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. (a) 55 minutes
B. (b) 110 minutes
C. (c) 220 minutes
D. (d) 330 minutes

Explanation

To solve the problem of determining the time required to produce 0.10 mol of chlorine gas during the electrolysis of molten sodium chloride using a current of 3 amperes, we can follow these steps:

### Step 1: Understand the Electrolysis Reaction
During the electrolysis of molten sodium chloride (NaCl), the chloride ions (Cl⁻) migrate to the anode where they lose electrons to form chlorine gas (Cl₂). The reaction can be summarized as:
\[ 2 \text{Cl}^- \rightarrow \text{Cl}_2 + 2 \text{e}^- \]
This indicates that 2 moles of electrons are needed to produce 1 mole of chlorine gas.

### Step 2: Calculate the Charge Required for 0.10 mol of Cl₂
From the reaction, we know that to produce 1 mole of Cl₂, we need 2 moles of electrons. The charge of 1 mole of electrons (1 Faraday) is approximately 96500 coulombs. Therefore, the charge required for 1 mole of Cl₂ is:
\[ \text{Charge for 1 mol of Cl}_2 = 2 \times 96500 \, \text{C} = 193000 \, \text{C} \]

Now, for 0.10 mol of Cl₂, the charge required will be:
\[ \text{Charge for 0.10 mol of Cl}_2 = 0.10 \times 193000 \, \text{C} = 19300 \, \text{C} \]

### Step 3: Use the Formula to Calculate Time
We know that charge (Q) is related to current (I) and time (t) by the formula:
\[ Q = I \times t \]
Where:
- \( Q \) = charge in coulombs
- \( I \) = current in amperes
- \( t \) = time in seconds

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

Substituting the values we have:
\[ t = \frac{19300 \, \text{C}}{3 \, \text{A}} = 6433.33 \, \text{s} \]

### Step 4: Convert Time from Seconds to Minutes
To convert seconds to minutes, we divide by 60:
\[ t = \frac{6433.33 \, \text{s}}{60} \approx 107.22 \, \text{minutes} \]

### Step 5: Round to the Nearest Option
The closest option to 107.22 minutes is 110 minutes.

### Final Answer
The time required to produce 0.10 mol of chlorine gas using a current of 3 amperes is approximately **110 minutes**.

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