The amount of chlorine evolved by passing 2 A of current in an aqueous solution of NaCI for 30 minutes is

Options

A. 2.64 g
B. 1.32 g
C. 3.62 g
D. 4.22 g

Explanation

To find the amount of chlorine evolved by passing 2 A of current in an aqueous solution of NaCl for 30 minutes, we can follow these steps:

### Step 1: Calculate the total charge (Q) passed through the solution.
The formula to calculate charge is:
\[ Q = I \times t \]
Where:
- \( I \) = current in amperes (A)
- \( t \) = time in seconds (s)

Given:
- \( I = 2 \, \text{A} \)
- \( t = 30 \, \text{minutes} = 30 \times 60 \, \text{s} = 1800 \, \text{s} \)

Now, substituting the values:
\[ Q = 2 \, \text{A} \times 1800 \, \text{s} = 3600 \, \text{C} \]

### Step 2: Use Faraday's law to find the amount of chlorine evolved.
According to Faraday's laws of electrolysis, the amount of substance evolved at an electrode is directly proportional to the quantity of electricity passed through the electrolyte.

The Faraday constant (F) is approximately:
\[ F = 96500 \, \text{C/mol} \]

Chlorine gas (\( Cl_2 \)) is produced from the reduction of chloride ions (\( Cl^- \)):
\[ 2Cl^- + 2e^- \rightarrow Cl_2 \]
This means that 2 moles of electrons are required to produce 1 mole of \( Cl_2 \).

### Step 3: Calculate the moles of electrons transferred.
To find the moles of electrons (n) transferred, we use the formula:
\[ n = \frac{Q}{F} \]
Substituting the values:
\[ n = \frac{3600 \, \text{C}}{96500 \, \text{C/mol}} \approx 0.0372 \, \text{mol of electrons} \]

### Step 4: Calculate the moles of \( Cl_2 \) produced.
Since 2 moles of electrons produce 1 mole of \( Cl_2 \):
\[ \text{Moles of } Cl_2 = \frac{0.0372}{2} \approx 0.0186 \, \text{mol} \]

### Step 5: Convert moles of \( Cl_2 \) to grams.
The molar mass of \( Cl_2 \) (chlorine gas) is:
\[ \text{Molar mass of } Cl_2 = 2 \times 35.5 \, \text{g/mol} = 71 \, \text{g/mol} \]

Now, we can calculate the mass of \( Cl_2 \):
\[ \text{Mass of } Cl_2 = \text{Moles} \times \text{Molar mass} \]
\[ \text{Mass of } Cl_2 = 0.0186 \, \text{mol} \times 71 \, \text{g/mol} \approx 1.32 \, \text{g} \]

### Final Answer:
The amount of chlorine evolved is approximately **1.32 grams**.

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