A current of 9.65 amp. is passed through an aqueous solution of NaCl using suitable electrodes for 1000 s. Given that 1 Faraday equals to 96,500 coulombs the amount of NaOH (mol. $wt.=40.00)$ formed on electrolysis is:

Question

Accepted Answer

To determine the amount of NaOH formed during the electrolysis of an aqueous solution of NaCl, we need to consider the electrochemical reactions and the amount of charge passed through the solution.

1. **Electrochemical Reaction:**
   - During the electrolysis of NaCl, the following reactions occur:
     - At the cathode: $ 2H_2O + 2e^- \rightarrow H_2 + 2OH^- $
     - At the anode: $ 2Cl^- \rightarrow Cl_2 + 2e^- $
   - The overall reaction for the formation of NaOH is:
     - $ 2NaCl + 2H_2O \rightarrow 2NaOH + Cl_2 + H_2 $

2. **Charge Calculation:**
   - The current passed is 9.65 amperes for 1000 seconds.
   - Total charge (Q) = Current (I) × Time (t) = 9.65 A × 1000 s = 9650 coulombs.

3. **Faraday's Laws of Electrolysis:**
   - 1 Faraday (F) = 96,500 coulombs is required to deposit 1 mole of a substance.
   - For the formation of NaOH, 2 moles of electrons are required to form 2 moles of NaOH (from the reaction above).

4. **Moles of NaOH Formed:**
   - Moles of electrons = Total charge / Faraday's constant = 9650 C / 96,500 C/mol = 0.1 moles of electrons.
   - Since 2 moles of electrons produce 2 moles of NaOH, 0.1 moles of electrons will produce 0.1 moles of NaOH.

5. **Mass of NaOH Formed:**
   - Molar mass of NaOH = 40.00 g/mol.
   - Mass of NaOH = Moles × Molar mass = 0.1 moles × 40.00 g/mol = 4.0 g.

Therefore, the amount of NaOH formed is 4.0 g, which corresponds to Option 3.

**Explanation for Incorrect Options:**

- **Option 1 (2.0 g):** This option is incorrect because it underestimates the amount of NaOH formed. The calculation shows that 0.1 moles of NaOH, equivalent to 4.0 g, are produced, not 2.0 g.

- **Option 2 (8.0 g):** This option is incorrect because it overestimates the amount of NaOH formed. The correct calculation yields 4.0 g of NaOH, not 8.0 g.

- **Option 4 (1.0 g):** This option is incorrect because it significantly underestimates the amount of NaOH formed. The correct calculation shows that 4.0 g of NaOH is produced, not 1.0 g.

In conclusion, the correct answer is Option 3, which accurately reflects the amount of NaOH formed during the electrolysis process.