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NEET CHEMISTRYElectrochemistryHard

Question

The three cells with their EcellE^{\circ}_{cell} values are given below:

  1. FeFe2+Fe3+Fe ;\0.404 VFe|Fe^{2+}||Fe^{3+}|Fe \ ; \0.404\text{ V}
  2. FeFe2+Fe3+,Fe2+Pt ;\1.211 VFe|Fe^{2+}||Fe^{3+}, Fe^{2+}|Pt \ ; \1.211\text{ V}
  3. FeFe3+Fe3+,Fe2+Pt ;\0.807 VFe|Fe^{3+}||Fe^{3+}, Fe^{2+}|Pt \ ; \0.807\text{ V} The standard Gibbs free energy change values for three cells are, respectively: (F represents the charge on 1 mole1\text{ mole} of electrons.)

A

–1.212 F, –1.211 F, –0.807 F

B

+2.424 F, +2.422 F, +2.421 F

C

–0.808 F, –2.422 F, –2.421 F

D

–2.424 F, –2.422 F, –2.421 F

Step-by-Step Solution

The relationship between the standard Gibbs free energy change (ΔG\Delta G^{\circ}) and standard cell potential (EcellE^{\circ}_{cell}) is given by: ΔG=nFEcell\Delta G^{\circ} = -nFE^{\circ}_{cell}

For Cell 1: FeFe2+Fe3+FeFe|Fe^{2+}||Fe^{3+}|Fe Oxidation at anode: FeFe2++2eFe \rightarrow Fe^{2+} + 2e^- Reduction at cathode: Fe3++3eFeFe^{3+} + 3e^- \rightarrow Fe To balance the electrons, we multiply the oxidation half-reaction by 3 and the reduction half-reaction by 2. Total electrons transferred, n=6n = 6. ΔG1=6×F×0.404=2.424 F\Delta G^{\circ}_1 = -6 \times F \times 0.404 = -2.424\text{ F}

For Cell 2: FeFe2+Fe3+,Fe2+PtFe|Fe^{2+}||Fe^{3+}, Fe^{2+}|Pt Oxidation at anode: FeFe2++2eFe \rightarrow Fe^{2+} + 2e^- Reduction at cathode: Fe3++eFe2+Fe^{3+} + e^- \rightarrow Fe^{2+} To balance the electrons, we multiply the reduction half-reaction by 2. Total electrons transferred, n=2n = 2. ΔG2=2×F×1.211=2.422 F\Delta G^{\circ}_2 = -2 \times F \times 1.211 = -2.422\text{ F}

For Cell 3: FeFe3+Fe3+,Fe2+PtFe|Fe^{3+}||Fe^{3+}, Fe^{2+}|Pt Oxidation at anode: FeFe3++3eFe \rightarrow Fe^{3+} + 3e^- Reduction at cathode: Fe3++eFe2+Fe^{3+} + e^- \rightarrow Fe^{2+} To balance the electrons, we multiply the reduction half-reaction by 3. Total electrons transferred, n=3n = 3. ΔG3=3×F×0.807=2.421 F\Delta G^{\circ}_3 = -3 \times F \times 0.807 = -2.421\text{ F}

The respective values are 2.424 F-2.424\text{ F}, 2.422 F-2.422\text{ F}, and 2.421 F-2.421\text{ F}.

Exam Context & Concepts Covered

This question aligns with the NEET CHEMISTRY syllabus, specifically targeting concepts from Electrochemistry. Mastering this topic is crucial for scoring well in the upcoming medical entrance examinations. Solving conceptually related problems will help you understand the nuances of these concepts and improve your problem-solving speed.

CHEMISTRYElectrochemistryecirccellvaluesfefefefefefefefefefe

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