`FeS+KMnO_(4)+H_(2)SO_(4)rarr Fe_(2)(SO_(4))_(3)+K_(2)SO_(4)`. The equivalent mass `FeS` in the above reaction is :

Options

A. `("Mol wt.")/(1)`
B. `("Mol wt.")/(3)`
C. `("Mol wt.")/(3)`
D. `("Mol wt.")/(9)`

Answer

To find the equivalent mass of FeS in the reaction \( \text{FeS} + \text{KMnO}_4 + \text{H}_2\text{SO}_4 \rightarrow \text{Fe}_2(\text{SO}_4)_3 + \text{K}_2\text{SO}_4 \), we will follow these steps:

### Step 1: Determine the oxidation states of iron and sulfur in FeS
In FeS, sulfur (S) has an oxidation state of \(-2\). Let the oxidation state of iron (Fe) be \(x\):
\[ x + (-2) = 0 \implies x = +2 \]
So, the oxidation state of Fe in FeS is \(+2\) and that of S is \(-2\).

### Step 2: Determine the oxidation states in the products
In the product \( \text{Fe}_2(\text{SO}_4)_3 \):
- The sulfate ion (\(\text{SO}_4^{2-}\)) has a charge of \(-2\).
- Let the oxidation state of Fe in \( \text{Fe}_2(\text{SO}_4)_3 \) be \(y\):
\[ 2y + 3(-2) = 0 \implies 2y - 6 = 0 \implies 2y = 6 \implies y = +3 \]
Thus, the oxidation state of Fe in \( \text{Fe}_2(\text{SO}_4)_3 \) is \(+3\).

### Step 3: Calculate the change in oxidation state for iron
The change in oxidation state for iron from FeS to \( \text{Fe}_2(\text{SO}_4)_3 \) is:
\[ +3 - (+2) = +1 \]
This indicates that each Fe atom loses 1 electron.

### Step 4: Determine the oxidation state of sulfur in K2SO4
In \( \text{K}_2\text{SO}_4 \):
- Potassium (K) has an oxidation state of \(+1\).
- Let the oxidation state of sulfur be \(z\):
\[ 2(+1) + z + 4(-2) = 0 \implies 2 + z - 8 = 0 \implies z - 6 = 0 \implies z = +6 \]
Thus, the oxidation state of sulfur in \( \text{K}_2\text{SO}_4 \) is \(+6\).

### Step 5: Calculate the change in oxidation state for sulfur
The change in oxidation state for sulfur from FeS to \( \text{K}_2\text{SO}_4 \) is:
\[ +6 - (-2) = +6 + 2 = +8 \]
This indicates that sulfur loses 8 electrons.

### Step 6: Total change in oxidation state
The total change in oxidation state for FeS is:
\[ \text{Change for Fe} + \text{Change for S} = +1 + 8 = +9 \]

### Step 7: Calculate the equivalent mass of FeS
The equivalent mass of a substance is given by:
\[ \text{Equivalent mass} = \frac{\text{Molar mass}}{n} \]
where \(n\) is the total change in oxidation state (number of electrons transferred).

For FeS:
- The molar mass of FeS = \(55.85 \, (\text{Fe}) + 32.07 \, (\text{S}) = 87.92 \, \text{g/mol}\).
- The total change in oxidation state \(n = 9\).

Thus, the equivalent mass of FeS is:
\[ \text{Equivalent mass of FeS} = \frac{87.92 \, \text{g/mol}}{9} \approx 9.77 \, \text{g/equiv} \]

### Final Answer
The equivalent mass of FeS in the given reaction is approximately \(9.77 \, \text{g/equiv}\).

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