# Your Monday answer

Mar 27, 2019
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On Friday, I asked “What weight could you hang from a chemical bond before it broke? How many atoms [is that]?”

Paul from ChemBark suggested “~350 pN or ~400 nanograms or so” and Ali Moeed guessed “1000+ atoms”.

To be honest, I have no idea what the right answer is! But the fun with these kind of problems is working them out, so here are two methods I used and the answers they gave. Basically, I needed to know/calculate the mechanical force required to break a bond, seamlessly convert that into a force-due-to-gravity, and then work out what mass/how many atoms would give that force (on earth). If there are any mistakes in the following, please let me know in the comments! And if you have a better way to go about it, please do so.

First method (no research): The ball-park figure for the strength of a bond in my head is 100 kJ/mol, or 2 x 10-22 J per bond. Unfortunately, that’s an energy, not a force. But energy is just force x distance, right? So let’s say the bond is broken when you’ve moved one atom 10 Å further away. The force required to do this is (2 x 10-22 J/10 x 10-10 m) = 2 x 10-11 Newtons. A mass of 0.1 kg ‘weighs’ 1 N, so the weight required to break a bond is 2 x 10-12 kg. Which is pretty small in the human-sized world, but pretty massive in the atomic world – but how many atoms? I decided to think about gold atoms, as these make pretty nice nanoparticles. Gold has an atomic weight of ~200 g/mol, or 0.2 kg/mol, so that’s 2 x 10-12 kg / 0.2 kg/mol = 10-11 mol of gold. And finally, 6 x 1023 atoms of gold/mol x 10-11 mol = 6 x 1012 atoms of gold.

Second method: Gav used popular internet-based search engine ‘Google’ to find this paper from Matyjaszewski et al in Nature, the abstract of which says “[C-C bond] strength is evident in the hardness of diamonds [etc]; on the single-molecule level, it manifests itself in the need for forces of several nanonewtons to extend and mechanically rupture one bond.” So repeating the calculations from 10-9 Newtons gives 10-10 kg, or 3 x 1014 atoms of gold.

So my two answers aren’t exactly the same, but I think they’re close enough (what’s a factor of 50 when things are between 10-12 and 1023??) to indicate that it would take a LOT of atoms – one fat ‘nano’particle – to break a bond by their weight alone. I see Paul’s answer is in a similar range, and Ali is technically right with “1000+” but that leaves quite a lot of wiggle room!

What does this teach us? Well, apart from the fact that chemical bonds are strong, perhaps just that gravity is weak, electrostatics are strong!

NOTE: As I am just about to press publish, I see John at It’s the Rheothing has tacked the problem too, but (naturally) from a polymer perspective – how long a polymer could a bond support? I won’t spoil the surprise – go and read his post!

Neil

Neil Withers (Associate Editor, Nature Chemistry)