now the next factor that can also affect diffusion rate is something known as total surface area to volume ratio in the exam they can also just put it as tsa2v in Brackets all right so you can write TSA to V in the exam but what that means is just the total surface area to volume ratio I like to ask my students a very simple question why is it that most cells in this world are microscopic there are exceptions where certain cells can be seen with the naked eye but under normal circumstances most cells are microscopic why don't we see giant cells the size of our smartphones or the size of a bid or the size of a pillow or the size of a car why are all cells microscopic the answer to that is due to this concept known as total surface area to volume ratio now imagine a situation that I'm going to give you over here where you have two clear jelly cubes the jelly cubes are transparent and you can see there is a there is a jelly Cube on the left and the jelly Cube on the right okay I'm just going to call them jelly Cube A and B and both these jelly cubes are immersed in a pink solution and what happens is the pink solution will then diffuse into the jelly Cube and start making the cube become a pink color as well so far so good my question is which jelly Cube A or B will become fully pink first which means which jelly Cube will become totally pink first the small jelly Cube or the large jelly queue now most students will mull this over and sometimes I'll get students saying it's the small jelly Cube that it fills up first but a lot of my students will also say Well it must be the larger jelly Cube that fills up first the reason is because the large jelly Cube has a larger surface area and in the previous video I said that larger surface area have a faster diffusion weight so diffusion happens faster and therefore it fills up faster compared to this smaller jelly queue in reality however this is where it becomes a bit interesting it's the small jelly Cube that actually becomes fully pink first so this is a bit weird isn't it because why why is the smaller jelly Cube becoming pink first even though it has a smaller surface area yes instead I'm still looking at it at a three-dimensional point of view let's just look at a two-dimensional view of each Cube which means to say we are going to look at the cross section Now for Jelly cube a you can see the cross section is on the left angelicube B the cross section is on the right and you can see the pink solution surrounding it for jelly cube a to totally become pink the pink solution only has to diffuse a very short distance to cover the entire volume or to fill up the cube as I have shown you in the arrows but for the jelly Cube on the right yes it has a larger surface area but even when the pink solution diffuses in as I've represented in the arrow has it covered the entire jelly Cube the answer is no there is still a lot of empty white spaces there and therefore it will actually have to diffuse a greater distance to fill up the cube and diffusion is weird because the longer or the larger the distance of diffusion the diffusion rate significantly slows down and that is why the jelly Cube fills up slowly so how can we try to conceptualize this with the calculation well let's do this again I'm going to show you here that there are three jelly cubes okay the cube on the left has one millimeter sides the cube in the middle has five millimeter sides and the cube in on the right hand side have has a 10 millimeter side on each side so the first thing you have to do when you're comparing these cubes is you will have to first calculate each Cube's total surface area remember each Cube has six surfaces so when you're calculating surface area the first one is six times one times one so you'll get six millimeter square the second one is six times five times five which is 150 millimeter square and the one on the right is six Surface Times Ten millimeter times 10 millimeter to get 600 millimeters Square so right off the bat you can see that the cube on the right has the largest total surface area but wait we are not done because it's not only surface area that increased in the cubes it's volume as well so the next thing we have to do is we have to calculate the volume of each Cube and the volume of each Cube I have written it down at the bottom the first Cube has a one millimeter Cube volume second one is 125 millimeter Cube volume and the third one is a 1 000 millimeter Cube volume you notice that even though total surface area increased the volume increased at an even more exponential rate so to make sure we understand what's going on here the third thing that we have to do is calculate its total surface area to volume ratio so the total surface area for the first R2 volume ratio for the first cube is 6 to 1 which I've represented as six millimeter square to one millimeter Cube okay so it's six to one the second one is 150 millimeters squared 225 millimeter Cube and I'll simplify this to six to five the third one is 600 millimeter square to one thousand millimeter Cube which we can simplify it to which we can simplify to three to five okay the smallest as you can see here when you're comparing the values it's not fair because the