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A 4.0M aqueous solution of NaCl is prepa...

A `4.0M` aqueous solution of `NaCl` is prepared and `500mL` of this solution is electrolyzed. This leads to the evolution of chlorine gas at one of the electrodes `(` atomic mass of `Na ` is 23 and `Hg` is `200)(1F=96500C)`.
The total charge `(` coulomb `)` required for complete electrolysis is
(a)24125
(b)48250
(c)96500
(d)193000

A

24125

B

48250

C

96500

D

193000

Text Solution

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The correct Answer is:
To determine the total charge required for the complete electrolysis of a 4.0 M aqueous solution of NaCl, we can follow these steps: ### Step 1: Calculate the number of moles of NaCl in the solution Given: - Molarity (M) = 4.0 M - Volume (V) = 500 mL = 0.5 L Using the formula for moles: \[ \text{Number of moles} = \text{Molarity} \times \text{Volume} \] \[ \text{Number of moles of NaCl} = 4.0 \, \text{mol/L} \times 0.5 \, \text{L} = 2.0 \, \text{mol} \] ### Step 2: Determine the number of moles of electrons required for electrolysis In the electrolysis of NaCl, the following reactions occur: - At the anode (oxidation): \[ 2 \text{Cl}^- \rightarrow \text{Cl}_2 + 2 e^- \] This means 2 moles of chloride ions produce 1 mole of chlorine gas and require 2 moles of electrons. Thus, for 2.0 moles of NaCl, the moles of electrons required will be: \[ \text{Moles of } e^- = 2 \times 2.0 \, \text{mol} = 4.0 \, \text{mol} \] ### Step 3: Calculate the total charge using Faraday's constant Using Faraday's constant, which is approximately \( F = 96500 \, \text{C/mol} \): \[ \text{Total charge (Q)} = \text{Moles of } e^- \times F \] \[ Q = 4.0 \, \text{mol} \times 96500 \, \text{C/mol} = 386000 \, \text{C} \] ### Step 4: Adjust for the correct stoichiometry However, we need to consider that the electrolysis of NaCl involves the discharge of 2 moles of electrons for every mole of chlorine gas produced. Therefore, the total charge required for complete electrolysis is: \[ Q = 2 \times 4.0 \, \text{mol} \times 96500 \, \text{C/mol} = 193000 \, \text{C} \] ### Conclusion The total charge required for complete electrolysis is: \[ \boxed{193000 \, \text{C}} \]
To determine the total charge required for the complete electrolysis of a 4.0 M aqueous solution of NaCl, we can follow these steps: ### Step 1: Calculate the number of moles of NaCl in the solution Given: - Molarity (M) = 4.0 M - Volume (V) = 500 mL = 0.5 L Using the formula for moles: ...
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