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 \( KHC_2O_4 \cdot H_2C_2O_4 \cdot 2H_2O \) are oxidized by 4 moles of potassium permanganate (\( KMnO_4 \)), we can follow these steps:

### Step 1: Determine the oxidation state of carbon in the potassium salt.
The formula for the potassium salt is \( KHC_2O_4 \cdot H_2C_2O_4 \cdot 2H_2O \).

For \( KHC_2O_4 \):
- Potassium (K) has an oxidation state of +1.
- Hydrogen (H) has an oxidation state of +1.
- Oxygen (O) has an oxidation state of -2.

Let the oxidation state of carbon (C) be \( x \). The equation for the oxidation states can be set up as follows:
\[ 1 + 1 + 2x - 8 = 0 \]
This simplifies to:
\[ 2x - 6 = 0 \implies 2x = 6 \implies x = 3 \]
Thus, the oxidation state of carbon in the salt is +3.

### Step 2: Determine the oxidation state of carbon in carbon dioxide (\( CO_2 \)).
In carbon dioxide, the oxidation state of carbon is +4.

### Step 3: Calculate the change in oxidation state.
The change in oxidation state for one carbon atom from +3 to +4 is:
\[ \Delta \text{oxidation state} = 4 - 3 = 1 \]
Since there are 2 carbon atoms in the salt, the total change in oxidation state for the salt is:
\[ \Delta \text{total} = 2 \times 1 = 2 \]

### Step 4: Determine the n-factor for the potassium salt.
The n-factor (valency factor) for the potassium salt is the total change in oxidation state, which is:
\[ \text{n-factor} = 2 \text{ (from carbon)} + 2 \text{ (from the other carbon)} = 4 \]

### Step 5: Determine the n-factor for potassium permanganate (\( KMnO_4 \)).
In permanganate, the oxidation state of manganese (Mn) is +7. When it is reduced to \( Mn^{2+} \), the oxidation state changes to +2. The change in oxidation state is:
\[ \Delta \text{oxidation state} = 7 - 2 = 5 \]
Thus, the n-factor for \( KMnO_4 \) is 5.

### Step 6: Set up the equivalence of the reducing agent and oxidizing agent.
The equivalents of the reducing agent (potassium salt) will equal the equivalents of the oxidizing agent (potassium permanganate):
\[ \text{Equivalents of salt} = \text{Equivalents of } KMnO_4 \]
Using the formula for equivalents:
\[ \text{Equivalents} = \text{number of moles} \times \text{n-factor} \]
Let \( n \) be the number of moles of the potassium salt:
\[ n \times 4 = 4 \times 5 \]
This simplifies to:
\[ 4n = 20 \implies n = 5 \]

### Conclusion:
The number of moles of potassium salt oxidized by 4 moles of potassium permanganate is **5 moles**.

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