M is the molecular mass of `KMnO_4` the equivalent mass of `KMnO_4` when it is converted into `K_2MnO_4` is

Options

A. M
B. M/3
C. M/5
D. M/7

Answer

To find the equivalent mass of `KMnO4` when it is converted into `K2MnO4`, we will follow these steps:

### Step 1: Determine the molecular mass of `KMnO4`
The molecular mass (M) of `KMnO4` can be calculated by adding the atomic masses of its constituent elements:
- Potassium (K): 39.1 g/mol
- Manganese (Mn): 54.9 g/mol
- Oxygen (O): 16.0 g/mol (and there are 4 oxygen atoms)

So, the molecular mass of `KMnO4` is:
\[ M = 39.1 + 54.9 + (4 \times 16.0) \]
\[ M = 39.1 + 54.9 + 64.0 \]
\[ M = 158.0 \, \text{g/mol} \]

### Step 2: Determine the oxidation states
In `KMnO4`, manganese (Mn) is in the +7 oxidation state. In `K2MnO4`, manganese is in the +6 oxidation state.

### Step 3: Calculate the change in oxidation state
The change in oxidation state when `KMnO4` is converted to `K2MnO4` is:
\[ \text{Change} = +7 - +6 = 1 \]
This indicates that manganese is reduced by gaining 1 electron.

### Step 4: Determine the n-factor
The n-factor is defined as the number of electrons gained or lost per molecule during the reaction. Here, since manganese is reduced by 1 electron:
\[ n = 1 \]

### Step 5: Calculate the equivalent mass
The equivalent mass is calculated using the formula:
\[ \text{Equivalent mass} = \frac{\text{Molar mass}}{n \text{-factor}} \]
Substituting the values we have:
\[ \text{Equivalent mass} = \frac{158.0 \, \text{g/mol}}{1} = 158.0 \, \text{g/equiv} \]

### Final Answer
The equivalent mass of `KMnO4` when it is converted into `K2MnO4` is **158.0 g/equiv**.

---