Total numberof species present in 1 mole of potash alum in terms of avagadro number, 'N' are

Options

A. 3 N
B. 5 N
C. 8 N
D. 32 N

Explanation

To find the total number of species present in 1 mole of potash alum in terms of Avogadro's number (N), we can follow these steps:

### Step 1: Identify the formula of potash alum
The chemical formula of potash alum is given as:
\[ K_2SO_4 \cdot Al_2(SO_4)_3 \cdot 24H_2O \]

### Step 2: Break down the components of potash alum
1. **Potassium ions (K⁺)**: There are 2 potassium ions from \( K_2SO_4 \).
2. **Aluminum ions (Al³⁺)**: There are 2 aluminum ions from \( Al_2(SO_4)_3 \).
3. **Sulfate ions (SO₄²⁻)**:
- 1 sulfate ion from \( K_2SO_4 \)
- 3 sulfate ions from \( Al_2(SO_4)_3 \)
- Total sulfate ions = 1 + 3 = 4 sulfate ions.
4. **Water molecules (H₂O)**: There are 24 water molecules.

### Step 3: Count the total number of species
Now, we can sum all the ions and water molecules:
- Potassium ions: 2
- Aluminum ions: 2
- Sulfate ions: 4
- Water molecules: 24

Total species = 2 (K⁺) + 2 (Al³⁺) + 4 (SO₄²⁻) + 24 (H₂O) = 32 species.

### Step 4: Express the total number of species in terms of Avogadro's number
Since 1 mole of any substance contains Avogadro's number of entities (N), the total number of species in 1 mole of potash alum can be expressed as:
\[ \text{Total species} = 32 \times N \]

### Final Answer
Thus, the total number of species present in 1 mole of potash alum in terms of Avogadro's number is:
\[ 32N \]

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