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SOLUTIONSMANUAL TO ACCOMPANY ATKINS' PHYSICAL CHEMISTRY 199
�e standard reaction Gibbs energy is related to the standard cell poten-
tial according to [6C.3–221], ∆rG−○ = −νFE−○cell.�erefore
∆rG−○ = −νFE−○cell = −4 × (96485Cmol−1) × (+1.57 V)
= −6.1 × 102 kJmol−1
E6D.4(b) Under basic conditions, the required reduction half-equations and their stan-
dard electrode potentials are
R: 2Cl2(g) + 4e− → 4Cl−(aq) E−○(R) = +1.36 V
L: O2(g) + 2H2O(l) + 4e− → 4OH−(aq) E−○(L) = +0.40 V
�e cell reaction (R−L) is 2Cl2(g) + 4OH−(aq)→ 4Cl−(aq) +O2(g) + 2H2O(l).
�e standard cell potential is
E−○cell = E−○(R) − E−○(L) = (+1.36 V) − (+0.40 V) = +0.96 V
�e positive value of E−○cell indicates that yes , chlorine has a thermodynamic
tendency to oxidize water to oxygen gas under standard conditions in basic
solution.
Solutions to problems
P6D.2 (a) �e reduction half-reactions for the reduction ofCO2 andCO tomethane
are
R: CO(g) + 6H+(aq) + 6e− → CH4(g) +H2O(l)
L: CO2(g) + 8H+(aq) + 8e− → CH4(g) + 2H2O(l)
�e right-hand reduction half-reaction is multiplied by four and the le�-
half reduction half-reaction by three so that both involve the same num-
ber of electrons, ν = 24. Subtraction of the le�-hand half-reaction from
the right-hand half-reaction gives the overall cell reaction as
4CO(g) + 2H2O(l)→ CH4(g) + 3CO2(g) ν = 24
�e standard reaction Gibbs energy of this reaction is calculated using
standard formation Gibbs energies from the Resource section.
∆rG−○ = 3∆fG−○(CO2 , g) + ∆fG−○(CH4 , g)
− 4∆fG−○(CO, g) − 2∆fG−○(H2O, l)
= 3 × (−394.36 kJmol−1) + (−50.72 kJmol−1)
− 4 × (−137.17 kJmol−1) − 2 × (−237.13 kJmol−1)
= −210.86 kJmol−1
�e negative value of ∆rG−○ indicates that the cell reaction as written is
spontaneous under standard conditions.�is means that, in the sponta-
neous cell reaction, reduction is taking place at the right-hand electrode.
�erefore the right-hand electrode is the cathode.