole molecule. For example, if you write 2H2O, this means that there are 2 molecules of water. In other words, there are 4 hydrogen atoms and 2 oxygen atoms.

If we write 3HCl, this means that there are 3 molecules of HCl. In other words there are 3 hydrogen atoms and 3 chlorine atoms in total. In the ﬁrst example, 2 is the coeﬃcient and in the second example, 3 is the coeﬃcient.

**Work Exmaples**

Balance the following equation

Mg + HCl → MgCl2 + H2

** Step 1** : Since the equation has been written, you can move straight on to counting the number of atoms of each element in the reactants and products Reactants: Mg = 1 atom; H = 1 atom and Cl = 1 atom Products: Mg = 1 atom; H = 2 atoms and Cl = 2 atoms

**Step 2** : Balance the equation The equation is not balanced since there are 2 chlorine atoms in the product and only 1 in the reactants. If we add a coeﬃcient of 2 to the HCl to increase the number of H and Cl atoms in the reactants, the equation will look like this: Mg + 2HCl → MgCl2 + H2

**Step 3** : Check that the atoms are balanced If we count the atoms on each side of the equation, we ﬁnd the following: Reactants: Mg = 1; H = 2; Cl = 2 Products: Mg = 1; H = 2; Cl = 2 The equation is balanced. The ﬁnal equation is: Mg + 2HCl → MgCl2 + H2

Balance the following equation

CH4 + O2 → CO2 + H2O

**Step 1** : Count the number of atoms of each element in the reactants and products Reactants: C = 1; H = 4; O = 2 Products: C = 1; H = 2; O = 3

**Step 2** : Balance the equation If we add a coeﬃcient of 2 to H2O, then the number of hydrogen atoms in the reactants will be 4, which is the same as for the reactants. The equation will be: CH4 + O2 → CO2 + 2H2O

**Step 3** : Check that the atoms balance Reactants: C = 1; H = 4; O = 2 Products: C = 1; H = 4; O = 4 You will see that, although the number of hydrogen atoms now balances, there are more oxygen atoms in the products.

You now need to repeat the previous step. If we put a coeﬃcient of 2 in front of O2, then we will increase the number of oxygen atoms in the reactants by 2.

The new equation is: CH4 + 2O2 → CO2 + 2H2O When we check the number of atoms again, we ﬁnd that the number of atoms of each element in the reactants is the same as the number in the products.

The equation is now balanced.

**Exercise**: Balance the following chemical equations:

Mg + P4 → Mg3P2

Ca + H2O → Ca(OH)2 + H2

CuCO3 + H2SO4 → CuSO4 + H2O + CO2

CaCl2 + Na2CO3 → CaCO3 + NaCl

C12H22O11 + O2 → CO2 + H2O