Complete the following table which will be used to determine the effect of surface area to volume ratio of each cube “cell” affects the diffusion rate of substances into the cell.
|Cube “cell” |Surface Area (cm2) |Volume (cm3) |Surface Area -to- |Diffusion Depth (mm) |Diffusion Rate (mm/min.) |
| | | |Volume Ratio | | |
|1 cm |12.56 |4.19 |3.0 | | |
|2 cm |50.24 |33.5 |1.5 | | |
|3 cm |113.04 |113.04 |1.0 | | |
Discussions and Conclusions
1. Describe any changes that you observe in the appearance of the cube “cells.”
The vinegar started eating the cell and the size of the cells started to get smaller .
2. Prepare a graph of the “Diffusion Depth (mm)” on the y-axis and “Surface-to-Volume Ratio” on the x-axis.
3. Using the graph from step 2, what relationship (if any) exists between the surface area to volume ratio and the depth of diffusion of the vinegar?
As a percentage of cube volume and with diffusion limited to a set short length of time, the larger cube would take up a smaller percentage of its complete volume relative to the smaller cube's similarly calculated percentage content. But, if you compare absolute content without regard to cube size, the larger cube will have taken up more. This is because diffusion rate is a linear function, but surface area to internal volume is an exponential function. This means that as the size of the cube increases, there is less and less surface area to volume ratio, and therefore much more agar to be serviced by a relatively smaller surface area.
4. Prepare a graph of the “Diffusion Rate (mm/min.)” on the y-axis vs. the “Surface Area (cm2)” on the x-axis.
Sphere area = 4 * pi * radius * radius
Sphere volume = (4/3) * pi * radius * radius * radius
radius = 1 area = 4 * pi * 1 * 1 = 12.56 volume = (4/3) * pi * 1 * 1 * 1 = 4.19 area : volume ratio = 12.56 / 4.19 = 3.0
radius = 2 area = 4 * pi * 2 * 2 = 50.24 volume = (4/3) * pi * 2 * 2 * 2 = 33.5 area : volume ratio = 50.24 / 33.5 = 1.5
radius = 3 area = 4 * pi * 3 * 3 = 113.04 volume = (4/3) * pi * 3 * 3 * 3 = 113.04 area : volume ratio = 113.04 / 113.04 = 1.0
5. Using the graph from step 4, construct a statement about the relationship between the surface area-to-volume ratio and the rate of diffusion of the
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