# Surface Area to Volume Ratio and the Relation to the Rate of Diffusion.

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• Published: May 26, 2003

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Surface Area to Volume Ratio and the Relation to the Rate of Diffusion

Aim and Background

This is an experiment to examine how the Surface Area / Volume Ratio affects the rate of diffusion and how this relates to the size and shape of living organisms.

The surface area to volume ratio in living organisms is very important. Nutrients and oxygen need to diffuse through the cell membrane and into the cells. Most cells are no longer than 1mm in diameter because small cells enable nutrients and oxygen to diffuse into the cell quickly and allow waste to diffuse out of the cell quickly. If the cells were any bigger than this then it would take too long for the nutrients and oxygen to diffuse into the cell so the cell would probably not survive.

Single celled organisms can survive as they have a large enough surface area to allow all the oxygen and nutrients they need to diffuse through. Larger multi-celled organisms need organs to respire such as lungs or gills.

Method

The reason I chose to do this particular experiment is because I found it very interesting and also because the aim, method, results- basically the whole experiment would be easily understood by the average person who knew nothing about Surface Area/Volume Ratio. The variable being tested in this experiment is the rate of diffusion in relation to the size of the gelatin cube. Another experiment one could do to determine the surface area to volume ratio is to construct a set of cubes out of construction paper- 1 x 1, 2 x 2, 3 x 3 and 4 x 4 (cm).Then use this formula to determine the surface area- L x W x 6 and compare it with the volumes. The formula to determine volumes of cubes is L x W x H. Although that type of experiment will show no insight into SA/V ratio in relation to the rate of diffusion.

Equipment

1. Agar-phenolphthalein - sodium hydroxide jelly

2. O.1 M hydrochloric acid

3. Ruler (cm and mm)

5. Paper towel

6. Beaker

Method

1. A block of gelatin which has been dyed with phenolphthalein should be cut into blocks of the following sizes (mm).

5 x 5 x 5

10 x 10 x 10

15 x 15 x 15

20 x 20 x 20

30 x 30 x 30

20 x 5 x 5

Phenolphthalein is an acid/alkali indicator dye. In the alkali conditions of the gelatin it is red or purple but when it gets exposed to acid it turns almost colorless.

Gelatin is used for these tests because it is permeable which means it acts like a cell. It is easy to cut into the required sizes and the hydrochloric acid can diffuse at an even rate through it.

2. A small beaker was filled with about 400ml of 0.1 molar Hydrochloric acid. This is a sufficient amount of acid to ensure that all the block sizes are fully covered in acid when dropped into the beaker.

3. One of the blocks is dropped into this beaker, left for 10 minutes, then removed, dried, and cut in two to measure the depth of penetration. This test should be repeated for all the sizes of blocks three times to ensure an accurate test. Fresh acid should be used for each block to make sure that this does not affect the experiment's results.

4. The Surface Area/Volume Ratio and an average of the results can then be worked out. A graph of Surface Area to Volume Ratio can then be plotted along with percentages left colored and uncolored . From this graph we will be able to see how surface area affects the rate of diffusion of materials into the cubes.

Results

I carried out the above experiment and these results were obtained.

Dimensions (mm) Surface Area Volume (V) (mm) Surface Area / Volume Ratio Test 1 Test 2 Test 3

5 x 5 x 5 150 125 1.2:1 1mm 1mm 1mm

10 x 10 x 10 600 1,000 0.6:1 1mm 1mm 1mm

20 x 20 x 20 2,400 8,000 0.3:1 1mm 1mm 1mm

30 x 30 x 30 5,400 27,000 0.2:1 1mm 1mm 1mm

The Surface Area to Volume Ratio is calculated by

SA = cm

From these results I was able to make a graph of the volume still coloured along with the percentages left coloured and uncoloured....