Question

For the relation \( \Delta_r G = -nF E_\text{cell} \), \( E_\text{cell} = E^\circ_\text{cell} \), in which of the following conditions?

• A. \( Concentration of any one of the reacting species should be unity.\)
• B. \( Concentration of all the product species should be unity.\)
• C. \( Concentration of all the reactant and product species should be unity.\)
• D. \( Concentration of all reacting and product species should be unity.\)

Hint:

To maintain standard-state conditions, all reactants and products must have unit concentrations, ensuring that \( E_\text{cell} = E^\circ_\text{cell} \).

Answer 1

The Correct Option is C

For \( E_\text{cell} = E^\circ_\text{cell} \) to hold true, the Nernst equation simplifies to:\[E_\text{cell} = E^\circ_\text{cell} - \frac{RT}{nF} \ln Q.\]This equality requires \( \ln Q = 0 \), meaning \( Q = 1 \). This condition is met when:\[Q = 1 \implies \text{The concentration of all reactant and product species must be unity}.\]Under this condition, the cell operates at standard conditions, thus \( E_\text{cell} \) equals \( E^\circ_\text{cell} \). Final Answer:\[\boxed{\text{The concentration of all reactant and product species must be unity.}}\]