(a) Substitute formulae for names and balance the following equation:
Calcium carbonate reacts with hydrochloric acid to produce calcium chloride, water and carbon dioxide gas.
(b) Write balanced chemical equation with state symbols for the following reaction :
Sodium hydroxide solution reacts with hydrochloric acid to produce sodium chloride solution and water.

Answer

### Step-by-Step Solution

#### Part (a): Balancing the Reaction of Calcium Carbonate with Hydrochloric Acid

1. **Identify the Reactants and Products**:
- Reactants: Calcium carbonate (CaCO₃) and Hydrochloric acid (HCl)
- Products: Calcium chloride (CaCl₂), Water (H₂O), and Carbon dioxide (CO₂)

2. **Write the Unbalanced Chemical Equation**:
\[ \text{CaCO}_3 + \text{HCl} \rightarrow \text{CaCl}_2 + \text{H}_2\text{O} + \text{CO}_2 \]

3. **Substitute the Chemical Formulae**:
- Calcium carbonate: CaCO₃
- Hydrochloric acid: HCl
- Calcium chloride: CaCl₂
- Water: H₂O
- Carbon dioxide: CO₂

4. **Write the Unbalanced Equation with Formulae**:
\[ \text{CaCO}_3 + \text{HCl} \rightarrow \text{CaCl}_2 + \text{H}_2\text{O} + \text{CO}_2 \]

5. **Balance the Equation**:
- Count the number of each type of atom on both sides:
- Reactants: 1 Ca, 1 C, 3 O, 1 H, 1 Cl
- Products: 1 Ca, 1 C, 3 O, 2 H, 2 Cl

- To balance chlorine and hydrogen, we need 2 HCl:
\[ \text{CaCO}_3 + 2 \text{HCl} \rightarrow \text{CaCl}_2 + \text{H}_2\text{O} + \text{CO}_2 \]

6. **Final Balanced Equation**:
\[ \text{CaCO}_3 + 2 \text{HCl} \rightarrow \text{CaCl}_2 + \text{H}_2\text{O} + \text{CO}_2 \]

#### Part (b): Balancing the Reaction of Sodium Hydroxide with Hydrochloric Acid

1. **Identify the Reactants and Products**:
- Reactants: Sodium hydroxide (NaOH) and Hydrochloric acid (HCl)
- Products: Sodium chloride (NaCl) and Water (H₂O)

2. **Write the Unbalanced Chemical Equation**:
\[ \text{NaOH} + \text{HCl} \rightarrow \text{NaCl} + \text{H}_2\text{O} \]

3. **Substitute the Chemical Formulae**:
- Sodium hydroxide: NaOH
- Hydrochloric acid: HCl
- Sodium chloride: NaCl
- Water: H₂O

4. **Write the Unbalanced Equation with Formulae**:
\[ \text{NaOH} + \text{HCl} \rightarrow \text{NaCl} + \text{H}_2\text{O} \]

5. **Balance the Equation**:
- Count the number of each type of atom on both sides:
- Reactants: 1 Na, 1 O, 1 H, 1 Cl
- Products: 1 Na, 1 Cl, 2 H, 1 O

- The equation is already balanced as there is 1 Na, 1 Cl, 1 O, and 1 H on both sides.

6. **Final Balanced Equation with State Symbols**:
\[ \text{NaOH (aq)} + \text{HCl (aq)} \rightarrow \text{NaCl (aq)} + \text{H}_2\text{O (l)} \]