Surface Area To Volume Ratio 4p4423

Surface area to volume ratio Introduction: Understanding the relationship between the size of a cell (volume) and its surface area helps to realize how the physical limitation of the size is important if they are to function effectively. Diffusion is a slow process and so, to be more effective, the surface area to volume ratio has to be increased. This investigation makes use of a model to investigate the effect of the surface area to volume ratio on cellular diffusion. Cells of different sizes are represented by the agar jelly cubes to help visualize and to better understand the concept. Aim: To investigate how the surface area to volume ratio effects the rate of diffusion. Hypothesis: The higher the surface area to volume ratio, the faster the rate of diffusion. The smallest cube with the highest surface area to volume ratio will turn white sooner than the other two jelly cubes as the rate of diffusion will be faster. Equipment:  Gelatin block ( 0.5 cm, 1cm, 2cm cubes)  150 ml hydrochloric acid  Ruler  Butter Knife (Plastic)  Paper Towel  250ml beaker  Plastic spoon  Stopwatch Procedure: 1. Calculate the surface area to volume ration of the three cubes and record it. 2. Place the cubes in the beaker and make sure that each cube is not touching each other. 3. Pour hydrochloric acid in the beaker and leave it for 15 minutes. 4. Using the plastic spoon turn the cubes over every 2 minutes. 5. Remove the cubes after 15 minutes and dry using the paper towel. 6. Cut each cube into two using a butter knife. 7. Measure the depth of the penetration of acid (white covering over the cubes) and record it. 8. Complete the remaining calculations in the table. Results: Cube Surfac size e Area (cm) (cm2) 0.5 1 2

1.5 6 24

Volum e (cm3)

SA/V ratio

0.125 1 8

12 6 0.25

Depth of penetrat ion (mm) 5 3 2

Volum e left colour ed 0 0.064 0.216

% left colour ed

% acid penetrat ion

0 6.4 2.7

100 99.936 99.784

Conclusion: The results obtained show that HCl penetrated faster in the small cube compared to the others. It also demonstrates that as the cell size increases, the surface area to volume ratio decreases. As the surface area to volume ratio increases, the rate of diffusion also increases. And as the surface area to volume ratio decreases, the rate of diffusion also decreases. This is why small cells are more effective at taking in nutrients. Discussion: The hypothesis has been proven right that the higher the surface area to volume ratio, the faster the rate of diffusion. This experiment was conducted to investigate the effect of the change in the surface area to volume ratio on the rate of diffusion. To carry out this experiment, agar jelly was cut into 3 different sized cubes of sides 0.5 cm, 1 cm and 2 cm. The agar jelly cubes were in small, medium and large sizes. They were then covered in hydrochloric acid for 20 minutes to find out on which cube the acid would penetrate the most. The small cube of sides 0.5 cm had a surface area of 1.5 cm2, volume of 0.125 cm3 and the surface area to volume ratio of 12:1. The depth of penetration was 5 mm, volume and percentage of volume left to be coloured was 0%. The percentage of acid penetration in the cube was 100%. The medium cube of sides 1 cm had a surface area of 6 cm2, volume of 1 cm3 and the surface area to volume ratio of 6:1. The depth of penetration of acid was 3 mm into the cube, volume left to be coloured was 0.064 cm3 and 1.07% was left to be coloured. Acid penetration was 99.34%. The large cube of sides 2 cm had a surface area of 24 cm2, volume of 8 cm3 and the surface area to volume ratio of 3:1. The depth of penetration was 2 mm, volume left to be coloured was 0.216 cm3 and percentage left to be coloured was 2.7%. HCl had penetrated 99.78% of the cell. The results obtained convey that as the volume of the cube increases, the surface area to volume ratio decreases. The surface area to volume ratio of the smallest cube was 12:1, medium cube was 6:1 and the largest cube was 3:1. This suggests that small cubes have a large surface area to volume ratio. Since the cube has a higher to the surroundings, it allows for a greater rate of diffusion. Therefore as a cell increases in size, its ability to diffuse nutrients in and wastes out will decrease. This is why cells are small and have a higher surface area to volume ratio. It is evident that diffusion had occurred in the cube because the colour of the agar jelly cube changed from pink to white. The cube that had the greatest rate of diffusion of HCl in 20 minutes was the smallest cube of sides 0.5 cm. The depth of penetration was 5mm and the percentage of acid penetration was 100%. The cube that showed the least depth of penetration was the largest cube of sides 2 cm. The depth of penetration as 2 mm and the percentage of penetration was 99.78%. HCl penetrated faster to the centre of the smallest cube. This suggests

that as the cube gets larger it takes longer for HCl to diffuse through to the centre even if the rate of diffusion is the same for all. Therefore cells must be small in order to effectively take in nutrients. The experiment was limited as the cubes do not have a selectively permeable membrane such as a cell membrane. Ways to improve the accuracy of the results include measuring the size of agar jelly cubes precisely. Another improvement is to measure the time taken for HCl to penetrate fully to the centre of all cubes so that way the time can be compared. Repeating the experiment few more times would increase the reliability of the results as mistakes can be corrected each time.