# True or false: "If a reaction has a large negative value of ∆G, then it will be a fast reaction."

I recently took a Gen. Chem. 2 exam that contained this question. I answered false, as I knew that thermodynamics and kinetics are separate matters. My professor said the answer is true. I pressed him on it, citing a specific portion of our textbook that stated that the spontaneity of a reaction must not be conflated with the reaction rate. He admitted that it's true that a highly negative ∆G value does not necessarily imply that a reaction will be fast, but he said that that's usually the case, so I should have answered "true". This strikes me as absurd, not only because it's not a reasonable interpretation of a true/false question (they're supposed to be interpreted strictly, and if there's no qualifier like "generally" or "typically", then an if/then proposition should be treated as a "necessarily true" claim), but also because most students probably answered "true" because they did conflate spontaneity with reaction rate, which is something the textbook specifically warned against.

My professor also sent me the following via email:

"Please note that delta G combines all the properties of thermodynamics, which includes kinetics. Delta G has two components. Delta H (enthalpy) and Delta S (entropy). A large negative delta H means the reaction is highly exothermic. A large positive delta S means the product "randomness" is highly favorable, the system wants to happen even if enthalpy isn't high. I know of no system with these two feature that isn't fast. Note: rust (iron + oxygen going to rust) is highly exothermic, but the delta S is negative (solid and gas going to a solid), and that's why the reaction is favorable but slow."

I was surprised by this, as it directly contradicts what our textbook says on the matter. My understanding is that the ∆G equation contains only thermodynamic state variables and simply expresses the magnitude of thermodynamic potential. I see nothing in the equation that could convey information about the rate at which a process happens.

I would greatly appreciate not only theoretical comments on this, but also some specific examples of reactions with "large negative ∆G values" that are not "fast". (The inherent ambiguity of the terms "large" and "fast" here also seems to be a problem.)

• This answer to an earlier question about spontaneity should support your case. They give the example of gasoline and oxygen, where combustion even at room temperature should be highly favorable (large positive entropy and large negative enthalpy), but it doesn't occur because the barrier is so high. Nov 25, 2021 at 17:15
• I think that "will" is supposed to be more like "would be if activation energy is applied". Such reactions tend to be fast, when they actually happen. For example burning of magnesium will be fast when it actually happens. Nov 25, 2021 at 17:57
• Indeed, delta G has nothing to do with kinetics. Ask him if he gave his wife a diamond ring… Nov 25, 2021 at 20:42
• The reaction $\ce{C + O2 -> CO2}$ has a large ∆G value. But this reaction is so slow at room temperature that it seems not to happen at all. In fact you are right, there is no connexion between kinetics and thermodynamics values. Nov 25, 2021 at 21:06
• @JonCuster, I agree with the general sentiment of your comment. However, your and the other examples are individual data points and therefore not suitable to exclude any correlation between kinetics and thermodynamics of reactions in general. Nov 26, 2021 at 7:46

There is the Bell–Evans–Polanyi principle stating that "the difference in activation energy between two reactions of the same family is proportional to the difference of their enthalpy of reaction" (from the linked Wikipedia page). Looking at the Arrhenius equation, it is clear that this should lead to an increase in reaction rate with an increase in reaction enthalpy. Your professor might have this in mind, although admittedly he does not mention that explicitly.

Acutually, as far as I can tell the work by Bell, Evans, Polanyi and co-workers from the 1930s and 1940s can also be used to state that there is no universal relationship between thermodynamics and kintics valid over all reaction types. However, it is also apparently not true that there never is any relationship, as it is often claimed. As usual, the real world is more complicated than we are taught in basic university courses. I must leave the detailed reading of the papers to you – I could only have a quick glance – but below are some possible sources that I extracted from this paper. As it is often the case, the original papers from back in the days appear to be a rewarding read.

Concerning your question, the entry on Bell–Evans–Polanyi principle in the IUPAC gold book is quite informative:

The linear relation between energy of activation ($$E_\mathrm{a}$$) and enthalpy of reaction ($$\Delta H_\mathrm{r}$$) sometimes observed within a series of closely related reactions.

As you can see, this statement is far from making any general claims.

• Bell, R. P., Proc R Soc London Ser A 1936, 154, 414.
• Bell, R. P.; Lidwell, O. M., Proc R Soc London Ser A 1940, 176, 114.
• Ogg, R. A., Jr.; Polanyi, M., Trans Faraday Soc 1935, 31, 604.
• Evans, M. G.; Polanyi, M. Trans Faraday Soc 1935, 31, 875.
• Evans, M. G.; Polanyi, M. Trans Faraday Soc 1936, 32, 1333.
• Evans, M. G.; Polanyi, M. Trans Faraday Soc 1937, 33, 448.
• Evans, M. G.; Polanyi, M. Trans Faraday Soc 1938, 34, 11.
• Evans, M. G.; Warhurst, E. Trans Faraday Soc 1938, 34, 614.
• Evans, M. G., Trans Faraday Soc 1939, 35, 824.
• Baughan, E. C.; Evans, M. G.; Polanyi, M., Trans Faraday Soc 1941, 37, 377.
• Baughan, E. C.; Polanyi, M., Trans Faraday Soc 1941, 37,648.
• Evans, M. G., Trans Faraday Soc 1946, 42, 719.
• Thank you for the response, @Snijderfrey. How relevant would you say this is to the general claim about the relationship between ∆G and reaction rates, though? I looked at several textbooks, and several of them explicitly state that kinetics and thermodynamics are different subjects, which seems to be enough to establish that the proposition I quoted is false. Nov 27, 2021 at 4:35
• @Logicus, yes, I agree with what you say, and the work by Bell, Evans, Polanyi et al. does not contradict you, either. As far as I can tell, it acutally supports your case. I edited in some extra info you might be interested in. You will have a hard time finding reliable sources saying that the more exergonic a reaction is, the faster it is (in this generality). Nov 27, 2021 at 19:53
• @Logicus I would say there is weak correlation, not causality between values of reaction enthalpy and activation energy ( reaction rate ). Nov 28, 2021 at 8:31

This is the complete question at the GenChem 2 level (found posted on Chegg):

The correct answer is C. Of course, there is a relationship between most concepts, but not one where the speed of a reaction would reliably predict the sign of the standard Gibbs energy. Also, fast reactions is a fuzzy concept. A given reaction will be faster or slower depending on reaction conditions. For any fast reaction, you can probably find a faster one, but does that make the other reaction slow?