The number of mole of potassium salt i.e. `KHC_(2)O_(4)H_(2)C_(2)O_(4).2H_(2)O` oxidized by 4 mole of potassium permanganate ion is :

Explanation

To solve the problem of how many moles of potassium salt (KHC₂O₄H₂C₂O₄·2H₂O) are oxidized by 4 moles of potassium permanganate (KMnO₄), we can follow these steps:

### Step 1: Identify the oxidation states
The potassium salt contains oxalate ions (C₂O₄²⁻). In the oxalate ion, the oxidation state of carbon can be determined. The overall charge of the oxalate ion is -2.

**Hint:** Remember that the oxidation state of oxygen is typically -2. Use the formula for the charge balance to find the oxidation state of carbon.

### Step 2: Calculate the change in oxidation state
In the oxalate ion (C₂O₄²⁻), the oxidation state of carbon is +3. When it is oxidized to carbon dioxide (CO₂), the oxidation state of carbon becomes +4.

The change in oxidation state for one carbon atom is:
- From +3 to +4 = +1

Since there are 2 carbon atoms in the oxalate ion, the total change in oxidation state for one C₂O₄²⁻ ion is:
- Total change = 2 × (+1) = +2

**Hint:** Consider how many carbon atoms are in the oxalate ion and how their oxidation states change during the reaction.

### Step 3: Determine the equivalent factor for KMnO₄
Potassium permanganate (KMnO₄) is reduced from +7 (in MnO₄⁻) to +2 (in Mn²⁺). The change in oxidation state for manganese is:
- From +7 to +2 = -5

**Hint:** Identify the change in oxidation state for the species being reduced (Mn in KMnO₄).

### Step 4: Calculate the number of equivalents
The number of equivalents for the potassium salt (KHC₂O₄H₂C₂O₄·2H₂O) can be calculated using the formula:
- \( n = \text{Total change in oxidation state} / \text{Change per mole} \)

For the potassium salt:
- Change per mole = 2 (from step 2)

For KMnO₄:
- Change per mole = 5 (from step 3)

### Step 5: Use the equivalence relation
Using the equivalence relation:
- \( N_1V_1 = N_2V_2 \)
Where:
- \( N_1 \) = number of equivalents of KMnO₄
- \( V_1 \) = volume of KMnO₄ (in moles)
- \( N_2 \) = number of equivalents of potassium salt
- \( V_2 \) = volume of potassium salt (in moles)

Given that we have 4 moles of KMnO₄:
- \( N_1 = 4 \) moles (since each mole of KMnO₄ corresponds to 5 equivalents)

Thus, we can set up the equation:
- \( 4 \text{ moles} \times 5 = N_2 \times V_2 \)

### Step 6: Solve for the number of moles of potassium salt
Since \( N_2 \) for the potassium salt is 2 (from step 4):
- \( 4 \times 5 = N_2 \times 2 \)
- \( 20 = N_2 \times 2 \)
- \( N_2 = 10 \)

Thus, the number of moles of potassium salt oxidized by 4 moles of potassium permanganate is **10 moles**.

### Final Answer:
The number of moles of potassium salt oxidized by 4 moles of potassium permanganate is **10 moles**.

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