Question

Balance the following equations:
(i) \(\text{Ca(OH)}_2 (aq) + \text{CO}_2 (g) \rightarrow \text{CaCO}_3 (s) + \text{H}_2\text{O} (l)\)
(ii) \(\text{CH}_4 (g) + \text{O}_2 (g) \rightarrow \text{CO}_2 (g) + \text{H}_2\text{O} (l)\)

Hint:

To balance chemical equations, start by balancing atoms that appear only once on both sides, followed by the atoms that appear in multiple compounds.

Answer 1

(i) Calcium Hydroxide reacts with Carbon Dioxide:
The unbalanced equation is: \[ \text{Ca(OH)}_2 (aq) + \text{CO}_2 (g) \rightarrow \text{CaCO}_3 (s) + \text{H}_2\text{O} (l) \] Now, balance the equation:
1. Balance the calcium atoms: We have one Ca on both sides, so it's balanced.
2. Balance the carbon atoms: There is one C on both sides.
3. Balance the oxygen atoms: On the left side, there are 2 O atoms in Ca(OH)₂ and 2 O atoms in CO₂, so we have a total of 4 oxygen atoms on the left. On the right side, CaCO₃ has 3 O atoms and H₂O has 1 O atom, totaling 4 oxygen atoms.
4. Balance the hydrogen atoms: On the left, Ca(OH)₂ has 2 H atoms, and on the right, H₂O has 2 H atoms, so it's balanced.
The balanced equation is: \[ \text{Ca(OH)}_2 (aq) + \text{CO}_2 (g) \rightarrow \text{CaCO}_3 (s) + \text{H}_2\text{O} (l) \] This equation is already balanced.

(ii) Combustion of Methane:
The unbalanced equation is: \[ \text{CH}_4 (g) + \text{O}_2 (g) \rightarrow \text{CO}_2 (g) + \text{H}_2\text{O} (l) \] Now, balance the equation:
1. Balance the carbon atoms: There is 1 C on both sides.
2. Balance the hydrogen atoms: On the left side, CH₄ has 4 H atoms. On the right side, H₂O has 2 H atoms, so we need 2 molecules of H₂O to balance the hydrogen atoms.
3. Balance the oxygen atoms: On the left, O₂ provides 2 O atoms. On the right, 1 molecule of CO₂ provides 2 O atoms, and 2 molecules of H₂O provide 2 O atoms, for a total of 4 O atoms on the right. Therefore, we need 2 O₂ molecules on the left.
The balanced equation is: \[ \text{CH}_4 (g) + 2\text{O}_2 (g) \rightarrow \text{CO}_2 (g) + 2\text{H}_2\text{O} (l) \]
Conclusion:
The balanced equations are: 1. \(\text{Ca(OH)}_2 (aq) + \text{CO}_2 (g) \rightarrow \text{CaCO}_3 (s) + \text{H}_2\text{O} (l)\)
2. \(\text{CH}_4 (g) + 2\text{O}_2 (g) \rightarrow \text{CO}_2 (g) + 2\text{H}_2\text{O} (l)\)