How many moles of `KMnO_(4)` will be needed to react completely with one mole of ferrous oxalate `(FeC_(2)O_(4))` in acidic solution?

Options

A. `(2)/(5)`
B. `(1)/(5)`
C. `(3)/(5)`
D. `(2)/(3)`

Answer

To determine how many moles of \( KMnO_4 \) are needed to react completely with one mole of ferrous oxalate \( (FeC_2O_4) \) in acidic solution, we will follow these steps:

### Step 1: Write the balanced chemical equations
In acidic medium, the reaction between \( KMnO_4 \) and ferrous oxalate can be broken down into two half-reactions:

1. **Oxidation of Ferrous Ion**:
\[ Fe^{2+} \rightarrow Fe^{3+} + e^{-} \]

2. **Reduction of Permanganate Ion**:
\[ MnO_4^{-} + 8H^+ + 5e^{-} \rightarrow Mn^{2+} + 4H_2O \]

### Step 2: Determine the stoichiometry
From the half-reactions, we can see that:
- 1 mole of \( MnO_4^{-} \) requires 5 moles of electrons to be reduced to \( Mn^{2+} \).
- Each mole of \( Fe^{2+} \) produces 1 mole of electrons when it is oxidized to \( Fe^{3+} \).

### Step 3: Combine the half-reactions
To balance the overall reaction, we need to ensure that the number of electrons lost in oxidation equals the number of electrons gained in reduction.

To do this, we can multiply the oxidation half-reaction by 5:
\[ 5Fe^{2+} \rightarrow 5Fe^{3+} + 5e^{-} \]

Now, we can combine the two half-reactions:
\[ MnO_4^{-} + 8H^+ + 5Fe^{2+} \rightarrow Mn^{2+} + 4H_2O + 5Fe^{3+} \]

### Step 4: Analyze the balanced equation
From the balanced equation, we see that:
- 1 mole of \( KMnO_4 \) reacts with 5 moles of \( Fe^{2+} \).

### Step 5: Calculate the moles of \( KMnO_4 \) needed for 1 mole of \( FeC_2O_4 \)
Since \( FeC_2O_4 \) contains 1 mole of \( Fe^{2+} \), we can set up a ratio based on the balanced equation:
\[ 1 \text{ mole of } KMnO_4 \text{ reacts with } 5 \text{ moles of } Fe^{2+} \]

Thus, for 1 mole of \( Fe^{2+} \):
\[ \text{Moles of } KMnO_4 = \frac{1 \text{ mole of } KMnO_4}{5 \text{ moles of } Fe^{2+}} \times 1 \text{ mole of } Fe^{2+} = \frac{1}{5} \text{ moles of } KMnO_4 \]

### Final Answer
Therefore, the number of moles of \( KMnO_4 \) needed to react completely with one mole of ferrous oxalate \( (FeC_2O_4) \) in acidic solution is:
\[ \frac{3}{5} \text{ moles of } KMnO_4 \]