Naked Science Forum
Non Life Sciences => Chemistry => Topic started by: scientizscht on 19/07/2023 00:10:14
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Hello
If I have two containers, one with a solution and another with plain water and I connect them with a tube, when will they reach same concentration?
Is there a simple (non differential) equation to calculate that time?
Thanks!
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Way too many variables missing to even begin to answer such as length and diameter of tube, what is in the tube at t=0, relative heights of containers. Unless the tube length is less than it's diameter I would guess any diffusion to be extremely slow. I would doubt that there is a rigorous equation to describe this.
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Never.
The solution is in A, the solvent in B
The probability of a solute molecule molecule moving in either direction depends on the relative concentrations {A} and {B} so the net transport rate d{A}/dt per unit time depends {A} - {B} and as {B} -> {A}, so d{A}/dt -> 0.
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The probability of a solute molecule molecule moving in either direction depends on the relative concentrations
How would it know?
The probability of a molecule moving in either direction is 50:50.
But net the movement of molecules as a whole is from the high to the low concentration, simply because there are more molecules where the concentration is higher.
If you regard the solution as homogeneous, then the answer is, as Alan says, "never".
But if you are looking at particles then you reach a point where the difference in concentrations is comparable with the natural fluctuations in concentration.
Imagine your solutions were so dilute that you only had 2 molecules (A and B) of solute.
There are 4 possible outcomes;
Molecule A is in container 1 or container 2
Molecule B is in container 1 or container 2
About half the time, both molecules will be in the same container.
So it pretty much starts off at "equilibrium".
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Is there a simple (non differential) equation to calculate that time?
Not really.
I presume that's why Alan decided to use a differential one. (Either that or he didn't read what was asked).
But for any given set up of solute, containers and pipes, the rate of mixing is first order decay, with a half life.
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The probability of a solute molecule moving in either direction depends on the relative concentrations {A} and {B} so the net transport rate d{A}/dt per unit time depends {A} - {B} and as {B} -> {A}, so d{A}/dt -> 0.
Apologies for oversimplifyng the model. Pedantically and etymologically, substitute "the probability P of net migration of molecules from A to B...." which is surely obvious.
And you can ignore the differential too. Say P(A→B) = f({A} - {B}), so as {A} → {B} so P → 0.
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@scientizscht
pi = iMRT ?
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@scientizscht
pi = iMRT ?
Thanks but where is time? 🤔
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@scientizscht
pi = iMRT ?
Thanks but where is time? 🤔
Won't Time be a Dependent Variable?
ps - an easy way to know " t " would be to conduct the Experiment.
" Answer thru Demonstration shall tc of that. "
(Isaac)
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@scientizscht
On second thought...
Your point seems Valid.
There should be a way to incorporate ' t ' into any Equations/Formulas.
Even if it's just a Symbolic representation, it would still define the Interdependence.
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pi = iMRT
IMO, it's hidden in the dimension of osmotic pressure pi, which is ML(-1)T(-2).
The higher the value of pi, the lower the equilibrium time will be. It can be done by increasing temperature.
As you said, diameter and length of the connecting tube will also be influential.
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pi = iMRT
IMO, it's hidden in the dimension of osmotic pressure pi, which is ML(-1)T(-2).
The higher the value of pi, the lower the equilibrium time will be. It can be done by increasing temperature.
As you said, diameter and length of the connecting tube will also be influential.
Thanks for clarifying that pi means the osmotic pressure rather than pi.
That makes more sense now.
But rates of reaction are not strongly related to osmotic pressure.
Osmotic pressure is, itself, an equilibrium process and "getting to equilibrium" has kinetics of its own and an associated timescale.
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But rates of reaction are not strongly related to osmotic pressure.
Osmotic pressure is, itself, an equilibrium process and "getting to equilibrium" has kinetics of its own and an associated timescale.
Imagine an extreme case where the solution is nearly identical to the solvent. There will be nearly zero osmotic pressure when the containers are connected, and there will be low flow of solvent to the container of the solution.
Hydrostatic pressure will reach equilibrium much earlier than equilibrium of concentration.
Osmotic pressure depends on concentration difference, which will be reduced when material flow is allowed. And you already mentioned about decaying process.
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A big molecule will have the same effect on osmotic pressure as a small one, but it will diffuse more slowly.
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I don't think that osmotic pressure describes a complete picture to the situation asked in this thread. But it's close enough to be a starting point towards the real solution.
