The volume of gases evolved at `STP` by passing `0.2A` of current for `965 s` through an aqueous solution of sodium furmarate is
a. 22.4 m L
b. 11.2 m L
c. 89.6 m L
d. 44.8 m L

Options

A. `22.4mL`
B. `11.2mL`
C. `89.6mL`
D. `44.8mL`

Explanation

To solve the problem of finding the volume of gases evolved at STP by passing 0.2 A of current for 965 seconds through an aqueous solution of sodium fumarate, we can follow these steps:

### Step 1: Calculate the total charge (Q) passed through the solution
The charge (Q) can be calculated using the formula:
\[ Q = I \times t \]
where:
- \( I \) = current in amperes (0.2 A)
- \( t \) = time in seconds (965 s)

Substituting the values:
\[ Q = 0.2 \, \text{A} \times 965 \, \text{s} = 193 \, \text{C} \]

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

Substituting the values:
\[ n = \frac{193 \, \text{C}}{96500 \, \text{C/mol}} \approx 0.002 \, \text{mol} \]

### Step 3: Determine the moles of gas produced
From the reaction of sodium fumarate, we know that:
- 2 moles of electrons produce 4 moles of gas (1 mole of ethyne, 2 moles of CO2, and 1 mole of H2).

Thus, for every 2 moles of electrons, we produce 4 moles of gas. Therefore, for 0.002 moles of electrons:
\[ \text{Moles of gas} = 0.002 \, \text{mol} \times \frac{4 \, \text{mol gas}}{2 \, \text{mol e}^-} = 0.004 \, \text{mol gas} \]

### Step 4: Calculate the volume of gas at STP
At standard temperature and pressure (STP), 1 mole of gas occupies 22.4 L. Therefore, the volume of gas produced can be calculated as:
\[ \text{Volume} = \text{Moles of gas} \times 22.4 \, \text{L/mol} \]
Substituting the values:
\[ \text{Volume} = 0.004 \, \text{mol} \times 22.4 \, \text{L/mol} = 0.0896 \, \text{L} \]

### Step 5: Convert the volume to mL
Since 1 L = 1000 mL:
\[ \text{Volume} = 0.0896 \, \text{L} \times 1000 \, \text{mL/L} = 89.6 \, \text{mL} \]

### Final Answer
The volume of gases evolved at STP is **89.6 mL** (Option c).

---