During the electrolysis of molten sodium chloride, the time required to produce `0.10 mol` of chlorine gas using a current of `3` amperes is

Options

A. 55 minutes
B. 110 minutes
C. 220 minutes
D. 330 minutes

Explanation

To determine the time required to produce 0.10 moles of chlorine gas (Cl₂) during the electrolysis of molten sodium chloride (NaCl) using a current of 3 amperes, we can follow these steps:

### Step 1: Understand the Electrolysis Reaction
During the electrolysis of NaCl, chloride ions (Cl⁻) are oxidized at the anode to form chlorine gas (Cl₂):
\[ 2 \text{Cl}^- \rightarrow \text{Cl}_2 + 2 \text{e}^- \]
This means that to produce 1 mole of Cl₂, we need 2 moles of electrons.

### Step 2: Calculate the Charge Required
Using Faraday's laws of electrolysis, the charge (Q) required to produce 1 mole of Cl₂ is given by:
\[ Q = n \cdot F \]
where:
- \( n \) is the number of moles of electrons,
- \( F \) is Faraday's constant (approximately \( 96500 \, \text{C/mol} \)).

For 0.10 moles of Cl₂, we need:
- Moles of electrons required = \( 2 \times 0.10 = 0.20 \, \text{mol} \)
- Charge required:
\[ Q = 0.20 \, \text{mol} \times 96500 \, \text{C/mol} = 19300 \, \text{C} \]

### Step 3: Use the Formula for Time
The relationship between charge, current, and time is given by:
\[ Q = I \cdot t \]
where:
- \( I \) is the current in amperes,
- \( t \) is the time in seconds.

Rearranging this formula to solve for time gives:
\[ t = \frac{Q}{I} \]

### Step 4: Substitute the Values
Now, substituting the values we have:
- \( Q = 19300 \, \text{C} \)
- \( I = 3 \, \text{A} \)

Calculating the time:
\[ t = \frac{19300 \, \text{C}}{3 \, \text{A}} = 6433.33 \, \text{s} \]

### Step 5: Convert Time to Minutes
To convert seconds to minutes, we divide by 60:
\[ t_{\text{minutes}} = \frac{6433.33 \, \text{s}}{60} \approx 107.22 \, \text{minutes} \]

### Final Answer
The time required to produce 0.10 moles of chlorine gas using a current of 3 amperes is approximately **107 minutes**.

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