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. $\mathrm{E_{cell}^{\circ}}$ cell is dependent on the pressure.

C. $$\frac{d E^{\theta} \text { cell }}{\mathrm{dT}}=\frac{\Delta_{\mathrm{r}} \mathrm{S}^{\theta}}{\mathrm{nF}}$$

D. A cell is operating reversibly if the cell potential is exactly balanced by an opposing source of potential difference.

<p>Let&#39;s go through the statements one by one:</p> <p>A. The electrical work that a reaction can perform at constant pressure and temperature is equal to the reaction Gibbs energy. </p> <p>This statement is <strong>correct</strong>. The maximum non-expansion work that a system can perform at constant temperature and pressure is given by the change in Gibbs free energy. This is especially relevant for electrochemical reactions where this non-expansion work appears as electrical work.</p> <p>B. E°cell is dependent on the pressure.</p> <p>This statement is <strong>incorrect</strong>. The standard cell potential, E°cell, is not dependent on pressure. It is dependent on the nature of the reactants and products (their identities and stoichiometric ratios), as well as temperature, but not pressure. The E°cell is calculated using standard conditions, which includes a standard pressure of 1 bar or approximately 1 atm.</p> <p>C. $$\frac{d E^{\theta} \text { cell }}{\mathrm{dT}}=\frac{\Delta_{\mathrm{r}} \mathrm{S}^{\theta}}{\mathrm{nF}}$$</p> <p>This statement is <strong>correct</strong>. This equation is derived from the Gibbs-Helmholtz equation, which describes the temperature dependence of the change in Gibbs free energy. In an electrochemical cell, the change in Gibbs free energy can be related to the cell potential.</p> <p>D. A cell is operating reversibly if the cell potential is exactly balanced by an opposing source of potential difference.</p> <p>This statement is <strong>correct</strong>. In a reversible electrochemical cell, the cell potential is exactly balanced by an external, opposing potential. This ensures that the reaction proceeds at an infinitesimally slow rate, allowing the system to maintain equilibrium at all times.</p> <p>So, among these four statements, only one (Statement B) is incorrect.</p>