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Question

Show that the reaction
CO(g)+12O2(g)CO2(g) at 300K
is spontaneous and exothermic, when the standard entropy change is 0.094kJmol1K1. The values of standard Gibbs free energy of formation of CO2 and CO are 394.4 and 137.2kJmol1, respectively.

A
ΔG=257.2kJ, spontaneous
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B
ΔG=+257.2kJ,non spontaneous
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C
ΔG=257.2kJ, non spontaneous
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D
None of these
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Solution

The correct option is A ΔG=257.2kJ, spontaneous
The balanced chemical reaction for the combustion of CO to CO2 is as shown.
CO(g)+12O2(g)CO2(g)
The expression for the standard Gibbs free energy change during the reaction is
ΔG={G(CO2)[G(CO)+12G(O2)]}
={394.4[137.2+0]}
=257.2kJ
The standard entropy change for the reaction is
ΔS=0.094kJmol1K1
Gibbs-Helmholtz equation gives the relationship between the standard Gibbs free energy change, the standard enthalpy change and the standard entropy change for the reaction.
ΔG=ΔHTΔS
or 257.2=ΔH300×(0.094)
or ΔH=285.4kJ
The reaction is spontaneous because ΔG is negative.
The reaction is exothermic because ΔH is negative.

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