How Surface Area / Volume Ratio Affects The Rate Of Diffusion

Background Information

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 specialist organs to respire such as lungs or gills.

Apparatus

Beakers
Gelatin blocks containing cresol red dye
0.1M Hydrochloric acid
Stop Watch
Scalpel
Tile
Safety glasses

Method

1. A block of gelatin which has been dyed with cresol red dye 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

Cresol red dye 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 a light yellow colour.

Gelatin is used for these tests as it is permeable and so 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 100cm³ of 0.1 molar Hydrochloric acid.

3. A gelatine block is put into this beaker and the time for all the red dye to disappear is noted.

4. This test should be repeated for all the sizes of blocks three times to ensure a fair test. Fresh acid should be used for each block to ensure that this does not affect the experiment’s results.

5. The surface area / volume ratio and an average of the results can then be worked out.

6.A graph of Time against Surface Area to Volume Ratio can then be plotted. From this graph we will be able to see how the surface area affects the time taken for the hydrochloric acid to penetrate to the centre of the cube.

Results

Dimensions (mm)	Surface Area	Volume (mm³)	Surface Area / Volume Ratio	Test 1 Time	Test 2 Time	Test 3 Time	Average Time (min:sec)
5 x 5 x 5	150	125	1.2:1	7.02	6.57	4.53
10 x 10 x 10	600	1,000	0.6:1	12.30	23.25	15.33
15 x 15 x 15	1,350	3,375	0.4:1	29.55	30.22	23.45
20 x 20 x 20	2,400	8,000	0.3:1	53.4	32.44	38.56

The Surface area to Volume ratio is calculated by

Surface Area To Volume Ratio = Surface Area / Volume

To Do .......

From these results calculate the average diffusion time for each block of gelatin

Plot a graph of the Surface Area to Volume Ratio against time, either as a bar chart or a scatter graph.

What can you conclude about the rate of diffusion of acid into the gelatin blocks?

How will this effect limit the size of the cell?