The molecules should move from one container to the other because of some kind of force. Let's just call it chemistromotive force, as an analogy to electromotive force coined by Faraday.
As mentioned before, that force depends on several factors, such as temperature, sizes of the connector, difference in concentration in each type of molecules or ions. Not just the difference in total osmotic pressure between the containers.
If one container contains acid, while the other contains base, then the motive will be higher than if they both contain acids or bases, or neutral.
Even if the opposite containers contain very similar molecules, like enantiomers, there will be a motive toward equilibrium, although the osmotic pressure is close to zero.
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The reason why molecules diffuse is simply "because they can".
The only driving "force" is entropy. (which is more or less why they all work equally well to raise osmotic pressure.)
If one container contains acid, while the other contains base, then the motive will be higher than if they both contain acids or bases, or neutral.
How will the molecules in one place know what molecules are in another place, in order to move towards it?
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How will the molecules in one place know what molecules are in another place, in order to move towards it?
I'm not sure yet, but perhaps it's related to electromagnetic fields. Suppose one container contains Na+ and OH- ions, while the other contains H+ and CL- ions. H+ ions are the lightest. For them to have the same temperature as the others, they must move faster in average. They would move to the other container quicker. Electrostatic charges imbalance then forces the movement of the other ions to rebalance them.
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I'm not sure yet, but perhaps it's related to electromagnetic fields.
We know what happens in the presence of such fields
https://en.wikipedia.org/wiki/Debye%E2%80%93H%C3%BCckel_theory
But no such field exists.
My question was rhetorical.
The molecules can not possibly know what is happening somewhere else.
So there's no way for that to affect the way they diffuse.
(It might stop them diffusing back- which would affect the net transfer rate)
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My question was rhetorical.
The molecules can not possibly know what is happening somewhere else.
So there's no way for that to affect the way they diffuse.
Do you think H+ diffuse at the same rate as Na+ at the same temperature?
Suppose one container contains Na+ and OH- ions, while the other contains H+ and CL- ions. H+ ions are the lightest. For them to have the same temperature as the others, they must move faster in average. They would move to the other container quicker. Electrostatic charges imbalance then forces the movement of the other ions to rebalance them.
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Do you think H+ diffuse at the same rate as Na+ at the same temperature
As I said
A big molecule will have the same effect on osmotic pressure as a small one, but it will diffuse more slowly.
Please try to keep up.
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Do you think H+ diffuse at the same rate as Na+ at the same temperature
As I said
A big molecule will have the same effect on osmotic pressure as a small one, but it will diffuse more slowly.
Please try to keep up.
Then you should know the implication.
H+ ions are the lightest. For them to have the same temperature as the others, they must move faster in average. They would move to the other container quicker. Electrostatic charges imbalance then forces the movement of the other ions to rebalance them.
Charge imbalance can be sensed from quite far away, and it propagates at near the speed of light.
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Charge imbalance
There isn't one.
Every H+ ion (Indeed, every positive ion) is accompanied by some negatively charged ion.
By the way, the effect of a charge doesn't carry beyond a faraday cage.
And if the solvent is conductive, the effect can't be detected at any meaningful distance.
Did you read the bit about DH theory?
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By the way, the effect of a charge doesn't carry beyond a faraday cage.
And if the solvent is conductive, the effect can't be detected at any meaningful distance.
Faraday cage works because the electrons are free to move through conductors.
In this case, the charge carriers are the ions, instead of electrons. There are some processes need to consider.
For simplicity, let's assume that at the start, the two containers have the same hydrostatic pressure and electric charge.
Difference in speed of diffusion. Light molecules or ions diffuse faster than heavier ones.
It creates difference in hydrostatic pressure and electric charge, at least momentarily. Consequently, it will force materials flow to rebalance them.
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Consider an ion in a polar medium. How far do you need to be from the ion before any electrostatic effect is negligible?
Consider an ion in a polar medium which also contains counter-ions in solution. How far do you need to be from the ion before any electrostatic effect is negligible?
Then tell me if you think the OP's question was about apparatus that small.
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Consider a telegraph wire. Both ends are connected to a van de graaff generator metal spheres. Charge one of the spheres.
How far the cable need to be before any electrostatic effect is negligible?
Then remove the wire with a hose containing electrolyte solution.
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An ion in solution will be in very close contact with counterions and field effects will be restricted to the scale of a couple of atoms, unless you are talking of near infinite dilution in a non polar solvent.
