The standard half-cell reduction potential for Ag ⁺ Ag is 0.7991 ~V at 25^ C . Given the experimental value K_ s p =1.56 10⁻¹⁰ for AgCl , calculate the standard half-cell reduction potential for the Ag AgCl electrode.

Step-by-step solution

For the desired reaction, AgCl +1 e⁻ Ag + Cl ⁻, E^ = - _r G^ (1) F The needed _r G^ can be obtained by adding the values of _r G^ for the reactions aligned & Ag ⁺+1 e⁻ Ag ; G^ =-n F E^ & AgCl Ag ⁺+ Cl ⁻ ; G^ =-R T K_ s p , giving & _r G^ =-(1 ~mol ) (9.648 10^4 ~J ~mol ⁻¹ ~V ⁻¹ )(0.7991 ~V ) & - (8.314 JK ⁻¹ ~mol ⁻¹ )(298 ~K ) (1.56 10⁻¹⁰ ) & =-77.10 ~kJ +55.95 ~kJ =-21.15 ~kJ aligned The potential is E^ = -(-21.15) (1)(96.485) =+0.2192 ~V .