For a closed circuit Daniell cell, which of the following plots is the accurate one at a given temperature ?
Show Hint
Be careful to distinguish between \( E_{cell} \) and \( E_{cell}^{\circ} \). Standard values are constants for a fixed temperature and reaction, much like an equilibrium constant \( K_{eq} \).
Step 1: Understanding the Concept:
The standard cell potential, denoted as \( E_{cell}^{\circ} \), is a fundamental thermodynamic property of an electrochemical cell.
It is defined under standard conditions: all reactants and products at 1 M concentration, 1 atm pressure for gases, and a specific temperature.
Step 2: Key Formula or Approach:
The instantaneous cell potential \( E_{cell} \) is related to concentrations by the Nernst equation:
\[ E_{cell} = E_{cell}^{\circ} - \frac{RT}{nF} \ln Q \]
While \( E_{cell} \) changes as the reaction proceeds (concentration changes), \( E_{cell}^{\circ} \) is the reference value at standard states.
Step 3: Detailed Explanation:
For a given chemical reaction at a fixed temperature, \( E_{cell}^{\circ} \) is calculated as:
\[ E_{cell}^{\circ} = E_{cathode}^{\circ} - E_{anode}^{\circ} \]
Since the standard reduction potentials of the electrodes are constant at a constant temperature, their difference is also a constant.
As time passes in a closed circuit, the concentrations of ions change, which causes \( E_{cell} \) to decrease until it reaches zero at equilibrium.
However, the standard reference value \( E_{cell}^{\circ} \) does not depend on time or concentration; it remains constant throughout the process.
Therefore, a plot of \( E_{cell}^{\circ} \) against time will be a horizontal line.
Step 4: Final Answer:
The accurate plot is the one where \( E_{cell}^{\circ} \) remains constant with respect to time, which is a horizontal line.
