Answer : The value of
and K is, -180 kJ/mol and ![3.6\times 10^{31}](https://tex.z-dn.net/?f=3.6%5Ctimes%2010%5E%7B31%7D)
Explanation :
The balanced cell reaction will be,
![Pb(s)+2Ag^+(aq)\rightarrow Pb^{2+}(aq)+2Ag(g)](https://tex.z-dn.net/?f=Pb%28s%29%2B2Ag%5E%2B%28aq%29%5Crightarrow%20Pb%5E%7B2%2B%7D%28aq%29%2B2Ag%28g%29)
The half-cell reactions are:
Oxidation reaction (anode) : ![Pb(s)\rightarrow Pb^{2+}(aq)+2e^-](https://tex.z-dn.net/?f=Pb%28s%29%5Crightarrow%20Pb%5E%7B2%2B%7D%28aq%29%2B2e%5E-)
Reduction reaction (cathode) : ![2Ag^+(aq)+2e^-\rightarrow 2Ag(g)](https://tex.z-dn.net/?f=2Ag%5E%2B%28aq%29%2B2e%5E-%5Crightarrow%202Ag%28g%29)
Relationship between standard Gibbs free energy and standard electrode potential follows:
![\Delta G^o=-nFE^o_{cell}](https://tex.z-dn.net/?f=%5CDelta%20G%5Eo%3D-nFE%5Eo_%7Bcell%7D)
where,
= standard Gibbs free energy
F = Faraday constant = 96500 C
n = number of electrons in oxidation-reduction reaction = 2
= standard electrode potential of the cell = 0.93 V
Now put all the given values in the above formula, we get:
![\Delta G^o=-2\times 96500\times 0.93](https://tex.z-dn.net/?f=%5CDelta%20G%5Eo%3D-2%5Ctimes%2096500%5Ctimes%200.93)
![\Delta G^o=-179490J/mol=-179.49kJ/mol\approx -180kJ/mol](https://tex.z-dn.net/?f=%5CDelta%20G%5Eo%3D-179490J%2Fmol%3D-179.49kJ%2Fmol%5Capprox%20-180kJ%2Fmol)
Now we have to calculate the value of 'K'.
![\Delta G^o=-RT\ln K](https://tex.z-dn.net/?f=%5CDelta%20G%5Eo%3D-RT%5Cln%20K)
where,
= standard Gibbs free energy = -180 kJ/mol
R = gas constant = ![8.314\times 10^{-3}kJ/mole.K](https://tex.z-dn.net/?f=8.314%5Ctimes%2010%5E%7B-3%7DkJ%2Fmole.K)
T = temperature = 298 K
K = equilibrium constant = ?
Now put all the given values in the above formula 1, we get:
![-180kJ/mol=-(8.314\times 10^{-3}kJ/mole.K)\times (298K)\times \ln K](https://tex.z-dn.net/?f=-180kJ%2Fmol%3D-%288.314%5Ctimes%2010%5E%7B-3%7DkJ%2Fmole.K%29%5Ctimes%20%28298K%29%5Ctimes%20%5Cln%20K)
![K=3.6\times 10^{31}](https://tex.z-dn.net/?f=K%3D3.6%5Ctimes%2010%5E%7B31%7D)
Therefore, the value of
and K is, -180 kJ/mol and ![3.6\times 10^{31}](https://tex.z-dn.net/?f=3.6%5Ctimes%2010%5E%7B31%7D)