The E^°(M⁺/M) of the cell, SHE||MX|M can be obtained from the plot of (E_cell is the cell potential and m is the molality of ideal dilute solution of MX)

Concept:

• The standard hydrogen electrode (SHE) is used as a reference electrode with any other electrode. The standard electrode potential for a standard hydrogen electrode (SHE) is taken as zero (0) at 298K temperature.
• The half-cell reaction of SHE can be written as 

           \(2{H^ + }(aq) + 2{e^ - } \to {H_2}(g)\) and \({E_{SHE}} = 0\).

• This half-cell reaction generally takes place on a platinum electrode. The pressure of the hydrogen gas present in the half cell is 1 bar.

Explanation:

• From the Nerst equation, for a standard hydrogen electrode (SHE) we get

\({E_{cell}} = {E_{cell}}^0 - {{RT} \over {nF}}\ln \left( {{{{p_{{H_2}}}} \over {{{\left[ {{H^ + }} \right]}_2}\left[ {{M^ + }} \right]}}} \right)\)

\({E_{cell}} = {E_{cell}}^0 - {{RT} \over {nF}} \times 2.303\log \left( {{{{p_{{H_2}}}} \over {{{\left[ {{H^ + }} \right]}_2}\left[ {{M^ + }} \right]}}} \right)\)

\({E_{cell}} = {E_{cell}}^0 + {{RT} \over {nF}} \times 2.303\log \left( {\left[ m \right]} \right)\)

as, \({{p_{{H_2}}}}\)=1 bar, \(\left[ {{H^ + }} \right]\)=1 M, and [M⁺]=m.

• By comparing the equation with the equation of a straight line (y = mx +c). we got intercept = \({E_{cell}}^0\)  by plotting Ecell against (T log m).

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• Thus, the E°(M+/M) of the cell, SHE||MX|M can be obtained from the plot of (Ecell is the cell potential and m is the molality of ideal dilute solution of MX) Ecell against (T log m).

Conclusion:-

So, The E°(M+/M) of the cell, SHE||MX|M can be obtained from the plot of (Ecell is the cell potential and m is the molality of ideal dilute solution of MX) Ecell against (T log m)