The question is asking for the volume of gas produced at the anode when a current of 2 A flows through a $\text{MgCl}_2$ solution for 9650 seconds, measured at standard temperature and pressure (STP).

To solve this, we can use Faraday's laws of electrolysis:

1. Calculate the total charge (Q) passed through the solution: $Q = I \times t = 2 \, \text{A} \times 9650 \, \text{s} = 19300 \, \text{C}$

2. Determine moles of electrons using Faraday's constant ($F \approx 96500 \, \text{C/mol}$): $\text{Moles of electrons} = \frac{Q}{F} = \frac{19300}{96500} \approx 0.2 \, \text{mol}$

3. Since chlorine gas ($\text{Cl}_2$) is produced at the anode in this reaction, and each molecule of $\text{Cl}_2$ requires two moles of electrons ($2e^-$), the moles of $\text{Cl}_2$ gas produced is: $\text{Moles of } \text{Cl}_2 = \frac{0.2}{2} = 0.1 \, \text{mol}$

4. Calculate the volume of gas at STP: At STP, 1 mole of gas occupies 22.4 liters. So, $\text{Volume of } \text{Cl}_2 = 0.1 \times 22.4 = 2.24 \, \text{liters}$

Answer: The volume of gas produced at the anode under STP is approximately 2.24 liters.

Would you like a further breakdown of any step, or have any questions?

Related Questions:

1. How does Faraday's constant relate to the amount of charge and moles of substance?
2. What is the role of MgCl2 in the electrolysis process?
3. Why does chlorine gas form at the anode instead of magnesium?
4. How would the result change if the current or time duration were different?
5. What are other practical applications of electrolysis in chemical industries?

Tip: Always check if the reaction environment (e.g., STP) is given, as it helps to use correct constants like the molar volume.