Kinetics Vs Thermodynamics : Apparent contradiction in the definition of Enthalpy in the two disciplines

My book gives the following curve: It gives the following relation :$$ΔH= E_{\mathrm{activation,forward}}-E_{\mathrm{activation,backward}} \tag{1}$$

But I suspect that $$E_{\mathrm{activation,forward}}-E_{\mathrm{activation,backward}}$$ corresponds to change in Internal Energy of the system ΔU.

or $$ΔU= E_{\mathrm{activation,forward}}-E_{\mathrm{activation,backward}} \tag{2}$$

However,at a constant pressure, heat of reaction or Enthalpy change $$ΔH = ΔU + PΔV \tag{3}$$

Statement (3) contradicts statements (1) and (2) or is valid only for $$ΔV=0$$

What is going on here?

In case, you feel that the graph is given only to cover a particular kind of reaction, please provide relevant comments.

– Zhe
Sep 1 '20 at 13:51
• @Zhe It does contain some misprints but overall it is a very good book for undergraduates. Moreover I have seen similar graphs in other books and on internet like chem.libretexts.org/Bookshelves/Introductory_Chemistry/… Sep 1 '20 at 13:55
• Instead of using what appears to be the Arrhenius equation, trying looking at the Eyring equation instead: en.wikipedia.org/wiki/Eyring_equation
– Zhe
Sep 1 '20 at 15:34
• @Zhe Sir I am just an undergrad and Erying equation seems a little beyond my understanding. Please explain what are you trying to convey here through this equation. Sep 1 '20 at 15:58
• The Eyring equation is from modern transition state theory. The Arrhenius equation is a fine starting point, and shares some similar features.
– Zhe
Sep 1 '20 at 16:06

The reason might be that while drawing the reaction energy profile, we forget to mention what energy we are mentioning in the Y-axis. The following conventions are generally used:

• If reaction conditions are constant NVT, energy in Y-axis should represent internal energy.
• If reaction conditions are constant NPT, energy in Y-axis should represent enthalpy.
• If reaction conditions are constant $$\mu$$VT, energy in Y-axis should represent Helmholtz free energy.
• If reaction conditions are constant $$\mu$$PT, energy in Y-axis should represent Gibbs free energy.
• If you are looking at single molecule, the energy will be the total energy of the molecule (kinetic energy + potential energy).

In case of reactions, the last three are generally used.

Hence, the "Energy" Y-axis changes based on reaction conditions. In the question, it seems you might have got mixed up somehow.

Summary of the terms used:

• N: No of molecules
• $$\mu$$: Chemical potential
• V: Volume
• P: Pressure
• T: Temperature
• Refer to NCERT Chemistry Class 12 Part 1 - Chemical Kinetics page 112 Graph 4.7 . It clearly mentions Potential Energy to Y-axis. Sep 1 '20 at 6:52
• Even here they are deliberately using Potential Energy on the Y-axis along with same Enthalpy representation chem.libretexts.org/Bookshelves/Introductory_Chemistry/… Sep 1 '20 at 7:09
• Please refrain from using a footnote that adds nothing to the answer. They can only reply in the comments and a greeting/footnote is unnecessary(adding very little value) in a Q&A forum. Sep 1 '20 at 16:11
• So are you saying that in the Y-axis of my diagram,it should contain Enthalpy? Sep 2 '20 at 2:15
• @TonyStark The Y axis is dependent on reaction conditions. You cannot expect to use Helmholtz free energy while studying reaction in $\mu$PT conditions. Sep 3 '20 at 6:30