Answer:
[tex]E^{0}[/tex] for [tex]Zn^{2+}\mid Zn[/tex] system would be -1.53 V
Explanation:
Determination of standard reduction potential of any system is done by placing the system in cathode and a reference half cell in anode and then evaluate the cell potential. The cell potential is the standard reduction potential of the system.
So [tex]E_{cell}^{0}=E_{system}^{0}-E_{reference}^{0}[/tex]
As [tex]E_{H^{+}\mid H_{2}}^{0}[/tex] is equal to 0 therefore cell potential is equal to reduction potential of any system by taking hydrogen electrode as a reference.
[tex]E_{Zn^{2+}\mid Zn}^{0}[/tex] equal to -0.76 V with respect to hydrogen
[tex]E_{Fe^{3+}\mid Fe^{2+}}^{0}[/tex] equal to 0.77 V with respect to hydrogen
Therefore standard reduction potential of [tex]Zn^{2+}\mid Zn[/tex] system when [tex]Fe^{3+}\mid Fe^{2+}[/tex] system is taken as reference is-
[tex]E_{cell}^{0}=E_{Zn^{2+}\mid Zn}^{0}-E_{Fe^{3+}\mid Fe^{2+}}^{0}[/tex]
= -0.76 V - 0.77 V
= -1.53 V
