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### Topic: State function differences for formation of CO2(g) and CO2(aq)  (Read 2191 times)

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#### ajkjmspe

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##### State function differences for formation of CO2(g) and CO2(aq)
« on: July 18, 2022, 01:13:43 PM »
Hello all:

I am a little confused by what is probably a very easy and basic question.

I have the following two reactions:
• C(s) + O2(g) <> CO2(g)
• C(s) + O2(g) <> CO2(aq)
I am given that the standard enthalpy of formation, standard Gibbs free energy of formation, and entropy of formation (respectively) of the reactions is as follows:
• CO2(g) - -393.5 kJ/mol, -394.4 kJ/mol, and 213.6 J/K mol
• CO2(aq) - -413.8 kJ/mol, -386.0 kJ/mol, and 117.6 J/K mol
I am asked to explain why there are differences between the state function values for the two reactions with identical reactants and products that differ only in state.

I explained it like the following:

For the standard enthalpy of formation, since the standard enthalpy of formation for a pure compound is the change in enthalpy when 1 mol of the compound forms and the change in enthalpy equals the change in energy plus pressure times the change in volume, the standard enthalpy of formation of the gaseous state of a compound will be different from the standard enthalpy of formation of the same compound in aqueous solution due to the formation of the gaseous state requiring a bigger change in volume.

For the entropy of formation, since this is the change in entropy from the formation of 1 mole of the compound and the change in entropy depends on the change in enthalpy of a system, different standard enthalpies of formation will result in different entropies of formation.  Also, the change in entropy for the formation of a gas is larger than the change in entropy for the formation of a liquid.

For the standard Gibbs free energy of formation, this is the change in Gibbs free energy that accompanies the formation of 1 mole of a substance.  Since the change in Gibbs free energy depends on the change in enthalpy and the change in entropy, the standard Gibbs free energy of formation will be different for a gas as compared to a liquid.

I would like to know if my answer is on the right track and at least somewhere in the ballpark.

(Also, I am pretty sure there is an easier way to explain why these differences exist.)

#### mjc123

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##### Re: State function differences for formation of CO2(g) and CO2(aq)
« Reply #1 on: July 18, 2022, 06:52:14 PM »
Your numbers are wrong; they don't agree with ΔG = ΔH - TΔS. I suspect you have used (or been given) values for the standard entropy of CO2, not the entropy of formation. (They differ because the standard entropy of an element is not zero). Maybe that doesn't matter, maybe they just want you to explain why the two standard entropy values are different.

You are right about the importance of the change of volume, but note that for equation 1 there is no change in volume (begin and end with 1 mole of gas), whereas in equation 2 there is a reduction in volume as gas is consumed.

Volume is also not the only thing to consider. You might like to draw a Hess's law cycle. If you subtract equation 1 from equation 2 you get the equation
CO2(g)  CO2(aq)
What could you say about the enthalpy and entropy changes of this reaction?

What do you mean by "the change in entropy depends on the change in enthalpy of a system"? Is that true?