How may litres of chlorine gas will be obtained by electrolysis of molten NaCl at 1.8 atm and `27^@C` ? The electrolysis continued for 9.65 sec using 1000 amp current .

Options

A. 460 L
B. 0.683 J
C. 1800 L
D. 1231.6 L

Answer

To solve the problem of how many liters of chlorine gas will be obtained by the electrolysis of molten NaCl, we can follow these steps:

### Step 1: Calculate the total charge (Q) passed during electrolysis
Using the formula:
\[ Q = I \times t \]
Where:
- \( I = 1000 \, \text{A} \) (current)
- \( t = 9.65 \, \text{s} \) (time)

Calculating:
\[ Q = 1000 \, \text{A} \times 9.65 \, \text{s} = 9650 \, \text{C} \]

### Step 2: Calculate the number of moles of electrons (n)
Using Faraday's law, the number of moles of electrons can be calculated using:
\[ n = \frac{Q}{F} \]
Where:
- \( F = 96500 \, \text{C/mol} \) (Faraday's constant)

Calculating:
\[ n = \frac{9650 \, \text{C}}{96500 \, \text{C/mol}} = 0.1 \, \text{mol} \]

### Step 3: Determine the moles of chlorine gas produced
From the electrolysis of NaCl, we know that:
\[ 2 \, \text{NaCl} \rightarrow \text{Cl}_2 + 2 \, \text{Na} \]
This means that 2 moles of electrons produce 1 mole of chlorine gas (Cl₂). Therefore, the moles of Cl₂ produced is:
\[ \text{Moles of Cl}_2 = \frac{n}{2} = \frac{0.1}{2} = 0.05 \, \text{mol} \]

### Step 4: Calculate the volume of chlorine gas at the given conditions
Using the ideal gas law, we can calculate the volume of gas using the formula:
\[ V = n \times R \times T \]
Where:
- \( R = 0.0821 \, \text{L atm/(K mol)} \)
- \( T = 27^{\circ}C = 300 \, \text{K} \) (convert Celsius to Kelvin)
- \( P = 1.8 \, \text{atm} \)

Using the rearranged ideal gas law:
\[ V = \frac{nRT}{P} \]

Calculating:
\[ V = \frac{0.05 \, \text{mol} \times 0.0821 \, \text{L atm/(K mol)} \times 300 \, \text{K}}{1.8 \, \text{atm}} \]
\[ V = \frac{1.2315}{1.8} \approx 0.6842 \, \text{L} \]

### Final Answer
Thus, the volume of chlorine gas obtained is approximately **0.6842 liters**.

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