I remember clearly the moment in which I learnt the most important fact I know. It was during a lecture course in the first year of my undergraduate degree in Sheffield, when we were privileged to be taught by Chris Hunter, now in Cambridge.
Chris is a Physical Organic Chemist and an excellent lecturer. The course, which I think was during the first semester, focused on inter-molecular interactions. In retrospect, I think the reason I enjoyed it so much was that it took the fundamental laws of Physical Chemistry that one is forced to learn in first year Thermodynamics and made them interesting by using them as tools, as a practicing Chemist should. After all, if an equilibrium constant falls in the forest and nobody is there to calculate a Gibbs energy from it, does it make a sound?
This leads us to the most important fact I know: at room temperature, a difference in Gibbs energy of 5.7 kJ mol-1 results in one order of magnitude difference in population in a Boltzmann distribution. The reason that I remember this fact is that during our lecture course, Chris would occasionally have examples of molecules in different conformations with some energy difference and ask us to guess the ratio between the two in solution. And undergraduates being undergraduates, we were unwilling to pipe up. But eventually, after much cajoling, somebody answered the question.
This of course was followed up with "and what if you add 10 kJ mol-1 to that?". I sat there in silence among the rest of my peers. Lectures, especially when you're presented with a lot of new information, don't tend to encourage the use of ones brain; however, on this particular morning my 19 year old mind fired its sleep deprived cylinders and it hit home. I put my hand up slowly and, on prompting, suggested that it would be about 100 times less. Chris smiled, said yes and moved on.
It was through that experience that I came to appreciate that facts are often less impactful without meaning. For example, there is little use in knowing that the difference in energy between two conformers is such and such an energy unless you know what that energy means. Your ring has to be in a boat conformation to be reactive and that conformation is 21.6 kJ mol-1 higher than the chair? Well then, it's not going to be very reactive. But if all you just need to swap from an equatorial chair to an axial one, and the energy difference is 3.4 kJ mol-1? That's more like it!
In the time since my first year, the +5.7 kJ mol-1 = 10% population equivalence has served me well, because it's allowed me contextualize many numbers during my career. It has also taught me to try to find the meaning behind many of the elements of Physical Chemistry, as well as within the research I do with my colleagues.