The user wants me to solve a problem related to the electrochemistry of an aqueous NaCl solution. The goal is to find the total charge required for the complete electrolysis of the given amount of NaCl.

Step 1: Calculate the number of moles of NaCl. First, we need to determine the amount of NaCl present in the solution. We are given the molarity and volume of the solution.

• Molarity (M) = 4.0 mol/L
• Volume (V) = 500 mL = 0.5 L

The number of moles (n) of NaCl is calculated using the formula: $n = M \times V$ $n = 4.0 \text{ mol/L} \times 0.5 \text{ L} = 2.0 \text{ moles of NaCl}$ So, the solution contains 2.0 moles of NaCl.

Step 2: Identify the relevant electrochemical reaction. The problem states that the electrolysis of aqueous NaCl leads to the evolution of chlorine gas (Cl₂) at one of the electrodes. This occurs at the anode (oxidation). The half-reaction for the oxidation of chloride ions is: $2Cl^-(aq) \rightarrow Cl_2(g) + 2e^-$ This equation shows the relationship between the amount of chloride ions reacted and the number of electrons transferred.

Step 3: Determine the moles of electrons transferred. From the dissociation of NaCl, we know that 1 mole of NaCl produces 1 mole of Na⁺ ions and 1 mole of Cl⁻ ions. $NaCl(aq) \rightarrow Na^+(aq) + Cl^-(aq)$ Therefore, 2.0 moles of NaCl will provide 2.0 moles of Cl⁻ ions.

From the stoichiometry of the anode half-reaction ($2Cl^- \rightarrow Cl_2 + 2e^-$), we can see that:

• 2 moles of Cl⁻ ions produce 2 moles of electrons.
• This simplifies to a 1:1 molar ratio: 1 mole of Cl⁻ ions produces 1 mole of electrons.

Since we have 2.0 moles of Cl⁻ ions to be completely electrolyzed, the total number of moles of electrons transferred will be: $\text{Moles of electrons} = 2.0 \text{ moles}$

Step 4: Calculate the total charge in coulombs. The charge of one mole of electrons is given by Faraday's constant (F).

• 1 Faraday (F) = 96500 coulombs per mole of electrons (C/mol e⁻)

The total charge (Q) is calculated by multiplying the moles of electrons by Faraday's constant: $Q = (\text{moles of electrons}) \times F$ $Q = 2.0 \text{ mol e}^- \times 96500 \text{ C/mol e}^-$ $Q = 193000 \text{ C}$

Thus, the total charge required for the complete electrolysis is 193000 coulombs.

Conclusion: Comparing our calculated value with the given options: A: 24125 B: 48250 C: 96500 D: 193000

The calculated charge matches option D.