The maximum efficiency of cell is given by-(A)HG (B)cellnFEG (C) –cellnFEH (D) Zero

To answer the question regarding the maximum efficiency of a cell, we must consider the context of electrochemical cells, particularly focusing on the Gibbs free energy change (ΔG) and its relationship to electromotive force (EMF), which is influenced by enthalpy change (ΔH), and other variables such as the number of moles of electrons transferred (n) and Faraday's constant (F).

Explanation of Options

1. (A) HGΔΔ: This expression is ambiguous and does not reflect the standard relationships in electrochemistry.

2. (B) cellnFEGΔ: This reflects a relationship where the change in Gibbs free energy (ΔG) is involved with cell potential (E), but the expression is not correctly structured for maximum efficiency.

3. (C) –cellnFEHΔ: This correctly states that the maximum efficiency of an electrochemical cell can be expressed in terms of Gibbs free energy and the electrical work done. According to thermodynamic principles, the maximum efficiency can indeed be determined from the efficiency relation involving Gibbs free energy and the cell potential.

4. (D) Zero: This does not hold true, as the efficiency of an electrochemical cell is not zero under operating conditions.

Final Answer

The correct answer is (C) –cellnFEHΔ. This reflects the proper thermodynamic relation that describes the maximum efficiency of the cell in terms of Gibbs free energy change.