## How small is a molecule of water?

Magpie - 17-11-2017 at 08:39

I was trying to demonstrate how extremely small is a molecule of water in comparison to ordinary objects using the following calculation. This was to a group of professionals that I have coffee with each morning: 1 electrical engineer and past vice president, 1 mechanical engineer, 1 biologist, and 1 chemist who turned to the dark side (HR manager).

Molecules in a Drop of Water vs Grains of Sand on All the Beaches on Earth

1. Grains of sand on Earth estimate: 7.5 x 10^18, or 7,500,000,000,000,000,000 grains. Source: University of Hawaii researchers

2. Molecules of water in a drop using Avogadro's number:

(6.023 x 10^23 molecules/mole)(mole/18.02 grams)(1 gram/20 drops) =
1.67 x 10^21 = 1,670,000,000,000,000,000,000 molecules

Therefore, there are 1000 times more molecules in a drop of water than all the grains of sand on all the beaches on Earth!

The EE checked my zeros. The chemist and the ME grunted "so what." The biologist said "there are 22 drops in a gram." Others just rolled their eyes.

LearnedAmateur - 17-11-2017 at 11:12

Here's one, if you scaled up a 2mm capillary tube so that it covers roughly the distance from New York City to Kansas City, a water molecule within it will be about the size of a basketball. These are my calculations:
-----------
(Di)
Water molecule = 2.75*10^-10m
Capillary tube = 0.002m

0.002/(2.75*10^-10) = 7272727 (#H2O to cover CT diameter)

0.24*7272727 = 1745km (scaling up ratio to basketball size)

NYC -> KC = ~1950km

aga - 17-11-2017 at 11:13

Well, i suppose people like something they can grab a hold of.

Maybe try relating that to something, a bit like the 'ton of bricks or a ton of feathers' thing.

Difficult to suggest anything else for your morning self-help meetings without talking to the supervising psychiatrist first

[Edited on 17-11-2017 by aga]

phlogiston - 17-11-2017 at 12:05

On the same scale, the nucleus of the hydrogen atoms is still only 1.6 micrometers.

The LIGO gravitational wave detectors detect movements in the distance between two mirrors that are 10,000 times smaller than that...

Mentally scaling things helps to gain an intuitive feel for the relative dimensions, but it remains really difficult to imagine these kinds of numbers in an absolute sense.

[Edited on 17-11-2017 by phlogiston]

NEMO-Chemistry - 17-11-2017 at 13:32

I was going to mention Hydrogen, when you look at a water molecule like this, then you see why its really hard to contain hydrogen.
Seems to escape from most things.

The other thing that popped in my head, does a water molecule have a fixed size? If electrons wiz around and bonds flex, then surely a molecule kinda pulses size wise?

[Edited on 17-11-2017 by NEMO-Chemistry]

LearnedAmateur - 17-11-2017 at 15:44

 Quote: Originally posted by NEMO-Chemistry The other thing that popped in my head, does a water molecule have a fixed size? If electrons wiz around and bonds flex, then surely a molecule kinda pulses size wise?

Nah, the size doesn't remain constant if the temperature is above absolute zero, it's the main why fluid density decreases with temperature - more energy in the bonds means they traverse a larger distance from their 'rest' point, which means the same mass is contained in a larger effective volume. Contrary to what we've been told in school, water doesn't actually have a density of 1g/cm^3, that's only at 0-10C - at STP, the density is 0.997, and this decreases further to 0.958 when it comes to a boil. Obviously this doesn't really matter on an amateur scale, but it's one of those little things which we have measured, and the same phenomenon gives rise to heat waves on roads and other surfaces exposed to direct, intense sunlight.

[Edited on 17-11-2017 by LearnedAmateur]

Dr.Bob - 20-11-2017 at 18:13

If you want to see how small water is, try to do truly anhydrous chemistry, where any water will kill the reaction. It is nearly impossible to keep it out, water gets into almost everything, if you wait a little while. Plus, one mg of water is a huge molar amount, compared to 1 mg of nearly any common organic chemical.