Molecular Size and Permeability
Date: Spring 2013
What is the diameter of a water molecule?
The issue is a little bit more complex than simply the diameter of the space occupied by a single water molecule.
I am sure you have heard of modern clothes that are "water proof" from the outside (preventing rain from soaking through the cloth) but allow sweat to evaporate (allowing water from the inside to pass through the cloth). The principle here is that sweat evaporates and is essentially a gas, and as a gas, water can pass through the cloth. But liquid water - because it has a strong cohesion, acts like many water molecules combined. As this big "supermolecule", the water cannot pass through the cloth.
You may also have seen of tricks that prevent water from falling out of a glass. Here is a YouTube video: http://www.youtube.com/watch?v=PzyKXWUy0yc In this video, the screen certainly has holes that are much larger than a spray of water, and yet it does not fall through. The principle here is the combination of the cohesion of water and air pressure (against a vacuum that would form at the top if the water were to fall straight down).
So, there are many other factors than just the size of a single molecule. Substances seldom act as individual and independent molecules, and as a bulk substance can be acted on by many other forces.
Greg (Roberto Gregorius)
I got this drawing from this URL:
pm is pico ( 10-12 ) meters.
While angle O is 104.450, Angles H are (180 – 104.45)/2 = 75.5500/2 = 37.7750
Sides OH are 95.84 x 10-12 meters
Side HH is (Using law of Cosines)
HH2 = OH2 +HO2 -2(OH)(HO)(Cos O)
Since OH = HO in length = 95.84 x 10-12 m; and
O = 104.450
HH2 = 2(OH)2 – 2(OH)2Cos(O)
HH2 = 2(95.84 x 10-12)2 - 2(95.84 x 10-12)2 (Cos 104.450)
HH2 = 2(9.185 x 103 x 10-24) - 2(9.185 x 103 x 10-24)(-0.250)
HH2 = 2(9.185 x 10-21) + 2(9.185 x 10-21)(0.250)
HH2 = 2(9.185 x 10-21) (1 + .250)
HH2 = (18.370 x 10-21) (1.250)
HH2 = 22.962 x 10-21
HH2 = 22,962 x 10-24
HH = 151.533 x 10-12 m
HH = 151.533 pm
So, two sides of the water molecule triangle are 95.84 pm
The third side of the water molecule triangle is 151.533 pm
This is an insightful question! The size of a water molecule ("diameter"
is not a good description since the molecule is not circular) is about
382 picometers, or 382 millionths of a millionth of a meter. That is an
unimaginably small size!
Individual molecules of water do not behave as liquids. Most organic
materials such as all plastics, or cell membranes, for example, have
their molecules arranged such that there are large enough distances
between them (distances larger than the size of the water molecule),
that water molecules can fit between them and the water can slowly
"diffuse" though the material, one water molecule at a time.
This can be demonstrated using, for example, the sealed plastic bag
of brown sugar, as commonly sold in stores. The bag appears to be
water-tight, yet if you leave it alone for long enough (months), the
moisture in the brown sugar will slowly diffuse through the plastic and
the brown sugar will eventually become hard.
This effect of water slowly diffusing though seemingly-sealed
containers made of plastic and rubber can be very troublesome.
Inexperienced designers often enclose sensitive electronics devices in
sealed plastic housings, and install outdoors in humid environments.
Months or years later, the circuit fails. When the housing is opened,
the designer is shocked to see there is moisture inside. This moisture
did not get in there in the usual way (through a defective gasket, for
example). Instead it diffused, one water molecule at a time, through
the housing itself. Housings made of metal or glass are the only
materials whose molecular spacing is small enough that water cannot
diffuse through them. Housings made of these materials are said to be
Water molecules are not in fact spherical, so it is hard to give you a single number for its dimension. However, an approximate end-to-end length is in the ballpark of 2-3 Angstroms (each Angstrom is 0.1 nm, or a tenth of a billionth of a meter). Thus, a pore that was orders of magnitude larger than 3 Angstroms would be likely to allow water to pass unimpeded.
However, when you get to sizes that small, effects other than purely size start to dominate its motion and transport properties. Notably, water is a highly polar molecule with very asymmetric average electron density. This means that it can interact (weakly) with other polar or charged molecules, and tends not to interact well with highly nonpolar molecules. These electronic properties mean that the EFFECTIVE size of a water molecule - for the purposes of passing through a membrane - may in fact be higher or lower than the 3 Angstrom estimate.
For example, if a membrane had very small pores but was composed of highly hydrophilic or charged molecules, the water molecule might be able to pass even if the pore size is ostensibly too small to allow passage. This is because the water can interact very strongly with the molecules of the membrane, bringing them closer than would otherwise be possible. The converse is also true - highly hydrophobic membranes can probably keep water from passing even with slightly larger pore sizes. Water also has different transport properties depending on other molecules in the solution. If the solution is mostly water, then other effects are less important, but if water is only a small proportion of the molecules in solution, its interaction with other solvent molecules will significantly effect transport - and permeability - properties.
What this all means is that transport of molecules at sub-nanometer scales is extremely complicated. We can't think of these molecules as balls being thrown at a net of given mesh size; we have to think about other subtle forces that start to get important at these length scales.
Dr. Shimon Unterman
First, you have to realize that a molecule (or atom) is NOT ?hard?. They are ?squishy? So the size one measures depends upon the method used to some extent. Also, in the case of liquid water, the molecules are collected in clusters. They are not simple isolated water molecules. Second, the barrier is not a simple hole in a piece of metal or ceramic. The ?hole? is a long circuitous ?tunnel? with which the water molecule or clusters can adhere change configuration and/or number of molecules in adhered cluster.
Keeping all these complications in mind chemists still treat water as single isolated molecules. The pertinent geometry is OH bond length = 0.0958 nanometers (= 0.958 angstroms). The H-O-H bond angle is 104.54 degrees. Notice that if the water molecule were ?simple?, the bond angle ?should? be 180 degrees. It is not. This is because an isolated water molecule has two pairs of electrons. These two "lone" pairs and the oxygen nucleus tend to repel. This repulsion takes up more space than the pendent H?s. If this did not happen one would ?expect? the H-O-H bond angle to be 180 degrees.
You student's question was a good one. The problem is there is no single simple answer. Many factors come into play.
Thanks for the question. A water molecule is not a sphere, so a diameter is not a well-defined quantity. A water molecule consists of 2 atoms of hydrogen bonded to one atom of oxygen. Roughly speaking, each atom has a diameter of 1/10 of a nanometer, so a water molecule has a size of about 3/10 nanometer. 1 nanometer equals 10^-9 m.
I hope this helps. Please let me know if you have more questions.
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Update: November 2011