This question involves calculating the standard electrode potential of the AgCl/Ag, Cl⁻ electrode using the Nernst equation for the given electrochemical cell. The cell is:

Pt(s) | H₂(g, 1 bar) | HCl(aq) | AgCl(s) | Ag(s) | Pt(s)

This is a galvanic cell where the hydrogen electrode (left) is the anode and the silver-silver chloride electrode (right) is the cathode. The overall cell reaction is:

$\frac{1}{2}{\mathrm{H}}_2\left(g\right)+\mathrm{AgCl}\left(s\right)\to \mathrm{Ag}\left(s\right)+{\mathrm{H}}^{+}\left(\mathrm{aq}\right)+{\mathrm{Cl}}^{-}\left(\mathrm{aq}\right)$

The Nernst equation for this cell is:

$E=E_{\mathrm{cell}}°-\frac{2.303\mathrm{RT}}{F}\log \left(\frac{\left[{\mathrm{H}}^{+}\right]\left[{\mathrm{Cl}}^{-}\right]}{P_{{\mathrm{H}}_2}^{1/2}}\right)$

Given that the HCl concentration is 10⁻⁶ molal, we can assume [H⁺] = [Cl⁻] = 10⁻⁶ M. The pressure of H₂ gas is 1 bar, so P_H₂ = 1. The cell potential E is given as 0.92 V. The constant (2.303RT/F) is given as 0.06 V. We need to find E° for the AgCl/Ag, Cl⁻ electrode. Note that the standard cell potential E°_cell is related to the standard electrode potentials:

$E_{\mathrm{cell}}°=E_{\mathrm{cathode}}°-E_{\mathrm{anode}}°=E_{\mathrm{AgCl}/\mathrm{Ag},{\mathrm{Cl}}^{-}}°-E_{{\mathrm{H}}^{+}/{\mathrm{H}}_2}°$

By definition, E° for the standard hydrogen electrode (SHE) is 0 V. Therefore, E°_cell = E°_AgCl/Ag,Cl⁻.

Now, plug the known values into the Nernst equation:

$0.92=E_{\mathrm{AgCl}/\mathrm{Ag},{\mathrm{Cl}}^{-}}°-0.06\times \log \left(\frac{\left({10}^{-6}\right)\left({10}^{-6}\right)}{1^{1/2}}\right)$

Simplify the term inside the log:

$\log \left(\frac{{10}^{-12}}{1}\right)=\log \left({10}^{-12}\right)=-12$

So the equation becomes:

$0.92=E_{\mathrm{AgCl}/\mathrm{Ag},{\mathrm{Cl}}^{-}}°-0.06\times (-12)$

$0.92=E_{\mathrm{AgCl}/\mathrm{Ag},{\mathrm{Cl}}^{-}}°+0.72$

Now, solve for E°_AgCl/Ag,Cl⁻:

$E_{\mathrm{AgCl}/\mathrm{Ag},{\mathrm{Cl}}^{-}}°=0.92-0.72=0.20\mathrm{V}$

Therefore, the standard electrode potential is 0.20 V.

Final Answer: 0.20 V

Related Topics and Formulae

Nernst Equation: Used to calculate the electrode potential of a half-cell or the cell potential of an electrochemical cell under non-standard conditions. For a general reduction reaction: aOx + ne⁻ → bRed, the Nernst equation is:

$E=E^{°}-\frac{2.303\mathrm{RT}}{\mathrm{nF}}\log \left(\frac{[\mathrm{Red}{]}^b}{[\mathrm{Ox}{]}^a}\right)$

Standard Hydrogen Electrode (SHE): The reference electrode with a standard potential defined as 0 V at all temperatures. It consists of a platinum electrode coated with platinum black in contact with 1 M H⁺ ion solution and hydrogen gas at 1 bar pressure.

Silver-Silver Chloride Electrode: A common reference electrode. Its half-cell reaction is AgCl(s) + e⁻ → Ag(s) + Cl⁻(aq). Its potential depends on the concentration of Cl⁻ ions.