For every scientist, there's this bunch of numbers worth knowing, that are a good guide for understanding and predicting stuff. Here's a short list of numbers (apart from the usual ones like Avogadro's, Planck's, Boltzmann's, pKa values etc.) which are quite useful for chemists and biochemists. It's really a personal list, but it can be generally useful.
1. 3 kcal/mol: the maximum difference that can exist between two or more conformers in solution to be able to observe the minor one by NMR. Because remembering that ∆G=-RTlnK, this means that with a difference of 3 kcal between two conformers, the major one will be present to the extent of 99.96%. Naturally for practical purposes, the difference usually cannot exceed about 2 kcal/mol (98% or so) to detect the minor conformer, as NMR's detection limit is about 2%...below that it's hard to see the stuff. This is an important issue, because for example in the binding of a drug to a receptor, a conformer that exists to the extent of 3% can be the bioactive one.
2. 1.54 A, 1.34 A, 1.22 A Lengths of C-C single, double, triple bonds
3. Milliseconds: NMR time scale
4. Energy at room temperature: 18-20 kcal/mol. Important because that means that if energy differences are below these numbers, interconversion at R.T. can take place. Note that this is the kinetic barrier at RT. Thermal energy at RT is 0.6 kcal/mol only. For reference, energetic input needed for cis-trans interconversion for a typical double bond is about 20 kca/mol.
5. 2-10 kcal/mol: Strength of hydrogen bond. This can widely vary though...2-5 kcal/mol is a better range to remember.
6. 1.2, 1.5, 1.7, 1.5 A, 1.35: Van der Waals radii for H, O, C, N, F from Bondi (JPC, 1966). Useful for noticing "short" contacts in crystals and molecular and protein structures
7. 1 kcal/mol ~ 350 /cm: One of those useful conversion factors, in this case between wave numbers and energies. For quantum chemists, another useful relationship is 1 hartree= 627.5 kcal/mol
8. Relevant dielectric constants: water 78, DMSO 47, ethanol 24, acetonitrile 37
9. Ionic radii of essential ions: Na+ 0.95 A, K+ 1.33 A, Mg2+ 0.65 A, Ca2+ 0.99 A
More when they strike me
Einstein's wonderful letter to David Hilbert: A message for our times
2 hours ago in The Curious Wavefunction