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: Determine the Reaction
The electrolysis of molten NaCl produces chlorine gas according to the reaction:
\[
2 \text{Cl}^- \rightarrow \text{Cl}_2 + 2 \text{e}^-
\]
### Step 2: Calculate the Charge Passed
Using Faraday's first law of electrolysis, we can calculate the total charge (Q) passed during the electrolysis:
\[
Q = I \times t
\]
Where:
- \( I = 1000 \, \text{A} \) (current)
- \( t = 9.65 \, \text{s} \)
Calculating the charge:
\[
Q = 1000 \, \text{A} \times 9.65 \, \text{s} = 9650 \, \text{C}
\]
### Step 3: Calculate the Number of Moles of Electrons
Using Faraday's constant (approximately \( 96500 \, \text{C/mol} \)), we can find the number of moles of electrons (n):
\[
n = \frac{Q}{F}
\]
Where:
- \( F = 96500 \, \text{C/mol} \)
Calculating the number of moles of electrons:
\[
n = \frac{9650 \, \text{C}}{96500 \, \text{C/mol}} = 0.1 \, \text{mol of e}^-
\]
### Step 4: Calculate the Moles of Chlorine Gas
From the reaction, we see that 2 moles of electrons produce 1 mole of chlorine gas. Therefore, the moles of chlorine gas produced (n(Cl2)) is:
\[
n(\text{Cl}_2) = \frac{n(e^-)}{2} = \frac{0.1}{2} = 0.05 \, \text{mol}
\]
### Step 5: Use the Ideal Gas Law to Find Volume
Using the ideal gas law:
\[
PV = nRT
\]
Where:
- \( P = 1.8 \, \text{atm} \)
- \( n = 0.05 \, \text{mol} \)
- \( R = 0.0821 \, \text{L atm/(mol K)} \)
- \( T = 27^\circ C = 300 \, \text{K} \) (convert Celsius to Kelvin)
Rearranging the ideal gas law to solve for volume (V):
\[
V = \frac{nRT}{P}
\]
Substituting the values:
\[
V = \frac{0.05 \, \text{mol} \times 0.0821 \, \text{L atm/(mol K)} \times 300 \, \text{K}}{1.8 \, \text{atm}}
\]
Calculating the volume:
\[
V = \frac{1.2315}{1.8} \approx 0.6842 \, \text{L}
\]
### Step 6: Final Answer
Thus, the volume of chlorine gas obtained is approximately:
\[
\text{Volume of Cl}_2 \approx 0.68 \, \text{L}
\]
