The weight (in gram )of pure potash Alum (`K_(2)SO_(4).Al_(2)(SO_(4) )_(3).24H_(2)O` ) which contains 0.64kg oxygen is . (Atomic weight of K = 39 , S = 32 ,Al = 27 )

Answer

To find the weight of pure potash alum \((K_2SO_4 \cdot Al_2(SO_4)_3 \cdot 24H_2O)\) that contains 0.64 kg of oxygen, we will follow these steps:

### Step 1: Determine the moles of oxygen present in potash alum
1. **Identify the number of oxygen atoms in one formula unit of potash alum.**
- Potash alum consists of:
- \(K_2SO_4\): Contains 4 oxygen atoms
- \(Al_2(SO_4)_3\): Contains \(3 \times 4 = 12\) oxygen atoms
- \(24H_2O\): Contains \(24 \times 1 = 24\) oxygen atoms
- Total oxygen atoms = \(4 + 12 + 24 = 40\) oxygen atoms.

### Step 2: Calculate the moles of oxygen in 0.64 kg
2. **Convert 0.64 kg of oxygen to grams.**
- \(0.64 \text{ kg} = 640 \text{ g}\)
3. **Calculate the number of moles of oxygen.**
- Molar mass of oxygen = 16 g/mol
- Moles of oxygen = \(\frac{640 \text{ g}}{16 \text{ g/mol}} = 40 \text{ moles}\)

### Step 3: Relate moles of oxygen to moles of potash alum
4. **Determine the moles of potash alum corresponding to the moles of oxygen.**
- Since 1 mole of potash alum contains 40 moles of oxygen, the moles of potash alum = 1 mole.

### Step 4: Calculate the molecular weight of potash alum
5. **Calculate the molecular weight of potash alum.**
- Molar mass calculation:
- Potassium (K): \(39 \times 2 = 78\)
- Sulfur (S): \(32 \times 3 = 96\)
- Aluminum (Al): \(27 \times 2 = 54\)
- Oxygen from sulfate: \(16 \times 12 = 192\)
- Water: \(24 \times 18 = 432\)
- Total molecular weight = \(78 + 96 + 54 + 192 + 432 = 852 \text{ g/mol}\)

### Step 5: Calculate the weight of potash alum
6. **Calculate the weight of potash alum.**
- Weight of potash alum = Moles of potash alum \(\times\) Molecular weight
- Weight = \(1 \text{ mole} \times 852 \text{ g/mol} = 852 \text{ g}\)

### Final Answer
The weight of pure potash alum that contains 0.64 kg of oxygen is **852 grams**.

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