Find the volume of gases evolved by passing `0.9655`. A current for `1` hr through an aqueous solution of `CH_(3)COONa` at `25^(@)C` and `1 atm`.

Explanation

To find the volume of gases evolved by passing a current through an aqueous solution of CH₃COONa, we can follow these steps:

### Step 1: Calculate the total charge (Q) passed through the solution
The total charge can be calculated using the formula:
\[ Q = I \times t \]
Where:
- \( I \) = current in amperes (0.9655 A)
- \( t \) = time in seconds (1 hour = 3600 seconds)

Calculating \( Q \):
\[ Q = 0.9655 \, \text{A} \times 3600 \, \text{s} = 3475.8 \, \text{C} \]

### Step 2: Determine the number of moles of electrons (n)
Using Faraday's constant (\( F \)), which is approximately 96500 C/mol, we can find the number of moles of electrons:
\[ n = \frac{Q}{F} \]
Calculating \( n \):
\[ n = \frac{3475.8 \, \text{C}}{96500 \, \text{C/mol}} \approx 0.0361 \, \text{mol} \]

### Step 3: Identify the reactions at the electrodes
In the electrolysis of CH₃COONa:
- At the cathode, water is reduced to produce hydrogen gas:
\[ 2 \, \text{H}_2O + 2e^- \rightarrow \text{H}_2 + 2 \, \text{OH}^- \]
- At the anode, the acetate ion (CH₃COO⁻) is oxidized to produce carbon dioxide and ethane:
\[ \text{CH}_3COO^- \rightarrow 2 \, \text{CO}_2 + 2e^- \]

### Step 4: Calculate the total moles of gas produced
From the reactions:
- 2 moles of electrons produce 1 mole of H₂ and 1 mole of CO₂, resulting in a total of 4 moles of gas for every 2 moles of electrons.

Thus, the total moles of gas produced can be calculated as:
\[ \text{Total moles of gas} = 2 \times n \]
Calculating total moles of gas:
\[ \text{Total moles of gas} = 2 \times 0.0361 \, \text{mol} = 0.0722 \, \text{mol} \]

### Step 5: Calculate the volume of gas at STP
Using the molar volume of a gas at standard temperature and pressure (STP), which is 22.4 L/mol:
\[ \text{Volume} = \text{Total moles of gas} \times 22.4 \, \text{L/mol} \]
Calculating the volume:
\[ \text{Volume} = 0.0722 \, \text{mol} \times 22.4 \, \text{L/mol} \approx 1.62048 \, \text{L} \]

### Final Answer:
The volume of gases evolved is approximately **1.620 L**.