Most physical constants are not particularly nice numbers. Yet for some reason the self-ionization constant of water is 1.0 * 10^-14. It suggests that things were defined in order for it to come out nice, but that seems a bit strange. The constant is the product of two molarities, or number of moles per liter. The size of a liter is governed solely by the length of the meter, which is currently somewhat arbitrary, but was originally determined by one ten-millionth of the distance from the north pole to the equator along the surface at sea level. Thus, it looks to fall on the definition of a mole, which is dependent on the size of the gram. But the gram was also originally defined based on the meter and a different property of water, its density at 4 degrees Celsius.
Ok, what about the Celsius scale? Well, 0 is the freezing point of water and 100 is the boiling point of water, thus perhaps 4 degrees was chosen in order to have this work out, but I was fairly sure that it was chosen because it was close to where water was its densest, 3.98 degrees, and perhaps within the range of experimental error those days.
Additionally, the self-ionization constant depends on both pressure and temperature, and is given as above at “standard temperature and pressure”(STP), a term which is actually not universal - there are two different standards. The fact that I only see one 0 after the 1 in 1.0 * 10^-14 suggests that at STP it’s only true for one significant figure and that more aren’t reported because it depends on what standard is used.
Is there anything I’ve missed, or is this just a big coincidence?