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A question in Thermodynamics of Natural Systems by G. M. Anderson is to find the "standard heat of reaction" of this reaction: $$\ce{C8H16N2O3(aq) + H2O(l) -> C6H13NO2(aq) + C2H5NO2(aq)}$$

As far as I understand it, it should be a rather simple problem of finding $\Delta_\mathrm r H$. So it should be:

$\Delta_\mathrm r H=\Delta_\mathrm fH (\ce{C6}) + \Delta_\mathrm fH (\ce{C2}) - \Delta_\mathrm fH (\ce{C8}) - \Delta_\mathrm fH (\ce{H2O})$ (note that I shortened the organic formulae)

According to the data from the same textbook, it's: $(-632077~\pu{J/mol}-513988~\pu{J/mol})-(-847929~\pu{J/mol}-285830~\pu{J/mol})=-12306~\pu{J/mol}$

However, the answer given is $−89475~\pu{J/mol}$.

Am I missing something? Do I need to add some terms of pressure or volume expansion? Is this not the enthalpy that I'm looking for?

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  • $\begingroup$ Have you considered estimating the enthalpy change using bond energies? It's more approximate than using standard formation enthalpies, but might be useful to compare against your value and the textbook value. It would require knowing the structures for the organic molecules, however. $\endgroup$ – Nicolau Saker Neto Mar 9 '15 at 14:31
  • $\begingroup$ @NicolauSakerNeto this is a basic textbook for introductory thermodynamics. I'm certain that using bond energies is not required as it is not even covered in this book. I'm thinking that it may be an error either in the data provided or in the answer given... $\endgroup$ – baffledu Mar 9 '15 at 14:41
  • $\begingroup$ It might not be required, but it's a way to check! Do you have the structures or the compound names? $\endgroup$ – Nicolau Saker Neto Mar 9 '15 at 14:43
  • $\begingroup$ Leucylglycine + water = leucine + glycine $\endgroup$ – DavePhD Mar 9 '15 at 14:43
  • $\begingroup$ Interesting, a calculation by bond energies assuming Dave has the right structures (Dave, are you a wizard?!) suggests the reaction enthalpy should be $-85\ kJ\ mol^{-1}$. Maybe there is a print error in the enthalpy data. $\endgroup$ – Nicolau Saker Neto Mar 9 '15 at 14:59
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There is a "readme" note from the author that says:

The answers are not guaranteed, in the sense that not only might I make a mistake here and there, but I might have used different sources of data, or the data in a database may have changed. I have not been able to check all the answers, or to make them all consistent with the data in Appendix B, although I believe that most are.

So I think that this problem is an example of one of those situations.

The book itself works out the problem on page 267 and gets the same answer as you: −12306 J/mol.

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