How many grams of chlorine can be produced by the electrolysis of molten NaCl with a current of 1.00 A for 15 min? Also calculate the number of chlorine molecules liberated.

Explanation

To solve the problem of how many grams of chlorine can be produced by the electrolysis of molten NaCl with a current of 1.00 A for 15 minutes, and to calculate the number of chlorine molecules liberated, we will follow these steps:

### Step 1: Write the Electrolysis Reaction
The electrolysis of molten sodium chloride (NaCl) can be represented by the following reaction:
\[ 2 \text{Cl}^- \rightarrow \text{Cl}_2 + 2 \text{e}^- \]
This indicates that 2 moles of chloride ions (Cl⁻) produce 1 mole of chlorine gas (Cl₂) and release 2 electrons.

### Step 2: Calculate the Total Charge (Q)
The total charge (Q) can be calculated using the formula:
\[ Q = I \times T \]
Where:
- \( I \) = current in amperes (1.00 A)
- \( T \) = time in seconds

First, convert the time from minutes to seconds:
\[ T = 15 \text{ minutes} \times 60 \text{ seconds/minute} = 900 \text{ seconds} \]

Now, calculate \( Q \):
\[ Q = 1.00 \, \text{A} \times 900 \, \text{s} = 900 \, \text{C} \]

### Step 3: Calculate Moles of Electrons Transferred
Using Faraday's law, the number of moles of electrons (n) can be calculated using the formula:
\[ n = \frac{Q}{F} \]
Where:
- \( F \) = Faraday's constant (approximately \( 96500 \, \text{C/mol} \))

Now, calculate \( n \):
\[ n = \frac{900 \, \text{C}}{96500 \, \text{C/mol}} \approx 0.00932 \, \text{mol} \]

### Step 4: Calculate Moles of Chlorine Produced
From the electrolysis reaction, we know that 2 moles of electrons produce 1 mole of Cl₂. Therefore, the moles of chlorine produced (n\(_{\text{Cl}_2}\)) can be calculated as:
\[ n_{\text{Cl}_2} = \frac{n}{2} = \frac{0.00932}{2} \approx 0.00466 \, \text{mol} \]

### Step 5: Calculate Mass of Chlorine Produced
The mass of chlorine (m) can be calculated using the formula:
\[ m = n_{\text{Cl}_2} \times M \]
Where:
- \( M \) = molar mass of Cl₂ (approximately \( 71 \, \text{g/mol} \))

Now, calculate \( m \):
\[ m = 0.00466 \, \text{mol} \times 71 \, \text{g/mol} \approx 0.331 \, \text{g} \]

### Step 6: Calculate the Number of Chlorine Molecules Liberated
To find the number of molecules of chlorine, we can use Avogadro's number (\( N_A = 6.022 \times 10^{23} \, \text{molecules/mol} \)):
\[ \text{Number of molecules} = n_{\text{Cl}_2} \times N_A \]
Now, calculate the number of molecules:
\[ \text{Number of molecules} = 0.00466 \, \text{mol} \times 6.022 \times 10^{23} \, \text{molecules/mol} \approx 2.80 \times 10^{21} \, \text{molecules} \]

### Final Answers
- **Mass of Chlorine Produced:** 0.331 grams
- **Number of Chlorine Molecules Liberated:** \( 2.80 \times 10^{21} \) molecules