`Cu_(2)S+MnO_(4)^(ө)rarrCu^(2+)+Mn^(2+)+SO_(2)`
The equivalent weight of `Cu_(2)S` is

Options

A. `(M)/(2)`
B. `(M)/(6)`
C. `(M)/(8)`
D. `(M)/(4)`

Explanation

To find the equivalent weight of \( Cu_2S \) in the given reaction:

\[ Cu_2S + MnO_4^- \rightarrow Cu^{2+} + Mn^{2+} + SO_2 \]

we will follow these steps:

### Step 1: Identify the changes in oxidation states
1. **Copper (Cu)** in \( Cu_2S \) is initially in the +1 oxidation state and is oxidized to +2 oxidation state in \( Cu^{2+} \).
2. **Sulfur (S)** in \( Cu_2S \) is in the -2 oxidation state and is oxidized to +4 oxidation state in \( SO_2 \).

### Step 2: Calculate the total change in oxidation states
- For **Copper**:
- Each Cu changes from +1 to +2, contributing a change of \( +1 \) per Cu atom.
- Since there are 2 Cu atoms, the total change for Cu is \( 2 \times 1 = 2 \).

- For **Sulfur**:
- The change from -2 to +4 is \( 4 - (-2) = 6 \).

### Step 3: Total change in oxidation states
- The total change in oxidation states (n-factor) for \( Cu_2S \) is:
\[ n = \text{change in Cu} + \text{change in S} = 2 + 6 = 8 \]

### Step 4: Calculate the molecular weight of \( Cu_2S \)
- The molecular weight of \( Cu_2S \) can be calculated as follows:
- Copper (Cu) has an atomic weight of approximately 63.5 g/mol.
- Sulfur (S) has an atomic weight of approximately 32.1 g/mol.

Therefore,
\[ \text{Molecular weight of } Cu_2S = (2 \times 63.5) + 32.1 = 127 + 32.1 = 159.1 \text{ g/mol} \]

### Step 5: Calculate the equivalent weight
- The equivalent weight is given by the formula:
\[ \text{Equivalent weight} = \frac{\text{Molecular weight}}{n} \]

Substituting the values we have:
\[ \text{Equivalent weight of } Cu_2S = \frac{159.1}{8} = 19.8875 \text{ g/equiv} \]

### Conclusion
The equivalent weight of \( Cu_2S \) is approximately **19.89 g/equiv**.

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