# What is intermolecular distance in water? [closed]

I am wondering what is an average intermolecular distance in liquid water (say under normal pressure and room temperature).

I need just order of magnitude. A reference would be helpful.

• Questions without explicit particular effort are not very welcome, and may be closed. Think thoroughly about possible answers to your questions and search for them before asking. Provide in the question elaboration what you already know, what you have thought about, what you tried to search for in textbooks and online resources, what you found, understood or not, where you failed. Elaborated questions attract elaborated answers and vice versa. Include in questions all eventual relevant circumstances to prevent wrong assumptions and requests for clarifications. – Poutnik Nov 19 '20 at 9:54
• You could actually calculate it yourself using the density of water, its molecular weight, and Avogadro's constant. I'd suggest giving it a shot and showing us your work. [Hint: the first part is to determine the number of water molecules per cm^3.] Forum members can help you if you get stuck. – theorist Nov 19 '20 at 10:00
• @Theorist I was just going to provide Wikipedia references to water molar mass, water density and Avogadro' constant. But the OP can easily find it. – Poutnik Nov 19 '20 at 10:02
• @Poutnik : I tried to find in internet of course, but could not. I am not a specialist in the field (I am a mathematician and need this data for some course I will teach, as an illustration). Thus I am wondering if there are any tables in chemical literature containing all such data for all kind of materials. – makt Nov 19 '20 at 10:14
• As an order of magnitude it is the same as in solid water, just a tip of an iceberg shorter. The structure of ice is known. Do you want center to center distance, closest neighboring atom distance, or vanderWaals radio overlap? – Karsten Theis Nov 19 '20 at 11:20

Not all data are provided in explicit form. They are often not frequently needed and can be often deduced from other data with using of high school knowledge.

You can calculate the volume occupied by 1 water molecule ( in average ) from the water molar mass $$\pu{M}$$, water density $$\pu{\rho}$$ and the Avogadro constant $$N_\mathrm{A}$$ as

$$V=\dfrac{M}{\rho \cdot N_\mathrm{A}}$$

Then you can calculate the side length $$a$$ of a cube of this volume:

$$a={\left( \dfrac{M}{\rho \cdot N_\mathrm{A}} \right)}^{1/3}$$

As a rough number, is is equal to

$$a \approx { \left( \dfrac{\pu{0.018 kgmol^-1}}{\pu{1000 kgm^-3} \cdot \pu{6.022e23 mol^-1}} \right)}^{1/3} \approx \pu{0.31 nm}$$

what can be taken as the typical "center to center" distance of water molecules within the order-like rough precision.

The more precise average distance would have to calculate with the size and shape of the water molecule ( $$\ce{O-H}$$ bond length about 0.096 nm, the bond angle 104.5 degrees) and to make the integral average over the directions. But it would be extremely complicated, considering also difficulties with molecule borders and hydrogen bonds. In some sense can be said the distance is zero or even "negative", as the molecules form bonds ands overlaps.

For an order of magnitude estimate, look at the structure of ice. The density of liquid water under ambient conditions is higher, so water molecules would be closer, but the difference is less than 10% (in terms of volume, so less in terms of distance).

In ice (hexagonal ice, to be specific), each water has 4 waters as closest neighbors. The oxygen atoms (i.e. roughly the centers of mass) are 277 nm apart, the closest atoms are 177 nm apart (and form hydrogen bonds), and the van der Waals radii of closest atoms overlap (as seen in the red-yellow "pillow"). The coordinates for this image are from ChemTube3d.