In the reaction,
`FeS_(2)+KMnO_(4)+H^(+) to Fe^(3+)+SO_(2)+Mn^(2+)+H_(2)O`
the equivalent mass of `FeS_(2)` would be equal to :

Options

A. M
B. `(M)/( 10) `
C. `(M)/( 11)`
D. `(M)/( 15)`

Answer

To find the equivalent mass of `FeS2` in the given reaction, we can follow these steps:

### Step 1: Determine the Molar Mass of `FeS2`
First, we need to calculate the molar mass of `FeS2` (Iron(II) sulfide). The molar mass can be calculated using the atomic masses:
- Iron (Fe) = 55.85 g/mol
- Sulfur (S) = 32.07 g/mol

The formula for `FeS2` indicates that there is one iron atom and two sulfur atoms:
\[ \text{Molar mass of } FeS2 = 55.85 + (2 \times 32.07) = 55.85 + 64.14 = 119.99 \text{ g/mol} \]

### Step 2: Determine the Change in Oxidation Number
Next, we need to analyze the change in oxidation states of the elements involved in the reaction:
- In `FeS2`, the oxidation state of Fe is +2 and that of S is -1.
- In the products, `Fe` is oxidized to `Fe^(3+)`, and sulfur is reduced to `SO2`, where sulfur has an oxidation state of +4.

The changes in oxidation states are:
- Iron (Fe): from +2 to +3 (a change of +1)
- Sulfur (S): from -1 to +4 (a change of +5)

Since there are two sulfur atoms in `FeS2`, the total change in oxidation number for sulfur is:
\[ \text{Total change for S} = 2 \times 5 = 10 \]

### Step 3: Calculate the Total Change in Oxidation Number
Now, we combine the changes in oxidation states:
- Total change in oxidation number = Change for Fe + Change for S = 1 (for Fe) + 10 (for S) = 11

### Step 4: Calculate the Equivalent Mass
The equivalent mass is calculated using the formula:
\[ \text{Equivalent mass} = \frac{\text{Molar mass}}{\text{Change in oxidation number}} \]
Substituting the values we found:
\[ \text{Equivalent mass of } FeS2 = \frac{119.99 \text{ g/mol}}{11} \approx 10.91 \text{ g/equiv} \]

### Conclusion
Thus, the equivalent mass of `FeS2` is approximately 10.91 g/equiv.

### Final Answer
The equivalent mass of `FeS2` would be equal to \( \frac{M}{11} \).

---