Ore is a naturally occuring rock found in Earth's crust that contains valuable minerals and metals. In an experiment, a researcher dissolved a sample of ore containing an unknown amount of iron in HCl(aq). The resulting aqueous solution, which contained both Fe2+(aq) and Fe3+(aq), was poured through a Jones reductor column containing Zn(Hg)(s) to convert all iron ions into a single oxidation state. The conversion of Fe3+(aq) to Fe2+(aq) in the Jones reductor column is shown in Figure 1.Figure 1 Jones reductor column used for the conversion of Fe3+(aq) to Fe2+(aq). The resulting Fe2+(aq) solution was collected using a syringe.To determine the total amount of iron in the sample, the Fe2+(aq) solution was then transferred to a container and titrated with 0.1 M K2Cr2O7(aq), which resulted in the conversion of Fe2+(aq) to Fe3+(aq) in an irreversible process. A reference electrode was used to monitor the solution potential as a function of K2Cr2O7(aq) volume added, and the equivalence point of the solution was reached after the addition of 9.50 mL of K2Cr2O7(aq). A schematic of the experimental setup is shown in Figure 2.Figure 2 Experimental setup for the titration of Fe2+(aq) with K2Cr2O7(aq) under acidic conditionsIn a second experiment, the researcher prepared another sample of Fe2+(aq) but used a 0.1 M I3−(aq) titrant solution instead of K2Cr2O7(aq).The standard reduction potentials for the species involved in the experiments are given in Table 1.Table 1 Standard reduction potentialsReduction half-reaction E°(V)Cr2O72−(aq) + 14 H+(aq) + 6 e− → 2 Cr3+(aq) + 7 H2O(l) +1.33Fe3+(aq) + e− → Fe2+(aq) +0.76I3−(aq) + 2 e− → 3 I−(aq) +0.53Zn2+(aq) + Hg(l) + 2 e− → Zn(Hg)(s) −0.76 Question 26Does the redox reaction between Cr2O72−(aq) and Fe2+(aq) require energy input?A.Yes; ∆G° = +2.09nF J/mol.B.Yes; ∆G° = +0.57nF J/mol.C.No; ∆G° = −0.57nF J/mol.D.No; ∆G° = −2.09nF J/mol.
Question
Ore is a naturally occuring rock found in Earth's crust that contains valuable minerals and metals. In an experiment, a researcher dissolved a sample of ore containing an unknown amount of iron in HCl(aq). The resulting aqueous solution, which contained both Fe2+(aq) and Fe3+(aq), was poured through a Jones reductor column containing Zn(Hg)(s) to convert all iron ions into a single oxidation state. The conversion of Fe3+(aq) to Fe2+(aq) in the Jones reductor column is shown in Figure 1.Figure 1 Jones reductor column used for the conversion of Fe3+(aq) to Fe2+(aq). The resulting Fe2+(aq) solution was collected using a syringe.To determine the total amount of iron in the sample, the Fe2+(aq) solution was then transferred to a container and titrated with 0.1 M K2Cr2O7(aq), which resulted in the conversion of Fe2+(aq) to Fe3+(aq) in an irreversible process. A reference electrode was used to monitor the solution potential as a function of K2Cr2O7(aq) volume added, and the equivalence point of the solution was reached after the addition of 9.50 mL of K2Cr2O7(aq). A schematic of the experimental setup is shown in Figure 2.Figure 2 Experimental setup for the titration of Fe2+(aq) with K2Cr2O7(aq) under acidic conditionsIn a second experiment, the researcher prepared another sample of Fe2+(aq) but used a 0.1 M I3−(aq) titrant solution instead of K2Cr2O7(aq).The standard reduction potentials for the species involved in the experiments are given in Table 1.Table 1 Standard reduction potentialsReduction half-reaction E°(V)Cr2O72−(aq) + 14 H+(aq) + 6 e− → 2 Cr3+(aq) + 7 H2O(l) +1.33Fe3+(aq) + e− → Fe2+(aq) +0.76I3−(aq) + 2 e− → 3 I−(aq) +0.53Zn2+(aq) + Hg(l) + 2 e− → Zn(Hg)(s) −0.76 Question 26Does the redox reaction between Cr2O72−(aq) and Fe2+(aq) require energy input?A.Yes; ∆G° = +2.09nF J/mol.B.Yes; ∆G° = +0.57nF J/mol.C.No; ∆G° = −0.57nF J/mol.D.No; ∆G° = −2.09nF J/mol.
Solution
To answer this question, we need to calculate the Gibbs free energy change (∆G°) for the redox reaction between Cr2O72−(aq) and Fe2+(aq). The Gibbs free energy change can be calculated using the Nernst equation:
∆G° = -nFE°
where:
- n is the number of electrons transferred in the redox reaction,
- F is the Faraday constant (96485 C/mol), and
- E° is the standard cell potential.
The standard cell potential can be calculated from the standard reduction potentials given in Table 1. For the redox reaction between Cr2O72−(aq) and Fe2+(aq), the reduction half-reactions are:
Cr2O72−(aq) + 14 H+(aq) + 6 e− → 2 Cr3+(aq) + 7 H2O(l) E° = +1.33 V Fe3+(aq) + e− → Fe2+(aq) E° = +0.76 V
The overall cell reaction is obtained by multiplying the second equation by 6 and adding it to the first equation, which gives:
Cr2O72−(aq) + 6 Fe2+(aq) + 14 H+(aq) → 2 Cr3+(aq) + 6 Fe3+(aq) + 7 H2O(l)
The standard cell potential for this reaction is E° = E°(Cr2O72−/Cr3+) - E°(Fe3+/Fe2+) = 1.33 V - 0.76 V = 0.57 V.
The number of electrons transferred in the overall reaction is 6. Therefore, the Gibbs free energy change is:
∆G° = -nFE° = -6 * 96485 C/mol * 0.57 V = -3295457 J/mol = -3.295457 kJ/mol
Since ∆G° is negative, the reaction is spontaneous and does not require energy input. Therefore, the correct answer is:
C. No; ∆G° = −0.57nF J/mol.
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