# Is there an example where interpreting reaction coordinate as time leads to an incorrect conclusion?

I have heard that we should not interpret the reaction coordinate in an energy diagram as time, but are there any situations in which we would arrive at an incorrect conclusion if we did so?

When I say interpreting reaction coordinate as time, I really mean as $\frac{\text{time so far}}{\text{total time for reaction}}$ (I would have written this instead of "time", but I'm not sure of a word or phrase for this).

• There's probably a monotonic mapping from reaction coordinate to time but there's no reason to believe this mapping is uniform or smooth. Also, it's not clear what you mean by "wrong conclusion." What conclusion can you draw from a reaction coordinate at all? – Zhe Jan 20 '18 at 13:12
• You can compute the free energy of a system as a function of a reaction coordinate. If you carry over that to time, the result is conceptually misleading. Thermodynamic calculations don't tell you about kinetics. – Curt F. Jan 21 '18 at 4:42
• @CurtF What does free energy plotted against time look like? – alphacapture Jan 21 '18 at 18:48
• A reaction coordinate is never time but a description of the distance between the reacting atoms as the reaction proceeds vs the energy. Time is not linear in this respect, i.e. the reaction moves with different speed at different points on the reaction coordinate. – porphyrin Jan 26 '18 at 13:56

## 2 Answers

Transition states are very short lived species, generally lasting less than a picosecond. At the single molecule level, crossing a transition state is a very fast event: it goes from reactants to products in less than a picosecond.

Some reactions are very slow because the probability of crossing the transition state is very low, but never because they spend a long time at the transition state. Thus, interpreting reaction coordinate as time is incorrect.

In a slow reaction, a small number of molecules will react early, but the majority will spend a long time in the reactants state, waiting to cross the transition state. If one could take a static picture of an ensemble of molecules, some would be in the reactants state, some would be in the products state, and it would be almost impossible to see any molecule at the transition state.

One of the oldest reactions to be understood in modern terms qualifies. Heat mercury in the presence of oxygen, the mercury is first oxidized only to be reduced again at higher temperature as the equilibrium constant shifts. The reaction coordinate, defined as the amount of mercury oxidized, doubles back as time advances in this nonisothetmal process.

• It is incorrect to define the reaction coordinate "as the amount of mercury oxidized". The reaction coordinate relates to breaking or forming chemical bonds, not to the number of molecules that are in the products state. – diogom Jan 25 '18 at 21:53
• The number of Hg-O bonds formed, maybe? – Oscar Lanzi Jan 26 '18 at 0:18
• Number of molecules is not a reaction coordinate. Bond length between Hg-O is a valid reaction coordinate. – diogom Jan 26 '18 at 0:29