denominator or the second value of the ratio is 1 is 5 and 5 which I've uh circled okay okay I want to make all the circuit all the values that I've circled to the same number so 6 to 1 1.221 and 0.621 by doing this we can then compare each Cube's total surface area to volume ratio we notice something very interesting here the smallest Cube has the largest total surface area to volume ratio the second Cube has a medium a slightly lower total surface area to volume ratio and the largest Cube has the smallest total surface area to volume ratio so you might go okay so what what does this mean what this means is as the size of the cube increases the total surface area to volume ratio decrease and when that decreases diffusion weights significantly decreases due to the larger distance of diffusion so if I were to show the cross section here what this means is the total surface area of the cell for the large cube is unable to support the cell by diffusion because the particles will have to move at a greater distance so diffusion weight for the larger Cube will be extremely slow that's what that means so the total surface area to volume ratio is just a measurement to tell us that can the surface area of the cell support the volume of the cell by diffusion the larger the ratio the better it means that diffusion can support the cell or the cube by diffusion but the smaller the value of this ratio it means that the surface area is unable to support the cube or the cell by diffusion so to come back to my first question I told you that most cells in nature are extremely small to a point that they are obviously microscopic okay why are they not large because for example let's just take two cells okay you have a cell that is 40 micrometers okay and you have a cell that is extremely large let's just say that this cell over here is way larger than 40 micrometers based on what we saw with the cube earlier if the cell is too big the total surface area to volume ratio decreases okay so how does that apply to real life you see let's imagine that each cell that's a small red dot inside the cell I hope you can see that and that small bit dot represents the mitochondrion now what's one function of the mitochondrion is to produce ATP and for it to produce ATP the mitochondrion means oxygen that's just the way it works through a process known as aerobic respiration obviously the smaller cell has a smaller surface area and the larger cell has a larger surface area so the larger cell can take in more oxygen but it will still die regardless the smaller cell even though it takes in lesser oxygen it will remain alive how is that possible the reason is because the smaller cell has a high total surface area to volume ratio which means to say the oxygen just needs to travel a short distance to reach the mitochondrion easily that's what that means but the cell the larger cell yes it can take in more oxygen but the oxygen has to diffuse a greater distance and this cell has a low total surface area to volume ratio so by the time the oxygen reaches the mitochondrion the cell was deprived of ATP because the diffusion was so slow that the cell eventually dies that is why large cells are just not evolutionarily feasible in the grand scheme of things there are exceptions to the rule obviously but under normal circumstances extremely large cells are just detrimental to life with that out of the way sometimes they can ask a few tricky questions now what I'm going to do here is I'm going to actually draw out three gel Cubes but a is a cube and C is also a cube but B is a cuboid between cube a and Cube C which one fills up first based on your knowledge you know for the fact that a will fill up first because it is much smaller and it also has a larger total surface area to volume ratio compared to cube C so that's quite simple and in C because it's larger okay due to its larger volume it will not fill up as easily as cube a all right now the focus here is basically between Cube A and cuboidal B okay which one will fill up you cannot fairly compare A and B because once a cube and one's a cuboid and a has a volume of one millimeter Cube and B has a volume of 10 millimeter Cube okay so immediately students will go well it has a smaller volume so it will fill up first but B has a larger volume so it's slower in this case it is wrong to make that assumption the reason is because they will fill up at almost the same time so you might be going wait how is that possible why does that happen the reason is because you just have to focus on the minimum distance of diffusion for a and b for a the minimum distance of diffusion is one millimeter which I've highlighted and for B it also has a minimum distance of diffusion of one millimeter which I've highlighted over that so A and B both have the same minimum distance of diffusion so when you compare the cross section of both A and B notice that for a the particles just have to move that short distance to to fully fill up the cube and for B it will also just have to move the same distance of diffusion to totally fill up q b that is why they will both fill up at the same time because of the minimum distance of diffusion that is a very important point that you must know as well