The required time to liberate one gram equivalent of an element by passing one ampere current through its solution is

Options

A. 6.7 hrs
B. 13.4 hrs
C. 19.9 hrs
D. 26.8 hrs

Explanation

To solve the problem of determining the time required to liberate one gram equivalent of an element by passing one ampere of current through its solution, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Concept of Faraday's Law of Electrolysis**:
- According to Faraday's law, to deposit one gram equivalent of a substance, we need to pass a charge equal to one Faraday.

2. **Charge Required for One Gram Equivalent**:
- One Faraday is equivalent to 96,485 coulombs (commonly rounded to 9600 coulombs for simplicity in calculations).

3. **Current and Time Relationship**:
- The relationship between current (I), charge (Q), and time (T) is given by the formula:
\[ Q = I \times T \]
- Where:
- \( Q \) is the charge in coulombs,
- \( I \) is the current in amperes,
- \( T \) is the time in seconds.

4. **Substituting Known Values**:
- We know that \( I = 1 \) ampere and \( Q = 9600 \) coulombs.
- Substituting these values into the equation gives:
\[ 9600 = 1 \times T \]
- Thus, we find:
\[ T = 9600 \text{ seconds} \]

5. **Converting Seconds to Hours**:
- To convert seconds into hours, we use the conversion factor \( 1 \text{ hour} = 3600 \text{ seconds} \):
\[ T = \frac{9600 \text{ seconds}}{3600 \text{ seconds/hour}} \approx 2.67 \text{ hours} \]

6. **Conclusion**:
- Therefore, the required time to liberate one gram equivalent of an element by passing one ampere of current through its solution is approximately 2.67 hours.

### Final Answer:
The required time is approximately **2.67 hours**.