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Combine the two half-reactions that give the spontaneous cell reaction with the smallest E∘. Fe2+(aq)+2e−→Fe(s) E∘=−0.45V I2(s)+2e−→2I−(aq) E∘=0.54V Cu2+(aq)+2e−→Cu(s) E∘=0.34V

Respuesta :

Answer: The spontaneous cell reaction having smallest [tex]E^o[/tex] is [tex]I_2+Cu\rightarrow Cu^{2+}+2I^-[/tex]

Explanation:

We are given:

[tex]E^o_{(Fe^{2+}/Fe)}=-0.45V\\E^o_{(I_2/I^-)}=0.54V\\E^o_{(Cu^{2+}/Cu)}=0.34V[/tex]

The substance having highest positive [tex]E^o[/tex] potential will always get reduced and will undergo reduction reaction. Here, iodine will always undergo reduction reaction, then copper and then iron.

The equation used to calculate electrode potential of the cell is:

[tex]E^o_{cell}=E^o_{oxidation}+E^o_{reduction}[/tex]

The combination of the cell reactions follows:

  • Case 1:

Here, iodine is getting reduced and iron is getting oxidized.

The cell equation follows:

[tex]I_2(s)+Fe(s)\rightarrow Fe^{2+}(aq.)+2I^-(aq.)[/tex]

Oxidation half reaction:  [tex]Fe(s)\rightarrow Fe^{2+}(aq.)+2e^-[/tex]   [tex]E^o_{oxidation}=0.45V[/tex]

Reduction half reaction:  [tex]I_2(s)+2e^-\rightarrow 2I_-(aq.)[/tex]   [tex]E^o_{reduction}=0.54V[/tex]

[tex]E^o_{cell}=0.45+0.54=0.99V[/tex]

Thus, this cell will not give the spontaneous cell reaction with smallest [tex]E^o_{cell}[/tex]

  • Case 2:

Here, iodine is getting reduced and copper is getting oxidized.

The cell equation follows:

[tex]I_2(s)+Cu(s)\rightarrow Cu^{2+}(aq.)+2I^-(aq.)[/tex]

Oxidation half reaction:  [tex]Cu(s)\rightarrow Cu^{2+}(aq.)+2e^-[/tex]   [tex]E^o_{oxidation}=-0.34V[/tex]

Reduction half reaction: [tex]I_2(s)+2e^-\rightarrow 2I_-(aq.)[/tex]   [tex]E^o_{reduction}=0.54V[/tex]

[tex]E^o_{cell}=-0.34+0.54=0.20V[/tex]

Thus, this cell will give the spontaneous cell reaction with smallest [tex]E^o_{cell}[/tex]

  • Case 3:

Here, copper is getting reduced and iron is getting oxidized.

The cell equation follows:

[tex]Cu^{2+}(aq.)+Fe(s)\rightarrow Fe^{2+}(aq.)+Cu(s)[/tex]

Oxidation half reaction:  [tex]Fe(s)\rightarrow Fe^{2+}(aq.)+2e^-[/tex]   [tex]E^o_{oxidation}=0.45V[/tex]

Reduction half reaction:  [tex]Cu^{2+}(aq.)+2e^-\rightarrow Cu(s)[/tex]   [tex]E^o_{reduction}=0.34V[/tex]

[tex]E^o_{cell}=0.45+0.34=0.79V[/tex]

Thus, this cell will not give the spontaneous cell reaction with smallest [tex]E^o_{cell}[/tex]

Hence, the spontaneous cell reaction having smallest [tex]E^o[/tex] is [tex]I_2+Cu\rightarrow Cu^{2+}+2I^-[/tex]

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