A mixture of CuS (molecular weight = `M_(1)`) and `Cu_(2)S` (molecular weight `=M_(2)`) is oxidised by `KMnO_(4)` (molecular weight `=M_(3)`) in acidic medium, where the product obtained are `Cu^(2+),Mn^(2+)` and `SO_(2)`. Find the equivalent weight of CuS, `Cu_(2)S` and `KMnO_(4)` respectively.

Answer

To find the equivalent weights of CuS, Cu₂S, and KMnO₄, we will follow these steps:

### Step 1: Determine the oxidation states in CuS
In CuS:
- The oxidation state of Cu is +2.
- The oxidation state of S is -2.

When CuS is oxidized, it forms Cu²⁺ and SO₂.

### Step 2: Calculate the change in oxidation number for CuS
- Cu remains +2 in both CuS and Cu²⁺, so there is no change in oxidation state for Cu.
- Sulfur changes from -2 in CuS to +4 in SO₂.

Thus, the change in oxidation number for sulfur is:
\[ \text{Change in oxidation number} = +4 - (-2) = +6 \]

### Step 3: Calculate the equivalent weight of CuS
The equivalent weight of CuS is given by the formula:
\[ \text{Equivalent weight} = \frac{\text{Molecular weight}}{\text{Change in oxidation number}} = \frac{M_1}{6} \]

### Step 4: Determine the oxidation states in Cu₂S
In Cu₂S:
- The oxidation state of Cu is +1 (since there are two Cu atoms contributing to a total of +2).
- The oxidation state of S is -2.

When Cu₂S is oxidized, it also forms Cu²⁺ and SO₂.

### Step 5: Calculate the change in oxidation number for Cu₂S
- For Cu: The oxidation state changes from +1 to +2. The change for one Cu atom is +1, and since there are two Cu atoms, the total change is +2.
- For S: The oxidation state changes from -2 to +4, which is a change of +6.

Thus, the total change in oxidation number for Cu₂S is:
\[ \text{Total change} = +2 + 6 = +8 \]

### Step 6: Calculate the equivalent weight of Cu₂S
The equivalent weight of Cu₂S is given by:
\[ \text{Equivalent weight} = \frac{M_2}{8} \]

### Step 7: Determine the oxidation state in KMnO₄
In KMnO₄:
- The oxidation state of Mn is +7.

When KMnO₄ is oxidized, it forms Mn²⁺.

### Step 8: Calculate the change in oxidation number for KMnO₄
The change in oxidation number for Mn is:
\[ \text{Change in oxidation number} = +2 - (+7) = -5 \]
However, we consider the absolute value for equivalent weight calculations, so it is +5.

### Step 9: Calculate the equivalent weight of KMnO₄
The equivalent weight of KMnO₄ is given by:
\[ \text{Equivalent weight} = \frac{M_3}{5} \]

### Final Summary of Equivalent Weights
- Equivalent weight of CuS = \(\frac{M_1}{6}\)
- Equivalent weight of Cu₂S = \(\frac{M_2}{8}\)
- Equivalent weight of KMnO₄ = \(\frac{M_3}{5}\)