The equivalent conductance of a substance is 1/3rd of the molar conductance . The time required to electrolyse 3 moles the substance using a current of 9 ampere is

Options

A. 4808 min
B. 1608 min
C. 2408 min
D. 2008 min

Answer

To solve the problem, we need to find the time required to electrolyze 3 moles of a substance using a current of 9 amperes. We will use Faraday's laws of electrolysis and the relationship between equivalent conductance and molar conductance.

### Step-by-Step Solution:

1. **Understand the relationship between equivalent conductance and molar conductance**:
- Given that the equivalent conductance (Λ_eq) is 1/3 of the molar conductance (Λ_m), we can express this as:
\[ Λ_{eq} = \frac{1}{3} Λ_{m} \]

2. **Use Faraday's laws of electrolysis**:
- The formula for the amount of substance deposited during electrolysis is given by:
\[ n = \frac{Q}{F} \]
where:
- \( n \) = number of moles of substance deposited
- \( Q \) = total electric charge (in coulombs)
- \( F \) = Faraday's constant (approximately 96500 C/mol)

3. **Calculate the total charge (Q)**:
- The total charge can also be expressed in terms of current (I) and time (t):
\[ Q = I \times t \]
- Here, \( I = 9 \) A (amperes).

4. **Set up the equation for the number of moles**:
- We need to deposit 3 moles of the substance:
\[ 3 = \frac{I \times t}{F} \]
- Substituting the values we have:
\[ 3 = \frac{9 \times t}{96500} \]

5. **Rearranging the equation to solve for time (t)**:
- Multiply both sides by 96500:
\[ 3 \times 96500 = 9 \times t \]
- Calculate \( 3 \times 96500 \):
\[ 289500 = 9 \times t \]
- Now, divide both sides by 9:
\[ t = \frac{289500}{9} = 32166.67 \text{ seconds} \]

6. **Convert seconds to minutes**:
- To convert seconds into minutes, divide by 60:
\[ t = \frac{32166.67}{60} \approx 536.11 \text{ minutes} \]

### Final Answer:
The time required to electrolyze 3 moles of the substance using a current of 9 amperes is approximately **536.11 minutes**.