Question

Consider the following cell reaction at $298K$ :
$2{Ag}^{+}+Cd\to 2Ag+{Cd}^{2+}$
The standard reduction potentials $\left(E^o\right)$ for ${Ag}^{+}/Ag$ and ${Cd}^{2+}/Cd$ are $0.80V$ and $-0.40V$ respectively :
(1) Write the cell representation.
(2) What will be the emf of the cell if the concentration of ${Cd}^{2+}$ is $0.1M$ and that of ${Ag}^{+}$ is $0.2M$?
(3) Will the cell work spontaneously for the condition given in (2) above?

Answer 1

(1) $Cd\left|{Cd}_{\left(0.1M\right)}^{2^{+}}\right|\left|2{Ag}_{\left(0.2M\right)}^{2^{+}}\right|2Ag$
Cell Representation
(2) $E_{\left(red\right)cell}^o=E_{\left(red\right)cathode}^o-E_{\left(red\right)anode}^o$
$=1.2$
$[n=2]$
$E_{cell}=E_{\left(red\right)cell}^o-\frac{0.059}{n}\log \left[\frac{M}{M^{n+}}\right]$
$=1.2-\frac{0.059}{n}\log \frac{\left[2Ag\right]\left[{Cd}^{2+}\right]}{\left[Cd\right]\left[{Ag}^{+}\right]}$
$=1.2-\frac{0.059}{2}\log \left[\frac{0.1}{0.04}\right]$
$E_{cell}=1.1882177$ volt
(3) Since $E_{cell}$ is +ve it will also favour spontaneous.
$\Delta Cl=-nF{E}_{cell}=-229.32kJ$
since $\Delta Cl$ also (-ve) it will also favour spontaneous reactions.