How many moles of `KMnO_(4)` are needed to oxidise a mixture of 1 mole of each `FeSO_(4) & FeC_(2)O_(4)` in acidic medium `:`

Options

A. `(4)/(5)`
B. `(5)/(4)`
C. `(3)/(4)`
D. `(5)/(3)`

Explanation

To solve the problem of how many moles of `KMnO4` are needed to oxidize a mixture of 1 mole of `FeSO4` and 1 mole of `FeC2O4` in acidic medium, we can follow these steps:

### Step 1: Identify the oxidation states and changes
- In `KMnO4`, manganese (Mn) is in the +7 oxidation state and gets reduced to +2 in acidic medium.
- The change in oxidation state for Mn is:
\[ +7 \text{ (Mn in KMnO4)} \rightarrow +2 \text{ (Mn}^{2+}\text{)} \]
This is a change of 5 units.

### Step 2: Analyze the oxidation of `FeC2O4`
- In `FeC2O4`, iron (Fe) is in the +2 oxidation state and gets oxidized to +3:
\[ +2 \text{ (Fe}^{2+}\text{)} \rightarrow +3 \text{ (Fe}^{3+}\text{)} \]
This is a change of 1 unit for Fe.
- The oxalate ion (`C2O4^{2-}`) is oxidized to carbon dioxide (`CO2`), which involves the loss of 2 electrons:
\[ C2O4^{2-} \rightarrow 2 \text{ CO2} + 2e^{-} \]
Therefore, the total change in oxidation state for `FeC2O4` is:
\[ 1 \text{ (for Fe)} + 2 \text{ (for C2O4)} = 3 \text{ units} \]

### Step 3: Analyze the oxidation of `FeSO4`
- In `FeSO4`, iron (Fe) is also in the +2 oxidation state and gets oxidized to +3:
\[ +2 \text{ (Fe}^{2+}\text{)} \rightarrow +3 \text{ (Fe}^{3+}\text{)} \]
This is a change of 1 unit.

### Step 4: Calculate the total equivalents of reducing agents
- The total change in oxidation states for the mixture is:
- For `FeC2O4`: 3 units
- For `FeSO4`: 1 unit
- Therefore, the total change in oxidation states for the mixture is:
\[ 3 + 1 = 4 \text{ units} \]

### Step 5: Set up the equation for moles of `KMnO4`
- Let \( x \) be the moles of `KMnO4` required. The total equivalents of `KMnO4` must equal the total equivalents of the reducing agents:
\[ 5x = 4 \text{ (total change in oxidation states)} \]
- Solving for \( x \):
\[ x = \frac{4}{5} \]

### Conclusion
Thus, the number of moles of `KMnO4` needed to oxidize the mixture of 1 mole of `FeSO4` and 1 mole of `FeC2O4` in acidic medium is:
\[ \boxed{\frac{4}{5}} \]