`KMnO_(4)` reacts with ferrous ammonium sulphate according to the equation `MnO_(4)^(-)+5Fe^(2+)+8H^(+) rarr Mn^(2+)+5Fe^(3+)+4H_(2)O`, here `10 ml` of `0.1 M KMnO_(4)` is equivalent to

Options

A. (a)`20 `ml of `0.1 M FeSO_(4)`
B. (b)`30` ml of`0.1 M FeSO_(4)`
C. (c )`40` ml of `0.1 M FeSO_(4)`
D. (d)`50` ml of `0.1 M FeSO_(4)`

Explanation

To solve the problem, we need to determine how many moles of ferrous ammonium sulfate (FeSO4) are equivalent to 10 mL of 0.1 M KMnO4 based on the given reaction.

### Step-by-Step Solution:

1. **Identify the Reaction**:
The balanced chemical equation is:
\[ \text{MnO}_4^{-} + 5 \text{Fe}^{2+} + 8 \text{H}^{+} \rightarrow \text{Mn}^{2+} + 5 \text{Fe}^{3+} + 4 \text{H}_2\text{O} \]
From this equation, we see that 1 mole of KMnO4 reacts with 5 moles of FeSO4.

2. **Calculate Moles of KMnO4**:
We are given the molarity and volume of KMnO4:
- Molarity (M) = 0.1 M
- Volume (V) = 10 mL = 10 × 10^(-3) L

Using the formula for moles:
\[ \text{Moles of KMnO}_4 = \text{Molarity} \times \text{Volume} = 0.1 \, \text{mol/L} \times 10 \times 10^{-3} \, \text{L} = 0.001 \, \text{mol} \]

3. **Determine Moles of FeSO4**:
According to the reaction, 1 mole of KMnO4 reacts with 5 moles of FeSO4. Therefore, the moles of FeSO4 required can be calculated as:
\[ \text{Moles of FeSO}_4 = 5 \times \text{Moles of KMnO}_4 = 5 \times 0.001 \, \text{mol} = 0.005 \, \text{mol} \]

4. **Convert Moles of FeSO4 to Volume**:
We need to find the volume of 0.1 M FeSO4 that corresponds to 0.005 moles. Using the formula for molarity:
\[ \text{Volume} = \frac{\text{Moles}}{\text{Molarity}} = \frac{0.005 \, \text{mol}}{0.1 \, \text{mol/L}} = 0.05 \, \text{L} = 50 \, \text{mL} \]

### Conclusion:
10 mL of 0.1 M KMnO4 is equivalent to 50 mL of 0.1 M FeSO4.