Question

Combine the equations$\Delta G^o=-nF{E}^o$and$\Delta G^o=\Delta H^o-T\Delta S^o$to derive an expression for E° as a function of temperature. Describe how one can graphically determine$\Delta H^o\&\Delta S^o$ from measurements of E° at different temperatures, assuming that$\Delta H^o\&\Delta S^o$ do not depend ontemperature. What property would you look for in designing a reference half-cell that would produce a potential relatively stable with respect to temperature?

Short answer

When the graph takes on $E^0$Vs T, the slope and intercepts of Y-axis are $\frac{\Delta S}{nF}\&-\frac{\Delta H^o}{nF}.$The values can also be calculated from the graph by determining the equation. $E^0$will depend on the temperature and $\Delta S^o$stable.

Step-by-step solution

Cell potential of an electrochemical cell

The measure of the potential difference between anode and cathode is cell potential of an electrochemical cell. The overall cell potential can be calculated using,

${E^o}_{cell}={E^o}_{cathode}-{E^o}_{anode}$

Finding of equation

On using the given expressions,

$$\begin{gathered} -nF{E}^o=\Delta H^o-T\Delta S^o \\ {E}^o=\frac{-\Delta H^o}{nF}+\frac{T\Delta S^o}{nF} \\ {E}^o=\left(\frac{-\Delta H^o}{nF}\right)+T\left(\frac{\Delta S^o}{nF}\right) \end{gathered}$$

This is in the form of$y=mx+C.$ When the graph takes on $E^0$Vs T, the slope and intercepts of Y-axis are $\frac{\Delta S}{nF}\&-\frac{\Delta H^o}{nF}.$The values can also be calculated by determining the equation. $E^0$will depend on the temperature and stable.