MCQEasyJEE 2026Electrochemical Cells

JEE Chemistry 2026 Question with Solution

For a closed circuit Daniell cell, which of the following plots is the accurate one at a given temperature ?

  • A
    Graph of standard cell potential on vertical axis versus time on horizontal axis, showing a straight line increasing with time from a positive intercept.
  • B
    Graph of standard cell potential on vertical axis versus time on horizontal axis, showing a horizontal straight line at a constant positive value.
  • C
    Graph of standard cell potential on vertical axis versus time on horizontal axis, showing a straight line decreasing with time from a positive value.
  • D
    Graph of standard cell potential on vertical axis versus time on horizontal axis, showing a vertical line at one instant of time.

Answer

Correct answer:B

Step-by-step solution

Standard Method

Given: A closed circuit Daniell cell at a fixed temperature, and plots of EcellE_{cell}^{\circ} versus time.

Find: Which plot correctly represents the behaviour of EcellE_{cell}^{\circ} with time.

The standard cell potential is a thermodynamic quantity defined under standard conditions. At a fixed temperature, it depends only on the standard electrode potentials of the two half-cells.

Ecell=EcathodeEanodeE_{cell}^{\circ} = E_{cathode}^{\circ} - E_{anode}^{\circ}

The instantaneous cell potential changes during cell operation according to the Nernst equation:

Ecell=EcellRTnFlnQE_{cell} = E_{cell}^{\circ} - \frac{RT}{nF} \ln Q

Here, EcellE_{cell} changes as concentrations change with time, but EcellE_{cell}^{\circ} does not change with time for a given reaction at a given temperature.

Therefore, the graph of EcellE_{cell}^{\circ} versus time is a horizontal line.

The correct option is B.

Conceptual Distinction

Given: The cell is a Daniell cell operating in a closed circuit.

Find: The correct time plot of the standard cell potential.

A common confusion is between EcellE_{cell} and EcellE_{cell}^{\circ}.

  • EcellE_{cell}^{\circ} is the standard cell potential.
  • EcellE_{cell} is the actual cell potential at the current concentrations.

At constant temperature, the standard reduction potentials of the electrodes remain constant. Hence their difference also remains constant:

Ecell=EcathodeEanodeE_{cell}^{\circ} = E_{cathode}^{\circ} - E_{anode}^{\circ}

Although the reaction proceeds with time in a closed circuit and the concentrations of ions change, that affects only EcellE_{cell} through the reaction quotient QQ.

Ecell=EcellRTnFlnQE_{cell} = E_{cell}^{\circ} - \frac{RT}{nF} \ln Q

So, with time:

  • EcellE_{cell} may decrease,
  • but EcellE_{cell}^{\circ} remains constant.

Hence the correct graph is the horizontal line, which corresponds to option B.

Common mistakes

  • Confusing EcellE_{cell} with EcellE_{cell}^{\circ}. This is incorrect because EcellE_{cell} depends on concentration through the Nernst equation, while EcellE_{cell}^{\circ} is constant at fixed temperature. Always check whether the question asks for actual cell potential or standard cell potential.

  • Assuming that every electrochemical quantity changes with time in a closed circuit. This is wrong because standard electrode potentials are reference values under standard conditions. Use time dependence only for quantities involving changing concentrations, such as EcellE_{cell}, not EcellE_{cell}^{\circ}.

  • Choosing the decreasing graph because the cell 'runs down' with time. This reasoning applies to the actual emf of the cell, not the standard cell potential. Distinguish between operational behaviour of the cell and the fixed thermodynamic reference value.

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