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Question #44767
The Question
A fully charged lead-acid battery contains of (anode) and of (cathode). Due to structural passivation, only of the and of the are electrochemically active. The battery is discharged at a constant current of at until it is completely dead. Assuming all the formed adheres strictly to the respective electrodes, calculate the total time of discharge and the final mass of the cathode.\n\n(Given: ; Molar masses in : , , )
Options
- A.
and
- B.
and
- C.
and
- D.
and
Check Your Answer
Correct Answer
Step-by-Step Solution
Explanation
How the Examiner Thinks
Numerical_Precision
Improve calculation stamina and avoid rounding errors in high-stakes competitive examinations.
Concepts Behind This Question
Secondary Battery Discharge Cycles|Faraday's First and Second Laws|Stoichiometric Coefficient Division
Why This Question Is Tricky
Common Mistakes
This question tests the intersection of Faraday's Laws, limiting reagent stoichiometry, and practical battery discharge mechanics.
The primary trap is the 'inactive material' constraint.
Students often default to using the total mass provided to find the limiting reagent, which would incorrectly identify PbO2 (2.0 mol) as limiting instead of the active Pb (1.2 mol).
The secondary trap lies in the mass calculation of the electrode.
Students frequently either add the entire mass of the deposited product (PbSO4) to the initial electrode mass without subtracting the consumed reactant (PbO2), or they confuse the anode mass change with the cathode mass change.
The net mass change at the cathode is strictly due to the addition of SO2 (effectively SO4 minus O2) from the electrolyte.
Quick Facts About This Question
Question Information
| Subject | Chemistry |
| Chapter | Electrochemistry - Class 12 |
| Concept | Secondary Battery Discharge Cycles |
| Difficulty | 8 |
| Cognitive Load | 7 |
| Target Solve Time | 160 sec |
| Access | Free |