June 23, 2021, 10:47:21 PM
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### Topic: Struggling with a problem in Elements of Physical Chemistry 2e  (Read 2455 times)

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#### Gustomer

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##### Struggling with a problem in Elements of Physical Chemistry 2e
« on: July 21, 2018, 10:57:07 PM »
The question is:  Estimate the enthalpy change for the reaction between 1 mol C2H5OH as liquid ethanol, a fuel made by fermenting corn, and O2(g) to yield CO2(g) and H2O(l) under standard conditions by using the bond enthalpies, mean bond enthalpies, and the appropriate standard enthalpies of vaporization.

I follow the suggested method and vaporize and atomize the reactants:
vaporize EtOH(l EtOH(g) (@ 25 °C, I calculated that to be ~42.6 kJ, but at EtOH vapor point, 78 °C, it can be found in the book as 43.5 kJ, so...) 43.5 kJ
dissociate 1 mol C - C bonds     348 kJ
dissociate 1 mol C - O bonds     360 kJ
dissociate 1 mol O - H bonds     463 kJ
dissociate 5 mol C - H bonds   5(412 kJ)
dissociate 3 mol O=O bonds   3(497 kJ)
total endothermic value is 4765.5 kJ

create and condense products
form 2 mol C=O bonds       2(743 kJ)
form 2 mol OC=O bonds     2(531 kJ)
form 3 mol O - H bonds      3(463 kJ)
form 3 mols HO - H bonds  3(492 kJ)
condense 3 mol H2O(g) 3 mol H2O(l)   3(44 kJ)
total exothermic value is 5545 kJ

I know the actual value is -1366 kJ.  The book says the estimated answer using the values in the tables should be -1305 kJ.  My calculations end up far off:  -779.5 kJ
Can anyone see what I am missing?  It's making me a little crazy.
Thanks for any input.

#### Enthalpy

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##### Re: Struggling with a problem in Elements of Physical Chemistry 2e
« Reply #1 on: July 23, 2018, 04:49:39 AM »
Your logic looks good to me.
I find the same number of moles.
The heat of vaporization depends on the temperature. At the critical point, evaporation needs no heat.
Bond energies make inaccurate estimates. -1366 and -1305kJ would be a reasonable difference (but -780 not).
For combustions, always check if water is liquid or gaseous. Here it seems liquid everywhere, OK.
Adding the numbers you give provides the same -780kJ you find.

BUT

The bond energies you use mix up individual bonds and average bonds. Tables differ always, some I have tell
428 H-O°
499 H-OH
464 mean H-O in H2O
1077 O=C° (first double bond between two atoms)
532 O=CO (second double bond)
799 mean C=O in CO2 (from a different table hence incompatible)

A very complete table is on the Web
Bond dissociation energies
Yu-ran Luo

More generally, besides the risk of such errors, computing heats of reaction through the bond energies is just plain bad.

The computation subtracts big quantities.
Bond energies aren't accurately known.
They depend on all neighbour atoms.
They depend on cycles, and for fused cycles no tables exist.
We lack some basic information. Is gaseous carbon C, C2, C3? When most tables were written this was unknown.

So you can use bond energies to estimate at what bond of a species a reaction proceeds. But to predict reaction enthalpies, use the enthalpy of formation of the compounds, or deduce it from similar compounds.

#### Gustomer

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##### Re: Struggling with a problem in Elements of Physical Chemistry 2e
« Reply #2 on: July 25, 2018, 01:21:42 PM »
Thanks! The other key word I overlooked was "estimate" .  I started messing around with some of the bond enthalpies (mean and other) and got my total up to 1325.  So, it's more of a challenge to select for the MOST correct numbers from numbers that aren't precise for those compounds.  It's not the best way of calculating, but I understand the exercise now, at least .  This board is a great resource.