# Surface area and diffusion relationship tips

### Fick's law of diffusion (video) | Khan Academy Diffusion is the process of which particles spread through regions of higher concentrations to regions of lower concentrations. The rate of. the larger the surface area, the greater the rate of diffusion. i think surely that with a larger cube of jelly, the surface is larger so therefore there is a greater rate of. Use cubes of agar to investigate how size impacts diffusion. All biological . What relationships do you notice between surface area, volume, Teaching Tips .

But of course, this is just going to extend out like that. And this is my new back wall. Right, this whole thing is my back wall. And so if I expand the area, now I have, of course, much more chance of getting some of these molecules back there. And the partial pressure is going to stay the same, so if I expand the area, I still have more molecules on this initial leftmost face. And so the pressure is going to stay the same. This is the P1 that we just got through talking about.

• Introduction
• Gas exchange
• Surface Area / Volume Ratio Biology Experiment

But because I have more area there's more chance that somewhere along this entire area a molecule will make its way across the thickness and hit that back wall. So something like that. And let me fill this in. So this is a fourth idea. Let me write that down as the fourth idea, is increase the area. So these are four good ideas, four good ideas for how you can maximize the amount of particles over time and hopefully make as much money as you can.

So this is exactly what Fick's law talks about. It talks about the idea of amounts of particles moving over time. So let me write out Fick's law, and this is actually how you most commonly will come across it, although there are some variations on it. It's going to look something like this. And I'm actually going to try to color code it to go along with the ideas that we already presented.

So we said there's some things you can do with pressure, some things you might do with the surface area, and also, remember we had that diffusion constant. And you divide all this stuff by the thickness of the wall. So it's very colorful, but this is Fick's law as you usually see it. There are some other variations I'll talk about. So to go through this piece by piece, this is V with a dot over it. This is the rate of particles moving. And when I say rate, you know that that means that there's some time component. So this gets to what the challenge was. We said, how many particles can you get to go to that blue back wall over some period of time.

And sometimes when we talk about particles we can think of them as giving that in terms of an amount. You might think of that as like a moles or some numerical value, or the volume of a gas that's moving across. So that's why sometimes you'll see it as V, to refer to volume.

On the other side, this bit makes perfect sense. If you have more molecules, that's going to cause more pressure, we said earlier.

And if there's a bigger pressure difference between what's on the first side versus what's on the second side-- remember the second side is the back wall-- then of course that's going to mean that more of the molecules are going to move over. So this is a bigger difference. So sometimes you'll see this as delta P, and delta just means difference. This A, we said, refers to just surface area. Of course if you have a greater surface area, that's going to allow for more of the molecules to get across.

This D, that's an interesting one. This is diffusion constant. And remember when we think about diffusion constant, there are two laws that might jump into your head. In fact, the first one was Henry's law, and you remember we talked about solubility, in terms of the amount of molecules that go from, for example, air to liquid.

This is Henry's law that told us about that. And of course if something is very soluble, then maybe that would be an increased P1, going back to the idea of pressure at the first wall. And then you have to divide by the molecular weight.

The square root, in fact, of the molecular weight. So that's the idea we had, and this actually comes from Graham's law. So whenever I talk about the diffusion constant, remember there are two laws that are in play here, Henry's law and Graham's law, that are coming together to offer us some information about the diffusion constant.

And that's actually why we said, well, if you have a small molecular weight molecule, maybe that'll help you out, because it's in the denominator it's going to cause the rate of particles moving across to go up. And finally, this T, this is thickness. This is the thickness of the wall. And this is totally intuitive. If you have a thick wall, it's going to be harder for molecules to make it across very quickly.

So without even knowing it, you kind of derived Fick's law all by yourself just kind of using intuition, and that's kind of the best way to learn this stuff. And sometimes, as I mentioned, you might see this formula written differently. In fact, let me actually just rearrange this formula in a different way.

I'm just going to sketch out how you might also see it, which is that sometimes you see area on this side of the equation. Of course, that's just rearranging it, right, dividing both sides by area. And then you might see the P actually up here, like P1 and then minus P2, something like this.

And in the denominator over here, you'll see the T. So you'll get this, and then very separately you'll see times D. So this might not look so different, but what happens is that then people lump things, and that's when things get kind of tricky. They'll say well, let's lump this together, and let's lump this together. And they'll call this flux. And this second part they'll call gradient. So you may see Fick's law written this way, where it says flux equals the gradient times diffusion constant.

Because of course the diffusion constant hasn't changed, it's the same thing, it just carries on down. And if you see it that way, let me just give you an example of what these things mean. Let's start with flux, which is basically the net rate of particles moving through an area, moving through some area. And you can kind of follow through the equation and that makes sense.

When the surface area to volume ratio goes down it takes longer for the hydrochloric acid to diffuse into the cube but if the ratio goes up then the hydrochloric acid diffuses more quickly into the block of gelatin.

Some shapes have a larger surface area to volume ratio so the shape of the object can have an effect on the rate of diffusion. It is important that cells have a large surface area to volume ratio so that they can get enough nutrients into the cell.

They can increase their surface area by flattening and becoming longer or by having a rough surface with lots of folds of cell membrane known as villi.

The cell membrane is made up of a lipid bi-layer with many proteins integrated into it. The concentration of oxygen in the cell is always lower than outside the cell which causes the oxygen to diffuse in.

Gases will always dissolve from an area of high to low pressure. The concentration of carbon dioxide outside the cell is lower than the concentration in the cell so the carbon dioxide will always dissolve out of the cell.

Single celled organisms such as amoebas have a large surface area to volume ratio because they are so small.

### How does surface area to volume ratio affect the rate of diffusion? | Socratic

They are able to get all the oxygen and nutrients they need by diffusion through the cell membrane. Larger organisms such as mammals have a relatively small surface area compared to their volume so they need special systems such as the lungs in order to get enough oxygen. Surface area to volume ratio is very important in lungs where a large amount of oxygen has to get into the lungs. The lungs have a very large surface area because they contain millions of sacs called alveoli which allow oxygen to diffuse into the bloodstream.

By having millions of these alveoli the lungs are able to cram a very large surface area into a small space. This surface area is sufficient for all the oxygen we need to diffuse through it and to let the carbon dioxide out. By increasing the surface area the rate of diffusion will go up. Precautions a All the gelatin used should be taken from the same block to ensure that all the blocks are made up of the same materials.

Limitations To help make this experiment more accurate, I repeated it three times for each block size and then used the average of all the results to plot a graph with a line of best fit. I tried to keep all the variables except for the size of the gelatin blocks the same for all the experiments.

## Fick's law of diffusion

However, in reality it is impossible to keep all the variables precisely the same. I measured the sizes to the nearest mm so the sizes of block that I used should be correct to the nearest mm. Anomolies The graph produced shows a smooth curve with a decreasing gradient as the surface area to volume ratio goes up.

The only anomaly is the result for the 5 x 5 x 5 block. The result here is higher than the curve of best fit for the graph.