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 can follow these steps:

### Step 1: Write the balanced reaction for \( KMnO_4 \) with \( C_2O_4^{2-} \)
The first reaction we need to consider is the reaction of \( KMnO_4 \) with oxalate ions \( (C_2O_4^{2-}) \) in an acidic medium. The balanced equation is:

\[ 2 KMnO_4 + 5 C_2O_4^{2-} + 16 H^+ \rightarrow 2 Mn^{2+} + 2 K^+ + 10 CO_2 + 8 H_2O \]

### Step 2: Determine the stoichiometry of \( KMnO_4 \) to \( C_2O_4^{2-} \)
From the balanced equation, we see that 2 moles of \( KMnO_4 \) are required to react with 5 moles of \( C_2O_4^{2-} \). This gives us the ratio:

\[ \frac{2 \text{ moles of } KMnO_4}{5 \text{ moles of } C_2O_4^{2-}} \]

### Step 3: Calculate the moles of \( KMnO_4 \) needed for 1 mole of \( FeC_2O_4 \)
Since \( FeC_2O_4 \) contains 1 mole of \( C_2O_4^{2-} \), we need to find out how many moles of \( KMnO_4 \) are needed for 1 mole of \( C_2O_4^{2-} \):

Using the ratio from Step 2, we can set up a proportion:

\[ \frac{2 \text{ moles of } KMnO_4}{5 \text{ moles of } C_2O_4^{2-}} = \frac{x \text{ moles of } KMnO_4}{1 \text{ mole of } C_2O_4^{2-}} \]

Cross-multiplying gives:

\[ x = \frac{2 \times 1}{5} = \frac{2}{5} \]

### Step 4: Consider the reaction with \( Fe^{2+} \)
Next, we need to consider the reaction of \( KMnO_4 \) with \( Fe^{2+} \):

\[ 5 Fe^{2+} + 8 H^+ + 2 KMnO_4 \rightarrow 5 Fe^{3+} + 2 Mn^{2+} + 4 H_2O + 2 K^+ \]

From this equation, we see that 2 moles of \( KMnO_4 \) react with 5 moles of \( Fe^{2+} \).

### Step 5: Calculate the total moles of \( KMnO_4 \) needed
Now, we need to combine the moles of \( KMnO_4 \) required for both reactions.

1. For 1 mole of \( FeC_2O_4 \), we need \( \frac{2}{5} \) moles of \( KMnO_4 \) for the oxalate.
2. For 1 mole of \( Fe^{2+} \) (which comes from 1 mole of \( FeC_2O_4 \)), we need \( \frac{2}{5} \) moles of \( KMnO_4 \) for the iron.

Thus, the total moles of \( KMnO_4 \) required is:

\[ \text{Total } KMnO_4 = \frac{2}{5} + \frac{2}{5} = \frac{4}{5} \]

### Conclusion
Therefore, the total moles of \( KMnO_4 \) needed to react completely with one mole of ferrous oxalate \( (FeC_2O_4) \) in acidic solution is \( \frac{4}{5} \).

### Final Answer
\[ \text{The answer is } \frac{4}{5} \text{ moles of } KMnO_4. \]

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