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An ion in solution will be in very close contact with counterions and field effects will be restricted to the scale of a couple of atoms, unless you are talking of near infinite dilution in a non polar solvent.
An electron in a wire is also very close to the positively charged metal lattice. It doesn't stop the electron flow when charge imbalance is created between its ends.
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True, but in a good conductor the electric field from one end to the other will be very small(zero in a superconductor). A significant field strength would be needed to move an ion through macroscopic distances. Now if you apply a voltage between the two containers then ions will migrate just as they do in your wire example. Just as electrons won't by themselves in the wire neither will ions in solution.
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True, but in a good conductor the electric field from one end to the other will be very small(zero in a superconductor). A significant field strength would be needed to move an ion through macroscopic distances. Now if you apply a voltage between the two containers then ions will migrate just as they do in your wire example. Just as electrons won't by themselves in the wire neither will ions in solution.
In my scenario, the charge difference was caused by difference in diffusion speed between H+ ions and other molecules. H+ would be able to spread first to the other container before it's counterparts. If nothing else follows, it will cause charge imbalance between those containers.
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Consider a telegraph wire. Both ends are connected to a van de graaff generator metal spheres. Charge one of the spheres.
How far the cable need to be before any electrostatic effect is negligible?
Then remove the wire with a hose containing electrolyte solution.
And then put the whole system in a huge tank of water to mimic what's really happening.
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If diffusion caused a charge imbalance, the subsequent charge would draw +&- ions back together. Diffusion of course happens but it will not separate ions, given the strength of the electrostatic attraction.
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Consider a telegraph wire. Both ends are connected to a van de graaff generator metal spheres. Charge one of the spheres.
How far the cable need to be before any electrostatic effect is negligible?
Then remove the wire with a hose containing electrolyte solution.
And then put the whole system in a huge tank of water to mimic what's really happening.
That's not what's really happening. There are two containers isolated from one another except through a tube.
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Consider a telegraph wire. Both ends are connected to a van de graaff generator metal spheres. Charge one of the spheres.
How far the cable need to be before any electrostatic effect is negligible?
Then remove the wire with a hose containing electrolyte solution.
And then put the whole system in a huge tank of water to mimic what's really happening.
That's not what's really happening. There are two containers isolated from one another except through a tube.
But, from the PoV of the electrostatic forces acting between the ions at each end, they are under water.
Either you consider an ion on one of the containers at each end, in which case it is surrounded by a lot of liquid or you consider an ion in the connecting tube- in which case it is surrounded by a lot of liquid.
In either case, if your Van de Graff can only produce one electro's worth of charge separation, it will only create a tiny energy difference.
The molecules get bounced around randomly.
They have a "mean free path" between collisions. For water it's something like 0.1 nm
In order for the charge and field to have an effect the movement the energy associated with the charge moving that distance in that field must be bigger than the thermal energy or it will simply get swamped.
How far from a big negative ion must a proton be in order for the potential gradient to be "too small to matter"?
How big is your apparatus?
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If diffusion caused a charge imbalance, the subsequent charge would draw +&- ions back together. Diffusion of course happens but it will not separate ions, given the strength of the electrostatic attraction.
I didn't say that it will separate ions. They don't separate exactly because small charge imbalance is enough to make larger ions move to rebalance the charge.
Do you agree that smaller ions diffuse faster than larger ones?
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But, from the PoV of the electrostatic forces acting between the ions at each end, they are under water.
Either you consider an ion on one of the containers at each end, in which case it is surrounded by a lot of liquid or you consider an ion in the connecting tube- in which case it is surrounded by a lot of liquid.
In either case, if your Van de Graff can only produce one electro's worth of charge separation, it will only create a tiny energy difference.
The molecules get bounced around randomly.
They have a "mean free path" between collisions. For water it's something like 0.1 nm
In order for the charge and field to have an effect the movement the energy associated with the charge moving that distance in that field must be bigger than the thermal energy or it will simply get swamped.
Do you think that pH difference of materials in two containers doesn't affect the speed of diffusion?
Why or why not?
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Hamdani, in post #28 you suggested a charge differential would arise due to the more rapid diffusion of H+. This is what I was replying to. It's actually immaterial as H+ does not exist in an aqueous or other protic solvent: in water the species will be H3O+, H5O2+ and possibly some others( can't remember offhand). Not relevant but in ether one gets (C2H5)2OH+
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How big is your apparatus?
Let's pretend that the apparatus is similar to what's shown here. Just replace the salt bridge with a tube, filled with a mixture of solutions from both containers.
