How much do water molecules move around within a stationary body of water?

Submitted by KpgIsKpg t3_104vosk in askscience

Let's say you leave a glass of water on a table. Over time, would you expect the water molecules to move around or would they tend to stay in the same relative position in the glass? I imagine there could be random walk behaviour where in each unit of time an individual molecule has a small chance of being jostled out of its position and pushed up or down.

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Chemomechanics t1_j37ttrh wrote

Over time T, the approximate distance L explored through diffusion (with diffusivity D) is related as T scaling with L^(2)/D.

Convection can be faster over longer distances, if convection is present.

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cpbayern24 t1_j37vbwz wrote

If you're talking about individual water molecules, they should be moving at very high speeds (average speed should be around 500 m/s at 20C) while breaking and reforming H bonds with other water molecules. However they do stay in their relative position when water freezes.

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ForeverInQuicksand t1_j386kr9 wrote

Replying to [deleted] (#1,296,781)

What if you took a 2ft pipe, that can be capped at both ends, and placed a valve you could open and close in the middle. Then you could place a small valve that allows a drop at a time to fall on both ends.

If you filled the left side with pure deuterated water, and the right side with pure water made with only normal hydrogen-1, and then opened the valve in the middle, while simultaneously collecting and isolating single drop samples of the water at each end of the tube over time.

By testing the samples in a mass spectrometer, wouldn’t it be possible to measure the deuterated water composition of each drop to see how long it would take both sides of the tube to release drops of the same d2O/H2O composition.

If the water molecules are distributing at a rate of 500m/s, there would be near instantaneous mixing of the two water types, as soon as the two samples touched.

I don’t think that would be the case.

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LiveNeverIdle t1_j388gxw wrote

Replying to ForeverInQuicksand (#1,297,161)

The individual molecules travel that fast, but soon bump into other molecules. Those other molecules get bumped and speed off into still other molecules. So the molecules move very fast but don't travel very far. Eventually all of the water would mix though, which we call diffusion.

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ELDOR-King t1_j395hq5 wrote

Replying to ForeverInQuicksand (#1,297,161)

the individual molecule speed is not necessarily the same as diffusion, as the movement is disordered. you can very easily measure this diffusion with NMR. (provided you have an NMR with pulsed field gradients. No need for valves or deuterium labelling etc.)

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OneTreePhil t1_j39rlya wrote

I remember calculating this in a ChemE class. If a bath tub of water no currents at all in it, any given molecule at one end would take something like six million years to diffuse to the other end. Any bulk current at all reduces the time to tens of seconds.

Please someone check me? It was an in-class problem in 1984 thanks for the memories Dr. Knickle & Coach

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flourishingvoid t1_j39y2wm wrote

From a Physicist working in the sphere of Biology

A lot.

Unless that stationary body is some kind of molecule fixed or arranged/bounded to a surface sort that would either restrict or minimize kinetic displacements of individual molecules ( each such displacement requiring input for entropy penalty )

Another way of fixing molecules is freezing the water...

PS. If the body refers to a container for transportation and storage, temperature of the water is all you need to know about the average displacement count/interaction count.

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purpleoctopuppy t1_j3a1c6u wrote

Replying to OneTreePhil (#1,299,300)

Diffusivity of water is on the order of 10⁻⁹ m² s⁻¹. Bath tub is on the order of a metre long, so it should take t ≈ L²/2D ≈ 10⁹ s. Since a year is e7.5 s, this means it would take on the order of 30 years.

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ProfessionalDaikon16 t1_j3a4ulw wrote

There really isn’t enough information in this question to answer properly. A glass of water on a table in Iceland will behave differently than a glass of water in the southern US which would act differently than a glass of water in Ecuador just from the different ambient temperatures alone.

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PerspectivePure2169 t1_j3acoh0 wrote

There's a lot to consider here. What's the body of water, a lake or a pipette? Is there a temperature difference?

Convection, capillary forces, diffusion, surface tension, vapor pressure, temperature and purity will all affect this.

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abat6294 t1_j3archb wrote

Replying to Verneke (#1,296,691)

Fun fact. The speed of sound through a substance is dictated by the average speed of the molecules within that substance. Speed of sound in air is about 750mph, so the average speed of each air molecule at any given moment is 750mph.

But they only go extremely short distances before bouncing of another molecule and going another direction.

Edit: The average speed of air molecules is actually closer to 1000mph at room temperature.

