When aqueous solution of sodium ethanoate is electrolysed, the volume of gases obtained at anode at a pressure of `1.0` bar and 298 K temperature when `2.0` Faraday of electricity is passed is:

Options

A. (a) `67.2` liters
B. (b) `68.1` liters
C. (c) `73.2` liters
D. (d) `74.1` liters

Explanation

To solve the problem of determining the volume of gases obtained at the anode during the electrolysis of an aqueous solution of sodium ethanoate when 2.0 Faraday of electricity is passed, we can follow these steps:

### Step 1: Write the Ionization Equation
When sodium ethanoate (CH₃COONa) is dissolved in water, it dissociates into its ions:
\[ \text{CH}_3\text{COONa} \rightarrow \text{CH}_3\text{COO}^- + \text{Na}^+ \]

### Step 2: Identify the Electrolysis Reactions
During electrolysis, oxidation occurs at the anode and reduction occurs at the cathode.

**At the Cathode (Reduction):**
Water is reduced to form hydrogen gas and hydroxide ions:
\[ \text{2H}_2\text{O} + 2e^- \rightarrow \text{H}_2(g) + 2\text{OH}^- \]

**At the Anode (Oxidation):**
The acetate ions (CH₃COO⁻) undergo oxidation:
\[ \text{2CH}_3\text{COO}^- \rightarrow \text{2CO}_2(g) + \text{C}_2\text{H}_6(g) + 2e^- \]

### Step 3: Determine Moles of Gas Produced
From the oxidation reaction at the anode, we see that:
- 2 moles of acetate ions produce 2 moles of carbon dioxide (CO₂) and 1 mole of ethane (C₂H₆).
- Therefore, for every 2 moles of acetate ions, 3 moles of gas are produced (2 moles of CO₂ + 1 mole of C₂H₆).

### Step 4: Calculate Moles of Gas for 2 Faraday
According to Faraday's laws of electrolysis:
- 1 Faraday corresponds to the transfer of 1 mole of electrons.
- Therefore, 2 Faraday corresponds to the transfer of 2 moles of electrons.

From the electrolysis reaction, we see that 2 moles of electrons produce 3 moles of gas. Thus, for 2 Faraday, we will produce:
\[ 3 \text{ moles of gas} \]

### Step 5: Calculate the Volume of Gas at STP
At standard temperature and pressure (STP), 1 mole of gas occupies 22.4 liters. Therefore, the total volume of gas produced can be calculated as:
\[ \text{Volume} = \text{Number of moles} \times \text{Volume per mole} \]
\[ \text{Volume} = 3 \text{ moles} \times 22.4 \text{ L/mole} = 67.2 \text{ L} \]

### Final Answer
The volume of gases obtained at the anode when 2.0 Faraday of electricity is passed is **67.2 liters**.

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