[scientizscht (OP)]

Hello

In a container with water, when we release a solute from a single point, it takes quite long time for this to diffuse in the water.

However, when we have a catalyst at a point that converts the existing solute in a water container, the diffusion to replenish the solute at the point of the catalyst is much faster. Basically it seems that nature does not like the creation of gaps in the diluted mass.

Are there different equations explaining those two situations?

How can I estimate the rate of replenishment that will feed the catalyst and keep the reaction going?

Thanks.

[evan_au]

Am I reading this correctly?

It seems you are comparing two scenarios:
1. drop some solute into solvent, with no stirring. The solute will diffuse slowly outward, with concentration at a distant point will slowly increase over time, until eventually the concentration will be uniform throughout the solution.
2. When the solute has partially spread through the solvent, drop a catalyst into a region where the solute has a fairly high concentration. The reaction will occur quickly.

It seems to me that these two scenarios are consistent.
- It takes a while for a solute to passively diffuse throughout the solvent
- But reactions will go faster where the concentration is higher than where it is lower

That's why industrial chemical reactions use a stirrer.

PS: Please explain what reaction is being promoted by the catalyst?
- You have one solute in the solvent
- The solvent doesn't participate in the reaction (otherwise you would call it a reactant rather than a solvent)
- The catalyst does not participate in the reaction (by definition)
- So we seem to be missing a critical factor in the description - some other reactant?

[scientizscht (OP)]

No, I didn't mean exactly that.

Scenario 1:
You have a large water container and you put inside some sugar (no sprinkling it from the top but let's say injecting it at the bottom of the container).
If you do not stir the water, the sugar will take significant time to diffuse across the whole container and establish a uniform sugar concentration.

Scenario 2:
You have a large water container that has sugar in it which has diffused across the whole container and a uniform sugar concentration has been established.
Then you inject some catalyst that reacts with sugar (and perhaps oxygen or something else but it does not really matter).
The concentration of sugar around the catalyst will drop as sugar is converted. However, sugar from further surrounding areas in the solution will diffuse towards the catalyst so that the sugar concentration is replenished constantly and it does not create a gap around the catalyst where sugar has not managed to replenish.

The diffusion in scenario 1 is very slow.
The diffusion is scenario 2 seems to be much faster.

Is that true? Do they really differ?
How do we calculate the propagation of sugar concentration in Scenario 1 and how the replenishment of sugar concentration in Scenario 2?

Thanks!

[Bored chemist]

Is that true? Do they really differ?

No.
The sugar molecules wander round at random.

[yor_on]

Scientizscht, it seems to me as if you're trying to build a world image of how things work?
Is that it, or do you have some other purpose with your questions?

[scientizscht (OP)]

I still have not received any answer. How can I calculate the rate at which concentration is replenished on a catalytic surface? How many molecules per cm2 per second for a solution of specific concentration?

Thanks!

[Bored chemist]

I still have not received any answer. How can I calculate the rate at which concentration is replenished on a catalytic surface? How many molecules per cm2 per second for a solution of specific concentration?

Thanks!

Yes you did.
https://www.thenakedscientists.com/forum/index.php?topic=77801.msg584055#msg584055

[scientizscht (OP)]

I still have not received any answer. How can I calculate the rate at which concentration is replenished on a catalytic surface? How many molecules per cm2 per second for a solution of specific concentration?

Thanks!

Yes you did.
https://www.thenakedscientists.com/forum/index.php?topic=77801.msg584055#msg584055

I do not think this is accurate. Does it take into account the formation of a diffusion layer? The concentration a little further from the catalytic surface, will be very small. Also, it does not consider the diffusion coefficient at all. The diffusion coefficient in water is several magnitudes smaller than the diffusion coefficient in air, not to say in vacuum.

Your equation for a 5mM solution of protons gives 10^27 molecules per m2 per sec.

This is a massive amount. It basically says that 10,000 moles of protons hit a surface of 1m2 per second!

That cannot be true. It may be true for a gas in vacuum but definitely not for a water solution. Also, it cannot be true that the concentration around an 1m2 electrode is replenished at 10,000 moles per second. That is a trully massive amount and diffusion would never limit reactions if it had such capacity.

[Bored chemist]

That cannot be true.

Are you sure about that?

[Bored chemist]

Your equation...

It's not my equation; it's THE equation.

[scientizscht (OP)]

That cannot be true.

Are you sure about that?

Something is missing obviously. You get kg of substrate onto a catalytic surface per second per cm2. This cannot be true because there wouldn't be a diffusion limited enzyme or a diffusion limited electrode.

I appreciate not all collisions result in reactions but there are *diffusion* limited reactions which means that the limit is the mass transport onto the catalyst and not the low rate of reactions over collisions.

[Jarek Duda]

There are two basic philosophies for choosing random walk/diffusion:
- GRW like "drunken sailor", locally maximizing entropy by assuming e.g. equal probability distribution among single choices,
- MERW maximizing mean entropy e.g. by assuming equal probability distribution among entire paths (like in path integrals).

GRW doesn't have localization property, MERW has (stationary probability distribution exactly as quantum ground state) - from https://en.wikipedia.org/wiki/Maximal_entropy_random_walk evolution on lattice with defects:


In practice GRW works well for macroscopic objects (like humans), but completely disagrees for electrons (no localization property) - what is repaired in MERW.
Maybe such additional localization property could help here?

[Bored chemist]

This cannot be true

OK, you think the established answer is wrong. What value do you calculate?

[scientizscht (OP)]

This cannot be true

OK, you think the established answer is wrong. What value do you calculate?

I list a calculation here: https://www.thenakedscientists.com/forum/index.php?topic=79911.msg606978#msg606978

[Bored chemist]

I think they made a mistake

[scientizscht (OP)]

I think they made a mistake

They show the current density x10 times larger but you are proposing it's x100,000 larger.