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Movpasd t1_j3bx7ym wrote

Replying to [deleted] (#1,296,781)

> How the temperature relates to other state variables is different (and difficult!) in liquids but that doesn't apply to kinetic energy

Is there a simple explanation for why this is the case? Given the presence of intermolecular potentials (which are not quadratic terms), I wouldn't expect equipartition to hold. Is the argument that this effect is negligible, and if so, how does one argue that it is?

Furthermore, does your calculation account for vibrational and rotational modes?

If you could point me to sources that cover these questions, I'd be very grateful. Thanks.

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badatmetroid t1_j3c0ket wrote

This question is deceptively complex. Because random motion is (wait for it) random the molecules move left as much as they move right. The result is that distance the average molecule grows with the square root of time. I'm pulling these number out of my ass, let's say it takes 1 microsecond for the average molecule to move 1 micrometer. How long does 2 micrometers take? Your gut instinct probably says 2 microseconds, but the random back and forth means it doesn't grow linearly.

It would take 4 microseconds to move 2 micrometers (because you doubled the distance and 2 squared is 4). It takes 8 microseconds to move twice as far as that and 16 to move twice as far as that... So to move a millimeter (1000x as far) it takes 1 second (1,000,000 times as long). To move a meter (1e6 micrometers) it takes 1e12 microseconds or 1 million seconds or ~11 days. 2 meters is 44 days, 4 meters is 176 days...

But that's diffusion. You said "stationary body of water" which means diffusion is the only thing acting on it. If only diffusion existed, our sense of smell would take days or even years to detect the fire across the room from us. But if the temperature is different in different parts of the room (like because of a fire or a human), then temperature differences lead to density differences which causes convection. The bulk of mass transport in fluids is caused by convection (wind, currents, etc). You waving your hand in the air is also convection (because your hand creates a pressure difference as it moves)

And just in case my graduated advisor is reading this, there's also migration which is caused by electrical gradients. Migration is relevant in electroplating, batteries, ion channels, and more. But that's like 5 lectures away from what we're talking about now.

Edit: someone in another comment used an actual diffusion coefficient and calculated that it takes years for a molecule to move from one side of a bath tub to the other. It's also worth pointing out that is the mean distance from the source, so half the molecules didn't move that far.

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uppen-atom t1_j3c12gl wrote

Brownian motion, water phase diagrams, triple point, and the relationship between Pressure and and Temperature. These topics will cover the idea well enough.

https://www.expii.com/t/phase-change-diagram-of-water-overview-importance-8031

one way to understand it is as the solid goes to liquid the molecules have more energy "ability to move" and depending on if S. L or Gas the molecules have more (S) attraction to each other or less (G) water is particularly "sticky" with itself so tends to congregate, lakes, clouds, icebergs in purer forms than say aluminum and iron which need to be mined out of rock. Temperature is really measuring the Kinetic (moving) energy of the substance. so higher T means more motion in the substance.

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badatmetroid t1_j3c1xpq wrote

Replying to cpbayern24 (#1,296,665)

They move (on average) at 500m/s but they are bouncing back and forth randomly. On average a molecule moves away from it's starting location at the square root of time. So if it takes 1 us to move 1 um then it takes 4 us to move 2 um, 1e6 us to move 1e3 um and 1e12 us to move 1e6 um (or 1 million seconds to move 1 meter).

I pulled those numbers out of my ass but if you know the root mean velocity (your 500m/s number) and the root mean path (average distance until collision) you can use the two numbers to derive the diffusion coefficient from first principles.

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TroubledWaterBridge t1_j3c4uyc wrote

Replying to nikanjX (#1,301,101)

This is why if you take a drop of food coloring and place it in a container, you can watch the diffusion process happen fairly quickly. A long time ago, a group I was in was tasked with measuring something just like this. We designed an experiment, and even modified glassware (sealing it) to minimize external factors. We were so confident that our design would yield the results that most closely mirrored the theoretical results. In the end, we were off by a very large factor, say 1000x or something, because we left the light from the spectrometer on, which increased the temperature on that point of our apparatus. Otherwise, our professor praised our design.

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KingSupernova t1_j3i3zac wrote

Replying to pzerr (#1,300,804)

Friction against what?

Heat is the average movement speed of the particles. The average isn't going to spontaneously increase without external energy being put into the system.

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Indemnity4 t1_j3jbmy6 wrote

Replying to Verneke (#1,296,691)

The self-diffusion coefficient of neat water is:

  • 2.3·10−9 m2·s−1 at 25 °C (room temperature, or close enough), and

  • 1.3·10−9 m2·s−1 at 4 °C (inside the fridge).

You can play around with equations for diffusion towards a target (on average a straight line velocity), diffusion over a certain distance (e.g. how long to randomly move from one wall to the opposite side), or collision frequency.

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