Calculate the equivalent masses of the following substances:
(i) `CaCO_(3)`
(ii) `HNO_(3)`
(iii) `Ca(OH)_(2)`
(iv) Br

Answer

To calculate the equivalent masses of the given substances, we will use the formula for equivalent mass:

\[ \text{Equivalent mass} = \frac{\text{Molar mass}}{n \text{ factor}} \]

Where the n factor depends on the type of substance (acid, base, salt, etc.) and its ability to donate or accept protons or electrons.

### Step-by-Step Solution:

#### (i) For `CaCO₃` (Calcium Carbonate):

1. **Calculate the Molar Mass**:
- Calcium (Ca) = 40 g/mol
- Carbon (C) = 12 g/mol
- Oxygen (O) = 16 g/mol × 3 = 48 g/mol
- Total Molar Mass of `CaCO₃` = 40 + 12 + 48 = 100 g/mol

2. **Determine the n Factor**:
- `CaCO₃` dissociates into `Ca²⁺` and `CO₃²⁻`.
- Each ion has a charge of 2, so the n factor = 2.

3. **Calculate Equivalent Mass**:
\[ \text{Equivalent mass of } CaCO₃ = \frac{100 \text{ g/mol}}{2} = 50 \text{ g/equiv} \]

#### (ii) For `HNO₃` (Nitric Acid):

1. **Calculate the Molar Mass**:
- Hydrogen (H) = 1 g/mol
- Nitrogen (N) = 14 g/mol
- Oxygen (O) = 16 g/mol × 3 = 48 g/mol
- Total Molar Mass of `HNO₃` = 1 + 14 + 48 = 63 g/mol

2. **Determine the n Factor**:
- `HNO₃` has 1 ionizable H⁺, so the n factor = 1.

3. **Calculate Equivalent Mass**:
\[ \text{Equivalent mass of } HNO₃ = \frac{63 \text{ g/mol}}{1} = 63 \text{ g/equiv} \]

#### (iii) For `Ca(OH)₂` (Calcium Hydroxide):

1. **Calculate the Molar Mass**:
- Calcium (Ca) = 40 g/mol
- Oxygen (O) = 16 g/mol × 2 = 32 g/mol
- Hydrogen (H) = 1 g/mol × 2 = 2 g/mol
- Total Molar Mass of `Ca(OH)₂` = 40 + 32 + 2 = 74 g/mol

2. **Determine the n Factor**:
- `Ca(OH)₂` has 2 hydroxide (OH⁻) ions, so the n factor = 2.

3. **Calculate Equivalent Mass**:
\[ \text{Equivalent mass of } Ca(OH)₂ = \frac{74 \text{ g/mol}}{2} = 37 \text{ g/equiv} \]

#### (iv) For `Br` (Bromine):

1. **Determine the Molar Mass**:
- Atomic mass of Bromine (Br) = 80 g/mol

2. **Determine the n Factor**:
- Bromine typically forms univalent ions (Br⁻), so the n factor = 1.

3. **Calculate Equivalent Mass**:
\[ \text{Equivalent mass of } Br = \frac{80 \text{ g/mol}}{1} = 80 \text{ g/equiv} \]

### Final Results:
- Equivalent mass of `CaCO₃` = 50 g/equiv
- Equivalent mass of `HNO₃` = 63 g/equiv
- Equivalent mass of `Ca(OH)₂` = 37 g/equiv
- Equivalent mass of `Br` = 80 g/equiv