Please Help with this ecell question

Question

Calculate the potential for each cell as written at 25 ∘C.. Indicate whether the metal electrode in the half‑reaction opposite the standard hydrogen electrode, S.H.E., would be the anode or the cathode if the cell was shorted and electrons were allowed to flow freely.

S.H.E.‖‖Zn2+(aq,0.0470 M)∣∣Zn(s). 𝐸∘Zn2+/Zn=−0.762 V

Ecell= Is the Zn electrode the anode or cathode?

Pt(s)∣∣V3+(aq,0.375 M),V2+(aq,0.00800 M)‖‖S.H.E. 𝐸∘V3+/V2+=−0.255 

Ecell=. is the pt electrode the anode or cathode?

Answer 1

SHE|| Zn²⁺(aq.0.0470 M)| Zn(s), the Reaction is: Zn²⁺(aq)+2e-⟶Zn(s)

Oxidation: H₂(g)⟶2H⁺(aq)+2e−

Overall cell reaction: Zn²⁺ (aq)+ H₂(g)⟶Zn(s)+2H⁺(aq)

The standard cell potential: E° = E°_red - E°_ox. Potential for Zn elec. is −0.762 V. Cell potential of the SHE electrode is 0 V. E°=-0.762-0, E°=-0.762 V. To calculate (Ecell), we will be using Nernst equation.

E_cell=E⁰(RT/nF)lnQ

where n is the number of moles of electrons (2 in this case) transferred during the oxidation-reduction reaction and Q is reaction quotient (reaction equilibrium shown above). At 25^∘C the term RT/nF is 0.0591n.

E_cell=-0.762 V-(0.059/2)log([1]²/.0470 [1]²)

E_cell=-0.762 V-(0.0296)(1.33) E_cell=-0.80 V

Second, let’s solve for the Pt electrode! Pt|V⁺³(0.375 M)| V⁺²(0.008 M)|| SHE

The reduction reaction: 2H⁺(aq)+2e-⟶H₂(g), while oxidation reaction: 2V⁺² (g)⟶2V⁺³ (aq)+2e−

The overall cell reaction: 2V⁺² (aq)+2H⁺(aq)⟶2V⁺³ (aq)+H₂(g)

The cell potential of the electrode containing V⁺²/V⁺³ = −0.255 V.

Then, E° = E°_red - E°_{ox ,} E⁰=0 V− (−0.255 V)=0.255 V

It is given that the concentration of V³⁺ and V²⁺is 0.375 M and 0.008 M respectively.

The reaction quotient of the cell (the same way as above except that we have in this case V³⁺ and V²⁺), hence: (Q) = 2197.26 On substituting the value in the Nernst equation: E_cell = 0.255 V - (0.0296) log(2197.26), E_cell = 0.156 V

Conclusion: Zn electrode with the potential of −0.80 V acts as a cathode. Pt electrode with the potential of 0.156 V acts as an anode.