The equivalent weight of potash alum
`(K_(2)SO_(4).Al_(2)(SO_(4))_(3).24H_(2)O)` is

Options

A. `M`
B. `(M)/(2)`
C. `(M)/(6)`
D. `(M)/(8)`

Explanation

To calculate the equivalent weight of potash alum (K₂SO₄·Al₂(SO₄)₃·24H₂O), we can follow these steps:

### Step 1: Determine the Molecular Weight of Potash Alum
The molecular formula of potash alum is K₂SO₄·Al₂(SO₄)₃·24H₂O. We need to calculate the molecular weight by adding the atomic weights of all the atoms in the formula.

1. **Potassium (K)**: 2 × 39.1 g/mol = 78.2 g/mol
2. **Sulfur (S)**: 3 × 32.1 g/mol = 96.3 g/mol (from 2 in K₂SO₄ and 3 in Al₂(SO₄)₃)
3. **Oxygen (O)**: 12 × 16.0 g/mol = 192.0 g/mol (4 from K₂SO₄ and 12 from Al₂(SO₄)₃)
4. **Aluminum (Al)**: 2 × 27.0 g/mol = 54.0 g/mol
5. **Water (H₂O)**: 24 × (2 × 1.0 + 16.0) g/mol = 24 × 18.0 g/mol = 432.0 g/mol

Now, we can sum these values:
- Total Molecular Weight = 78.2 + 96.3 + 192.0 + 54.0 + 432.0 = 852.5 g/mol

### Step 2: Determine the n-factor
The n-factor is the number of moles of reactive species produced or consumed in a reaction. For potash alum, we need to consider the total positive charge contributed by the cations.

1. **Cations**:
- Potassium contributes: 2 × K⁺ = 2
- Aluminum contributes: 2 × Al³⁺ = 6 (since each Al contributes +3)

Total positive charge = 2 (from K) + 6 (from Al) = 8

Thus, the n-factor for potash alum is 8.

### Step 3: Calculate the Equivalent Weight
The equivalent weight can be calculated using the formula:

\[ \text{Equivalent Weight} = \frac{\text{Molecular Weight}}{n \text{-factor}} \]

Substituting the values we have:

\[ \text{Equivalent Weight} = \frac{852.5 \, \text{g/mol}}{8} = 106.56 \, \text{g/equiv} \]

### Final Answer
The equivalent weight of potash alum is approximately **106.56 g/equiv**.

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