Question

Calculate the standard cell potentials of galvanic cell in which the following reactions take place:
(i) $2Cr\left(s\right)+3C{d}^{2+}\left(aq\right)\to 2C{r}^{3+}\left(aq\right)+3Cd$
(ii) $F{e}^{2+}\left(aq\right)+A{g}^{+}\left(aq\right)\to F{e}^{3+}\left(aq\right)+Ag\left(s\right)$
Calculate the ${\Delta }_r{G}^{\ominus }$ and equilibrium constant of the reactions

Answer 1

(i) $E_{cell}^o=E_{cathode}^0-E_{anode}^0=-0.40-(-0.74)=0.34$ V

$\Delta G^0=-nF{E}_{cell}^o=-6\times 96500\times 0.34=196860J/mol=196.86kJ/mol$

$log{K}_c=\frac{n{E}_{cell}^o}{0.059}=\frac{6\times 0.34}{0.059}=34.576$

$K_c=3.76\times {10}^{34}$

(ii) $E_{cell}^o=E_{cathode}^0-E_{anode}^0=0.80-(-0.77)=0.03$ V

$\Delta G^0=-nF{E}_{cell}^o=-1\times 96500\times 0.03=2895J/mol=2.895kJ/mol$

$log{K}_c=\frac{n{E}_{cell}^o}{0.059}=\frac{1\times 0.03}{0.059}=0.508$

$K_c=3.22$