<u>Answer:</u> The activity KI for the given electrochemical cell is 0.0310
<u>Explanation:</u>
The given chemical cell follows:
![Ag|AgCl(s),NaCl(aq.,a=0.1)||KI(aq,a=x)|I_2(s)|Pt](https://tex.z-dn.net/?f=Ag%7CAgCl%28s%29%2CNaCl%28aq.%2Ca%3D0.1%29%7C%7CKI%28aq%2Ca%3Dx%29%7CI_2%28s%29%7CPt)
<u>Oxidation half reaction:</u> ![Ag(s)+Cl^-(aq.,)\rightarrow AgCl(s)+e^-;E^o_{AgCl/Cl^-}=0.22V](https://tex.z-dn.net/?f=Ag%28s%29%2BCl%5E-%28aq.%2C%29%5Crightarrow%20AgCl%28s%29%2Be%5E-%3BE%5Eo_%7BAgCl%2FCl%5E-%7D%3D0.22V)
<u>Reduction half reaction:</u> ![\frac{1}{2}I_2(s)+e^-\rightarrow I^-(aq.);E^o_{I_2/I^-}=0.54V](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7DI_2%28s%29%2Be%5E-%5Crightarrow%20I%5E-%28aq.%29%3BE%5Eo_%7BI_2%2FI%5E-%7D%3D0.54V)
<u>Net cell reaction:</u> ![Ag(s)+Cl^-(aq.)+\frac{1}{2}I_2(s)\rightarrow AgCl(s)+I^-(aq.)](https://tex.z-dn.net/?f=Ag%28s%29%2BCl%5E-%28aq.%29%2B%5Cfrac%7B1%7D%7B2%7DI_2%28s%29%5Crightarrow%20AgCl%28s%29%2BI%5E-%28aq.%29)
Oxidation reaction occurs at anode and reduction reaction occurs at cathode.
To calculate the
of the reaction, we use the equation:
![E^o_{cell}=E^o_{cathode}-E^o_{anode}](https://tex.z-dn.net/?f=E%5Eo_%7Bcell%7D%3DE%5Eo_%7Bcathode%7D-E%5Eo_%7Banode%7D)
Putting values in above equation, we get:
![E^o_{cell}=0.54-(0.22)=0.32V](https://tex.z-dn.net/?f=E%5Eo_%7Bcell%7D%3D0.54-%280.22%29%3D0.32V)
To calculate the EMF of the cell, we use the Nernst equation, which is:
![E_{cell}=E^o_{cell}-\frac{0.059}{n}\log \frac{a_{I^-}}{a_{Cl^-}}](https://tex.z-dn.net/?f=E_%7Bcell%7D%3DE%5Eo_%7Bcell%7D-%5Cfrac%7B0.059%7D%7Bn%7D%5Clog%20%5Cfrac%7Ba_%7BI%5E-%7D%7D%7Ba_%7BCl%5E-%7D%7D)
where,
= electrode potential of the cell = 0.350 V
= standard electrode potential of the cell = +0.32 V
n = number of electrons exchanged = 1
![a_{Cl^-}=0.1](https://tex.z-dn.net/?f=a_%7BCl%5E-%7D%3D0.1)
![a_{I^-}=x](https://tex.z-dn.net/?f=a_%7BI%5E-%7D%3Dx)
Putting values in above equation, we get:
![0.350=0.32-\frac{0.059}{1}\times \log(\frac{x}{0.1})](https://tex.z-dn.net/?f=0.350%3D0.32-%5Cfrac%7B0.059%7D%7B1%7D%5Ctimes%20%5Clog%28%5Cfrac%7Bx%7D%7B0.1%7D%29)
![x=0.0310](https://tex.z-dn.net/?f=x%3D0.0310)
Hence, the activity KI for the given electrochemical cell is 0.0310