Which of the following statements are incorrect for thermodynamic pro…

The correct answer is Option (1) → (A), (B) and (D) only

A property is intensive if it does not depend on the amount of substance (temperature, density, electrode potential). It is extensive if it changes with the amount (mass, volume, enthalpy, Gibbs energy).

For a cell reaction, the Gibbs energy and the cell potential are linked by:

    \( \displaystyle \Delta_rG=-nFE_{cell} \)

E_cell is a potential difference; it is the same whatever amount of the reaction is written. Δ_rG contains n, the number of moles of electrons, so it grows with the amount of reaction. Writing the Daniell cell reaction for 2 mol of zinc doubles n and doubles Δ_rG, while E_cell stays the same:

    \( \displaystyle \ce{Zn + Cu^2+ -> Zn^2+ + Cu}\qquad \Delta_rG=-2FE_{cell} \)

    \( \displaystyle \ce{2Zn + 2Cu^2+ -> 2Zn^2+ + 2Cu}\qquad \Delta_rG=-4FE_{cell} \)

So E_cell is intensive and Δ_rG is extensive. The question asks for the incorrect statements:

• (A) Both E_cell and Δ_rG of reaction are extensive properties. — Incorrect. Δ_rG is extensive, but E_cell does not change with the amount of reaction, so it is intensive.

• (B) Both E_cell and Δ_rG of reaction are intensive properties. — Incorrect. E_cell is intensive, but Δ_rG depends on n, so it is extensive.

• (C) E_cell is an intensive property while Δ_rG of reaction is an extensive property. — Correct. This is the relation shown above, so it is not one of the incorrect statements.

• (D) E_cell is an extensive property while Δ_rG of reaction is an intensive property. — Incorrect. Both parts are the wrong way round.

NCERT (2026-27 edition):
Electrochemical Cell and Gibbs Energy of the Reaction – “Electrical work done in one second is equal to electrical potential multiplied by total charge passed. If we want to obtain maximum work from a galvanic cell then charge has to be passed reversibly. The reversible work done by a galvanic cell is equal to decrease in its Gibbs energy and therefore, if the emf of the cell is E and nF is the amount of charge passed and Δ_rG is the Gibbs energy of the reaction, then

    \( \displaystyle \Delta_rG=-nFE_{(cell)} \)    (2.15)

It may be remembered that E_(cell) is an intensive parameter but Δ_rG is an extensive thermodynamic property and the value depends on n. Thus, if we write the reaction

    \( \displaystyle \ce{Zn(s) + Cu^2+(aq) -> Zn^2+(aq) + Cu(s)} \)    (2.1)

    \( \displaystyle \Delta_rG=-2FE_{(cell)} \)

but when we write the reaction

    \( \displaystyle \ce{2Zn(s) + 2Cu^2+(aq) -> 2Zn^2+(aq) + 2Cu(s)} \)

    \( \displaystyle \Delta_rG=-4FE_{(cell)} \)”