Chigozie's Cell Size and Diffusion Argumentation

Cell Size and Diffusion Argumentation

       Almost all living cells depend on the process of diffusion to obtain essential nutrients that are needed for survival. As these nutrients are taken in by the cells, they are broken down. The resulting energy and molecular building blocks from the nutrients are used to make more cellular components. Because of this, a cell would grow by increasing in size. However, cells never get too big; they are always small. So, why are cells so small? In this lab, my lab group and I worked towards answering this one question. We were given two potential answers to this question. Explanation 1 stated, “Cells that have a larger surface area to volume ratio are more efficient at diffusing essential nutrients”. Explanation 2 stated, “The rate of diffusion is related to cell size. Nutrients diffuse at a faster rate through small cells than they do through large cells. After collecting and analyzing data with my lab group, I concluded that although our data seemed to support both explanations, Explanation 2 was more valid.

My lab group and I tested the validity of these different explanations by constructing a model cell using agar. Agar is a gel-like substance that we could easily manipulate and cut into a variety of shapes. In this lab, phenolphthalein (a chemical indicator that changes color when it comes in contact with an acid) was added to agar so that we could see how far the acid (in this case, vinegar) diffused into the model cell. The agar was blue and would turn a yellowish-clear color when the phenolphthalein in it came in contact with the vinegar. My group cut four different rectangular prisms from the agar. Two were relatively small, and two were relatively big. We measured the dimensions of the cubes and then placed them in a plastic container filled with vinegar.

Rectangular Prism Dimensions Before Diffusion

Rectangular Prism	Length	Width	Height
1 (Small)	2 cm.	2 cm.	1.5 cm.
2 (Big)	3.5 cm.	3.5 cm.	1.7 cm.
3 (Big)	3.5 cm.	3.5 cm.	1.6 cm.
4 (Small)	1.9 cm.	1.9 cm.	1.5 cm.

Rectangular Prisms of Agar before diffusion

 

We started timing the diffusion process with a stopwatch as soon as the cubes were placed in the vinegar. The cells began to change color (from blue to yellowish-clear) at approximately 7.3 seconds. We left the rectangular prisms in the vinegar for as long as time permitted us, which was 32 minutes and 9 seconds. At this time, we pulled out the rectangular prisms. Because of this time restriction, the vinegar was not able to diffuse all the way through the rectangular prism and we had to measure the dimensions of the part of the rectangular prism that the vinegar had not touched.

Dimensions of the Rectangular Prism Not Touched by Vinegar

Rectangular Prism	Length	Width	Height
1 (Small)	1 cm.	0.8 cm.	0.7 cm.
2 (Big)	2.5 cm.	2.5 cm.	0.5 cm.
3 (Big)	2 cm.	2.5 cm.	0.9 cm.
4 (Small)	0.9 cm.	0.5 cm.	0.5 cm.

Rectangular Prism after diffusion

 

            Afterwards, my lab group and I calculated the diffusion rates. Instead of just averaging the dimensions (length, width, height) and putting that average distance over time to find the rate, we had to find the dimensions of the space that had been touched by vinegar since the vinegar did not diffuse all the way through the rectangular prism. Mr. Hammer helped us greatly with the visualization and explanation displayed below. In order to find the dimensions of this space, we had to take the dimensions of the rectangular prism not touched by the vinegar, subtract it from its respective dimension of the original rectangular prism, and divide by two. For example, if the original length was 14 and the length of the rectangular prism not touched by vinegar was 5, we would do 14-5, which is 9, and divide by 2 and get 4.5 as one of the new dimensions that we will use to find the rate of diffusion.

How to Calculate the Sides Needed for the Calculation of the Rates of Diffusion

Side one= (original length minus non-diffused cube length) ∕2

Side two= (original width minus non-diffused rectangular prism width) ∕2

Side three= (original height minus non-diffused rectangular prism height) ∕2

Mr. Hammer's very useful diagram

 

Results of Calculations of Sides Used for Rates of Diffusion Calculations

Rectangular Prism	Side One	Side Two	Side Three
1 (Small)	0.5 cm.	0.6 cm.	0.4 cm.
2 (Big)	0.5 cm.	0.5 cm.	0.6 cm.
3 (Big)	0.75 cm.	0.5 cm.	0.35 cm.
4 (Small)	0.5 cm.	0.7 cm.	0.5 cm.

           

To find the rate of diffusion, we had to divide total distance travelled by the vinegar into the rectangular prism by the total amount of time the rectangular prisms spent in the vinegar. First, we had to average out the dimensions of in the table above for each rectangular prism (sum of length, width, and height divided by three). We then converted the total time, 32 minutes and 9 seconds, into seconds and got 1929 seconds in total. We divided each average dimension by 1929 seconds, the total time, to get the rate of diffusion for each rectangular prism.

Rates of Diffusion for Each Rectangular Prism

Rectangular Prism	Average Dimension	Rate of Diffusion
1 (Small)	.5 cm.	.000259 cm/sec.
2 (Big)	.53 cm.	.000276 cm/sec.
3 (Big)	.53 cm.	.000276 cm/sec.
4 (Small)	.57 cm.	.000294 cm/sec.

           

My lab group and I also calculated the surface area, volume, and ratio of surface area to volume.

All Calculations

Rectangular Prism	Surface Area (SA)	Volume (V)	Ratio of SA to V	Decimal Representation of SA to V Ratio	Rate of Diffusion
1 (Small)	20 cm.2	6 cm.3	10 : 3	3.33	.000259cm/sec.
2 (Big)	48.3 cm.2	20.825 cm.3	48.3 : 20.825	2.32	.000276cm/sec.
3 (Big)	46.9 cm.2	19.6 cm.3	46.9 : 19.6	2.39	.000276cm/sec.
4 (Small)	18.6 cm.2	5.415 cm.3	18.6 : 5.415	3.43	.000294cm/sec.

 

After analyzing all of this data, I concluded that Explanation 2 was more valid. Again, Explanation 2 states, “The rate of diffusion is related to cell size. Nutrients diffuse at a faster rate through small cells than they do through large cells”. At first, it looked like the data that we collected supported both explanations. Explanation 1 states, “Cells that have a larger surface area to volume ratio are more efficient at diffusing essential nutrients”. For Explanation 1, the rectangular prism with the largest surface area to volume ratio also had the highest rate of diffusion. However, rectangular prism 1 refutes this statement because it has the second largest surface area to volume ratio but the lowest rate of diffusion. For Explanation 2, the smallest cell (rectangular prism 4) had the fastest rate of diffusion. However, the other small cell (rectangular prism 1) also had the slowest rate of diffusion, so that rectangular prism also disproved Explanation 2. Because of this, I decided that rectangular prism 1 should not be totally considered for this conclusion. It is the only rectangular prism that refutes both explanations. After taking all of this into consideration, I noticed that the surface area to volume ratios for rectangular prisms 2 and 3 are different, but their rates of diffusion are not. One would expect them to have different rates of diffusion since their surface area to volume ratio is different. However, they have the same rate of diffusion. Because of this key piece of evidence, Explanation 2 is more valid. Rectangular prism 2 and 3 are both the two pieces of agar that we made relatively big, so they support Explanation 2 in that the bigger cells have the same rate of diffusion and also a lower rate of diffusion than that of the smallest cell.