Constructing and Balancing Chemical Equations for the ESAT

Chemical reactions involve the rearrangement of atoms and their electrons to form new substances. Crucially, no nuclei are destroyed or created during this process. This means that the total mass of the reactants must always equal the total mass of the products. For instance, if 4 g of hydrogen reacts with 32 g of oxygen, the atoms rearrange to produce exactly 36 g of water.

How to Construct Balanced Equations

Balanced equations use coefficients to show how many particles of each substance are involved. For example, the following equation demonstrates that two molecules of $H_{2}$ react with one molecule of $O_{2}$ to form two molecules of $H_{2}O$.

In a balanced equation, the count of atoms for each element must be identical on both sides. In the water example above, there are 4 H atoms and 2 O atoms on both the reactant and product sides.

To balance an equation correctly, follow these three steps:

1. Write the formula of each substance. For the combustion of methane, we write: $CH_{4} + O_{2} \rightarrow CO_{2} + H_{2}O$.
2. Count the atoms of each element on each side. In the initial equation, the reactants have C = 1, H = 4, O = 2. The products have C = 1, H = 2, O = 3. The hydrogen and oxygen are not balanced.
3. Add coefficients to balance the atoms. You must never change the chemical formula itself, such as changing $H_{2}O$ to $H_{2}O_{2}$, as this creates a different substance. Instead, add more of the existing substances.
   • To balance H, we add another $H_{2}O$ on the right: $CH_{4} + O_{2} \rightarrow CO_{2} + 2H_{2}O$.
   • Now count again: Reactants (C=1, H=4, O=2); Products (C=1, H=4, O=4).
   • To balance O, we add another $O_{2}$ on the left: $CH_{4} + 2O_{2} \rightarrow CO_{2} + 2H_{2}O$. The equation is now balanced.

State Symbols

State symbols provide essential information about the physical state of the reactants and products. These are typically written in parentheses after the formula:

• (s) for solid
• (l) for liquid
• (g) for gas
• (aq) for aqueous solution (dissolved in water)

Writing Ionic Equations

When ionic compounds dissolve in water, their ions separate and act independently. In many reactions, some ions do not participate in the chemical change. These are called spectator ions. An ionic equation omits spectator ions to focus only on the species that react.

Neutralisation Reactions

In the reaction between hydrochloric acid and sodium hydroxide:

• Full equation: $HCl(aq) + NaOH(aq) \rightarrow NaCl(aq) + H_{2}O(l)$
• Showing ions: $H^{+}(aq) + Cl^{-}(aq) + Na^{+}(aq) + OH^{-}(aq) \rightarrow Na^{+}(aq) + Cl^{-}(aq) + H_{2}O(l)$
• Removing spectator ions ($Na^{+}$ and $Cl^{-}$): $H^{+}(aq) + OH^{-}(aq) \rightarrow H_{2}O(l)$

Common ionic equations include:

• Acid + Carbonate: $2H^{+}(aq) + CO_{3}^{2-}(aq) \rightarrow H_{2}O(l) + CO_{2}(g)$
• Acid + Ammonia: $H^{+}(aq) + NH_{3}(aq) \rightarrow NH_{4}^{+}(aq)$

Precipitation Reactions

When two solutions react to form an insoluble solid (a precipitate), we only show the ions that form that solid. For example, forming a blue precipitate of copper(II) hydroxide:

• $Cu^{2+}(aq) + 2OH^{-}(aq) \rightarrow Cu(OH)_{2}(s)$

Constructing Half-Equations

Half-equations are used in redox reactions, displacement, and electrolysis to show the gain or loss of electrons separately.

Electrolysis

In the electrolysis of molten aluminium oxide, $Al^{3+}$ ions gain electrons at the cathode, and $O^{2-}$ ions lose electrons at the anode:

• Reduction: $Al^{3+} + 3e^{-} \rightarrow Al$
• Oxidation: $2O^{2-} \rightarrow O_{2} + 4e^{-}$ Note that for oxygen, two ions are required to form one $O_{2}$ molecule, resulting in the loss of 4 electrons in total.

Displacement

When copper displaces silver from silver nitrate, copper atoms lose electrons and silver ions gain them:

• Silver half-equation: $Ag^{+} + e^{-} \rightarrow Ag$
• Copper half-equation: $Cu \rightarrow Cu^{2+} + 2e^{-}$