How Do You Calculate the Resonance Energy for CO2 Using Hess's Law?

[mooncrater]

Homework Statement

The question says that:
Calculate the resonance energy for CO₂ from the following
ΔH(C=O)=339 kJ/mol
ΔH(O=O)=498kJ/mol
ΔH(C_(s)→C_(g))=718kJ/mol
ΔH_combustion
(carbon)=-393kJ/mol.

Homework Equations

none

The Attempt at a Solution

I am completely unable to understand how will we make an equation using hess' law including this resonance energy.

 

[Quantum Defect]

Homework Statement

The question says that:
Calculate the resonance energy for CO₂ from the following
ΔH(C=O)=339 kJ/mol
ΔH(O=O)=498kJ/mol
ΔH(C_(s)→C_(g))=718kJ/mol
ΔH_combustion
(carbon)=-393kJ/mol.

Homework Equations

none

The Attempt at a Solution

I am completely unable to understand how will we make an equation using hess' law including this resonance energy.

Try drawing an energy diagram, using the enthalpies. You have a number of different kinds of enthalpies here. The first two are bond dissociation enthalpies:

C=O ----> C (g) + O (g)

The gistof the problem is to compare the energies using bond dissociation enthalpies (approximate) and the heat of combustion of C (g) (exact). The former, does not take into account the delocalization of electrons over the entire CO2 frame, while the latter does.

 

[mooncrater]

Hmmm...so after reading your post what I did is:
Consider two paths to produce CO₂:
C_(S)→C_(g) which can be converted into CO₂ by the following two methods(what I made out):

1. C_(g)→CO₂[combustion]
2. C_(g)+O₂→CO₂

And the resonance energy should be the difference of the enthalpy of formation of CO₂...
So heat of combustion given is -393 kJ/mol + heat of sublimation ----(for 1st path)=325 kJ/mol
And for the second part:
BDE (O=O)-2BDE(C=O)+ Heat of sublimation.=538 kJ/mol
And their difference=-213 kJ /mol
But the answer given is -913 kJ/mol.
So where am I wrong?

 

[Quantum Defect]

Hmmm...so after reading your post what I did is:
Consider two paths to produce CO₂:
C_(S)→C_(g) which can be converted into CO₂ by the following two methods(what I made out):

1. C_(g)→CO₂[combustion]
2. C_(g)+O₂→CO₂

And the resonance energy should be the difference of the enthalpy of formation of CO₂...
So heat of combustion given is -393 kJ/mol + heat of sublimation ----(for 1st path)=325 kJ/mol
And for the second part:
BDE (O=O)-2BDE(C=O)+ Heat of sublimation.=538 kJ/mol
And their difference=-213 kJ /mol
But the answer given is -913 kJ/mol.
So where am I wrong?

Here are the steps that I would use in making the ladder of enthalpies:

C(s) [+ O2 (g) ] --> C (g) [ + O2 (g) ]
O=O (g) --> 2 O (g) (Use bond enthalpy O=O)
C(s) + O2 (g) --> CO2 (g)
CO2 (g) --> C (g) + 2 O (g) (2 x bond enthalpy C=O)

The number you have for C=O is way too small (it is the value for a C-O single bond) it should be closer to 732 kJ/mol http://wps.prenhall.com/wps/media/objects/4678/4790506/ch07_02.htm

Create a ladder of species on an enthalpy scale. Compare the enthalpies for C(s) + O2 (g) --> CO2 (g) from the enthalpy of combustion with the enthalpy using the heat of subblimation and the bond enthalpies.

 

[Raghav Gupta]

CO + 1/2 O₂ → CO₂
So I think resonance energy of CO₂ should be bond dissociation energy of CO + 1/2 bond dissociation energy of O₂ ?
I may be wrong here, but what wrong I am doing?

 

[Quantum Defect]

CO + 1/2 O₂ → CO₂
So I think resonance energy of CO₂ should be bond dissociation energy of CO + 1/2 bond dissociation energy of O₂ ?
I may be wrong here, but what wrong I am doing?

The "resonance energy" is a bit of a misnomer in the case of CO2. Sure, you have resonance structures with different kinds of mulitple bonds
(triple-single <--> double-double <--> single-triple), but most of the energy lowering is due to the fact that the pi electrons are in orbitals delocalized over the entire molecule, which is not there if you think only about the Lewis stuctures -- where you would draw two p-pi bonds in planes at right angles to each other.

 

[Raghav Gupta]

So what is that energy that I am talking in post 5?