A chemist designs an ion-specific probe for measuring [Ag⁺] in an NaCl solution saturated with AgCl. One halfcell has an Ag-wire electrode immersed in the unknown AgCl-saturated NaCl solution. It is connected through a salt bridge to the other half-cell, which has a calomel reference electrode [a platinum wire immersed in a paste of mercury and calomel (Hg₂Cl₂)] in a saturated KCl solution. The measured E_{\text {cell }} is 0.060 V.(a) Given the following standard half-reactions, calculate [Ag⁺]. Calomel: Hg₂Cl₂(s) + 2e⁻ → 2Hg(l) + 2Cl⁻(aq) E°=0.24VSilver Ag⁺(aq) + e⁻ → Ag(s) E° = 0.80 V(Hint: Assume that [Cl⁻] is so high that it is essentially constant.)

Respuesta :

{Ag^+] is 2.759 M.

Given ,

Calomel: Hg2Cl2 + 2e^- ==> 2Hg(l) + 2Cl^- (aq)   ,  E^0 = 0.24V

Silver :  Ag^+ (aq) + e^- ==> Ag(s)   ,   E^0 = 0.80 V

Ecell = 0.060V

We know , E^0 cell =( 0.80-0.24)V =0.56 V

According the Nernst equation ,

Ecell = E^0cell - 0.0592/2 log [product/reactant ]

Ecell =  E^0cell - 0.0592/2 log {[Ag^+]2/[Cl^-]2}

0.060 = 0.56 - 0.0592/2log{[Ag^+]2/[1]}

0.5 = 0.0592/2 ( 2 log[Ag^+] )

0.5/0.0592= log [Ag^+]

taking antilog on both sides ,

[Ag^+] =2.759 M

Hence , [Ag^+] is 2.759 M .

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