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Hamdani, in post #28 you suggested a charge differential would arise due to the more rapid diffusion of H+. This is what I was replying to. It's actually immaterial as H+ does not exist in an aqueous or other protic solvent: in water the species will be H3O+, H5O2+ and possibly some others( can't remember offhand).
Then the diagrams shown here are misleading.
https://www.electroniclinic.com/ph-meter-working-principle-ph-sensor-working-principle-explained/
Or these videos.
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Not so. That article is explaining PH and for that purpose it's quite acceptable to assume H+, there is no need to actually determine what degree of proton hydration is occurring.
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How big is your apparatus?
Let's pretend that the apparatus is similar to what's shown here. Just replace the salt bridge with a tube, filled with a mixture of solutions from both containers.
OK
And how far do you think the electrostatic effect of an ion's charge reaches before it is too small to influence things?
It's related to this
in water the species will be H3O+, H5O2+ and possibly some others( can't remember offhand).
A fairly common model assumes that the species (in dilute solutions ) is H9O4 +
It's about a nanometre across.
It's obviously got a positive charge on it and it will attract the water molecules around it.
But that attraction isn't strong enough to overcome the forces arising from the random molecules in the liquid.
If it was then there would be more water molecules "stuck on" and you would have H11O5+ or H13O6+
So we know that the effective range of teh electrostatic forces on a H+ ion in solution in water is only about a nanometre.
So, once again; how big is your apparatus?
If it's more than a few nm you can pretty much ignore the direct electrostatic effects.
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So, once again; how big is your apparatus?
If it's more than a few nm you can pretty much ignore the direct electrostatic effects.
I thought you can estimate the size from the video, that they are significantly larger than 1 cm.
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So, once again; how big is your apparatus?
If it's more than a few nm you can pretty much ignore the direct electrostatic effects.
I thought you can estimate the size from the video, that they are significantly larger than 1 cm.
I thought they would be.
In that case, shocking as you may find this, I was correct to say
The molecules can not possibly know what is happening somewhere else.
So there's no way for that to affect the way they diffuse.
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So, once again; how big is your apparatus?
If it's more than a few nm you can pretty much ignore the direct electrostatic effects.
I thought you can estimate the size from the video, that they are significantly larger than 1 cm.
I thought they would be.
In that case, shocking as you may find this, I was correct to say
The molecules can not possibly know what is happening somewhere else.
So there's no way for that to affect the way they diffuse.
So you won't think that this experiment below would work.
(https://www.palmsens.com/app/uploads/2021/06/Salt-bridge.png)
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So you won't think that this experiment below would work.
How long have you been having these hallucinations, and have you consulted a doctor?
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So you won't think that this experiment below would work.
How long have you been having these hallucinations, and have you consulted a doctor?
Why can't you just tell why it works?
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So you won't think that this experiment below would work.
How long have you been having these hallucinations, and have you consulted a doctor?
Why can't you just tell why it works?
Again with the nonsense.
I can tell how it works.
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Hamdani, it depends on what is in those two beakers. Lead is quite electropositive but it often appears to be less so.
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(https://mirjamglessmer.com/wp-content/uploads/2014/09/double-bucket-system2.png)
When the clamp is released, some of salt water will flow to the left container. They don't have to know what's there on the other side. It's just chained interactions among particles in those containers.
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I'm pretty sure the right hand tank would drain before anything else happened.
To make the system work properly you need to make it airtight.
I also think there's a problem because salt water is denser than fresh.
The water in the tube with the clamp would initially flow from right to left
Once you fix that...
Initially, when you first open the clamp, nothing happens in the salt- or fresh- water tanks.
After a short interval the message that there's a pressure gradient gets through and the liquid starts flowing.
That message arrives at the speed of sound in the liquid.
That's how it "knows" what to do and when.
What point were you trying to illustrate?
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Let's just remove the tube to bottom tank. I was too lazy to draw it myself, so I just search online images resembling what I meant.
What point were you trying to illustrate?
They don't have to know what's there on the other side.
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Let's just remove the tube to bottom tank.
OK
What point were you trying to illustrate?
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Let's just remove the tube to bottom tank.
OK
What point were you trying to illustrate?
It's contradicting your rhetoric.
The molecules can not possibly know what is happening somewhere else.
So there's no way for that to affect the way they diffuse.
Here is a video demonstrating diffusion with gas, but the effects have similarities with liquids.