The formula of alum is

Options

A. `K_2SO_(4).Al_2(SO_4)_(3).24H_2O`
B. `K_4[Fe(CN)_6]`
C. `K_2SO_4.Al_2(SO_4)_(3).6H_2O`
D. `Na_2CO_(3).10H_2O`

Answer

To determine the formula of alum, we can follow these steps:

### Step 1: Understand the Composition of Alum
Alum is a type of double salt that typically consists of a combination of a monovalent cation, a trivalent cation, and sulfate ions. The general formula for alum can be expressed as:
\[ M_2SO_4 \cdot R_2(SO_4)_3 \cdot nH_2O \]
where:
- \( M \) is a monovalent cation (e.g., Na\(^+\), K\(^+\)),
- \( R \) is a trivalent cation (e.g., Al\(^{3+}\), Fe\(^{3+}\)),
- \( n \) is the number of water molecules of hydration.

### Step 2: Identify the Common Types of Alum
The most common type of alum is potash alum, which has the formula:
\[ K_2SO_4 \cdot Al_2(SO_4)_3 \cdot 24H_2O \]
This indicates that it contains potassium (K) as the monovalent cation and aluminum (Al) as the trivalent cation.

### Step 3: Analyze the Given Options
The options provided are:
1. \( K_2SO_4 \cdot Al_2(SO_4)_3 \cdot 24H_2O \)
2. \( K_4Fe(CN)_6 \)
3. \( K_2SO_4 \cdot Al_2(SO_4)_3 \cdot 6H_2O \)
4. \( Na_2CO_3 \cdot 10H_2O \)

### Step 4: Evaluate Each Option
- **Option A**: \( K_2SO_4 \cdot Al_2(SO_4)_3 \cdot 24H_2O \) - This is the correct formula for potash alum.
- **Option B**: \( K_4Fe(CN)_6 \) - This is not an alum; it is potassium ferrocyanide.
- **Option C**: \( K_2SO_4 \cdot Al_2(SO_4)_3 \cdot 6H_2O \) - This is incorrect because it has only 6 water molecules instead of 24.
- **Option D**: \( Na_2CO_3 \cdot 10H_2O \) - This is sodium carbonate and not an alum.

### Step 5: Conclusion
The correct formula for alum is:
\[ K_2SO_4 \cdot Al_2(SO_4)_3 \cdot 24H_2O \]

### Final Answer
The formula of alum is \( K_2SO_4 \cdot Al_2(SO_4)_3 \cdot 24H_2O \).

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