So we’re in the grandstand looking at a sphere 150 feet in diameter, which contains 15,000,000 feet of linguini which is 3/8 of an inch thick. The sphere is a 10 micron spherical nucleus blown up. The volume of the nucleus is 523 x 10^-18 meters, but a meter has 10^3 liters in it as a liter is 1000 cubic centimeters. The 3/8 of an inch is what 20 Angstroms looks like at this magnification. Can we see water? Well water is about 4 Angstroms across, or 1/16 of an inch. We’re not going to see any water from our perch, even with good binoculars. But there’s an even better reason why. Try and figure out what it is before reading the next paragraph.
Let’s assume that everything in the sphere is at Superbowl temperature (27 Centigrade, 80 Farenheit — it is New Orleans after all). How fast is water moving at this temperature? The average velocity of water (mass 18 Daltons, or 0.18 kiloGrams/mole = M) at 300 Kelvin is
Sqrt[ 3 * R * T /M ] in Meters/second
R is the gas constant = 8.314 Joules/mole * Kelvin
T is 300 Kelvin
This is 645 Meters/second. That’s a lot of times around a 10 micron nucleus. It’s also why molecular dynamics simulations have trouble computing times longer than 1 microSecond, and why they need to see what’s happening on a nanoScond to picoSecond scale. Things happen fast at the chemical level.
But we’ve blown up 10 microns to 150 feet, or increased distances by a factor of 4,500,000, so 645 meters/second times 4,500,000 is a bit faster than the speed of light (which we know is impossible). So the water molecules can’t be seen — even if they were quite large, and they’re not.
We’re going to be dealing with far heavier entities than water, so what is the mean speed of something with a mass of 1,000 Daltons (1 kiloGram/Mole). It’s 87 meters/second. 10,000 Daltons (10 kiloGrams/Mole) has an average speed of 27 meters/second, 100,000 Daltons (100 kiloGrams/Mole) moves at 9 meters/second, 1,000,000 Daltons (1 megaDalton or 1000 kiloGrams/Mole) clips along 2.7 meters/second (about as fast as you walk) .
Is it meaningful to even think about something with a molecular mass of 1,000,000,000 Daltons (a gigaDalton)? Of course it is; any chromosome has a mass far greater than this, figuring around 1000 Daltons per base pair of the double helix (including the sugars and the phosphates) a gigaDalton is only a megaBase The velocity is .08 meters/second. The smallest chromosome contains 47 megabases giving a velocity of .012518 meters/second. Well, that’s about one centiMeter/second, and our nucleus is 10 microns or 1/1000th of a centimeter.
This means that even something as big (and this long) as a chromosome will be all over the nucleus many times in the course of a second. We’ll see a writhing 15,000,000 feet of linguini, if we see anything at all. We’re going to have to slow time down if we want to see anything at all. That’s for next time.
How many water molecules can our nucleus hold? By a previous calculation we know that the volume of our nucleus is 523 * 10^-18 cubic meters. But there are 10^3 liters in a cubic meter. A liter is 1,000 cubic centimeters (pretty nearly). So nuclear volume is 523 * 10^-15 liters. The concentration of water is 1000/18 or 55.5 molar, and there are 6.023 * 10^23 molecules/mole so a liter of water contains 55.5 * 6.023 x 10^23 molecules, and our nucleus contains 1.7 * 10^13 molecules of water (convert that to dollars and you have something of the order of magnitude of the national debt).
So it’s amazing that DNA holds up against the pounding that it takes. 645 Meters/second is 1465 miles/hour, and if there’s nothing in our nucleus but DNA and water (with the DNA making up only 6% of the volume of nucleus) I shudder to think of how many times a second our DNA is getting hit throughout its extent (perhaps one of you can figure it out). It seems nothing short of miraculous that DNA holds up for a second, let alone a lifetime. Familiarity does not breed contempt.
But every compound chemists deal with is this strong. Most solvents have molecular masses under 1,000 daltons, so the solvent molecules are moving faster than 87 meters/second. Most compounds chemists deal with are at most an order of magnitude greater than the solvent, so they’re getting clobbered by something nearly their size (and surviving).
Most chemistry books (even the magnificent Clayden) mention solvent, but never show it in any reaction mechanism. It’s the elephant no one sees. I don’t know enough about molecular dynamics simulations to talk about how (or whether) they handle solvent.
Here’s a link to the next paper in the series