Question

Use the tabulated half-cell potentials below to calculate AG ( in Kilojoules for the following balanced redox reaction. F= 96,500 J/. mole e Pb2+(aq) + Cu(s) - Pb(s) + Cu2+(aq) Cu2+ (aq) + 2e -> Cu(s) E". Cu = -0.34 Volt Pb2+ (aq) + 2e-> Pb(s) E,Pb = -0.13 volt a. -41 kJ b. -81 kJ C. +46 kJ d. +91 kl e..91 kb

Answer 1

1st Question:

The ΔG⁰ of a reaction is related to the cell potential(E⁰_cell) as follows:

$\Delta G^{\circ}=-nFE^{\circ}_{cell}$

where n is the number of moles of electrons transferred in the cell reaction.

The E⁰_cell of a reaction is given by:

$E^{\circ}_{cell}=E^{\circ}_{cathode}-E^{\circ}_{anode}$

where E⁰_anode and E⁰_cathode represents the standard reduction potentials of anode and cathode respectively.

Cathode is the half cell in which reduction happens. Here Pb²⁺ is getting reduced to Pb. Therefore Pb is the cathode. Therefore we have:

E⁰_cathode = -0.13 V

Anode is the half cell in which oxidation happens. Here Cu is getting oxidized to Cu²⁺. Therefore Cu is the anode. Therefore we have:

E⁰_anode = -0.34 V

Therefore we have:

$E^{\circ}_{cell}=E^{\circ}_{cathode}-E^{\circ}_{anode}$

$E^{\circ}_{cell}=-0.13V-(-0.34V)=0.21\: V$

Therefore we have:

E⁰_cell = 0.21 V

n = 2 mole e (since 2 electrons are involved in the reaction)

F = 96500 J/V. mole e

Therefore ΔG⁰ of the reaction is:

$\Delta G^{\circ}=-nFE^{\circ}_{cell}$

$\Delta G^{\circ}=-2mole\: e\times 96500\frac{J}{V\cdot mole\: e}\times 0.21V=-41000\: J=-41\: kJ$

Therefore the correct answer is the first option, that is:

a. -41 kJ

2nd Question:

The ΔS⁰_rxn of a reaction is given by:

$\Delta S_{rxn}^{\circ}=\sum S^{\circ}\: of\: products-\sum S^{\circ}\: of\: reactants$

The ΔS⁰ of C₂H₃ is 24 J/mol.K

The ΔS⁰ of C₄H₂ is 18 J/mol.K

The ΔS⁰ of H₂ is 3.0 J/mol.K

Therefore ΔS⁰_rxn of the reaction is:

$\Delta S_{rxn}^{\circ}=\sum S^{\circ}\: of\: products-\sum S^{\circ}\: of\: reactants$

$\Delta S_{rxn}^{\circ}=(2mol\times 24J/mol\cdot K)-(1mol\times18J/mol\cdot K+2mol\times 3.0J/mol\cdot K)$

$\Delta S_{rxn}^{\circ}=(48J/K)-(24J/ K)=24\: J/ K$

Therefore the correct answer is the first option, that is:

a. +24 J/K