Electrolysis of a solution of `MnSO_(4)` in aqueous sulphuric acid is a method for the preparation of `MnO_(2)`. Passig a curret of 27 A for 24 hours gives 1 kg of `MnO_(2)`. The current efficiency in this process is:

Options

A. `100%`
B. `95.185%`
C. `80%`
D. `82.951%`

Explanation

To find the current efficiency of the electrolysis process for the preparation of MnO2 from MnSO4, we can follow these steps:

### Step 1: Determine the Equivalent Weight of MnO2
The equivalent weight of a substance can be calculated using the formula:
\[ \text{Equivalent Weight} = \frac{\text{Molecular Weight}}{n} \]
where \( n \) is the number of electrons transferred during the reaction.

**Molecular Weight of MnO2:**
- Manganese (Mn) = 55 g/mol
- Oxygen (O) = 16 g/mol
- Therefore, Molecular Weight of MnO2 = \( 55 + (2 \times 16) = 55 + 32 = 87 \) g/mol

**Determine \( n \):**
From the reaction:
\[ \text{Mn}^{2+} + 2 \text{e}^- \rightarrow \text{MnO}_2 \]
The change in oxidation state indicates that 2 electrons are transferred, so \( n = 2 \).

**Calculate Equivalent Weight:**
\[ \text{Equivalent Weight of MnO2} = \frac{87}{2} = 43.5 \text{ g/equiv} \]

### Step 2: Calculate the Total Charge Passed
Using the formula:
\[ Q = I \times t \]
where \( Q \) is the total charge in coulombs, \( I \) is the current in amperes, and \( t \) is the time in seconds.

**Convert Time to Seconds:**
\[ t = 24 \text{ hours} \times 3600 \text{ seconds/hour} = 86400 \text{ seconds} \]

**Calculate Total Charge:**
\[ Q = 27 \text{ A} \times 86400 \text{ s} = 2332800 \text{ C} \]

### Step 3: Calculate the Number of Equivalents of MnO2 Produced
Using Faraday's law:
\[ \text{Number of Equivalents} = \frac{Q}{F} \]
where \( F \) (Faraday's constant) = 96500 C/equiv.

**Calculate Number of Equivalents:**
\[ \text{Number of Equivalents} = \frac{2332800 \text{ C}}{96500 \text{ C/equiv}} \approx 24.19 \text{ equiv} \]

### Step 4: Calculate the Theoretical Mass of MnO2 Produced
Using the equivalent weight:
\[ \text{Theoretical Mass} = \text{Number of Equivalents} \times \text{Equivalent Weight} \]
\[ \text{Theoretical Mass} = 24.19 \text{ equiv} \times 43.5 \text{ g/equiv} \approx 1058.26 \text{ g} \]

### Step 5: Calculate Current Efficiency
Current efficiency can be calculated using the formula:
\[ \text{Current Efficiency} = \left( \frac{\text{Actual Mass}}{\text{Theoretical Mass}} \right) \times 100\% \]
where the actual mass of MnO2 produced is given as 1 kg (1000 g).

**Calculate Current Efficiency:**
\[ \text{Current Efficiency} = \left( \frac{1000 \text{ g}}{1058.26 \text{ g}} \right) \times 100\% \approx 94.5\% \]

### Conclusion
The current efficiency in this process is approximately **95.185%**.