The number of incorrect statements from the following is ___________.
A. The electrical work that a reaction can perform at constant pressure and temperature is equal to the reaction Gibbs energy.
B. E_(cell)° cell is dependent on the pressure.
C. (d E^θ cell)/dT=(Δᵣ S^θ)/nF
D. A cell is operating reversibly if the cell potential is exactly balanced by an opposing source of potential difference.

Solution

Chemistry ma’am · 3 steps

Check each statement against Δᵣ G° = -nFE°; only the one about pressure breaks down.

1. Link Gibbs energy. For a cell, Δᵣ G = -nFE_(cell). This is the maximum electrical work, and it equals Δᵣ G in size when the cell runs reversibly at constant T and p.
2. Temperature dependence. Differentiate Δᵣ G° = -nFE°_(cell) with respect to T. Since (dΔᵣ G°)/dT = -Δᵣ S°, the two minus signs cancel.

   dE°_(cell)/dT = (Δᵣ S°)/nF

   Statement	Check	Verdict
   A	Maximum electrical work at constant T, p equals Δᵣ G	correct
   B	E°_(cell) is defined at the fixed standard pressure of 1 bar, so it cannot depend on pressure	incorrect
   C	Follows from Δᵣ G° = -nFE° and (dΔᵣ G°)/dT = -Δᵣ S°	correct
   D	An exactly balancing opposing potential lets no current flow, which is the reversible condition	correct

3. So. Only statement B is incorrect, so the number of incorrect statements is 1.

The common slip: 2. Marking A as wrong because of the minus sign in Δᵣ G = -nFE gives 2. The statement is about the size of the work, and that size equals Δᵣ G.

The idea to keep. A standard quantity like E° is fixed at standard conditions, so it does not change with pressure. Almost every cell thermodynamics result comes from Δ G = -nFE.

Answer from the NTA final answer key. Solution by PrepWiser.