Investigate the effect of changing surface area to volume ratio on diffusion using agar blocks of different sizes
Investigate the effect of changing surface area to volume ratio on diffusion using agar blocks of different sizes
Answered
To investigate the effect of changing surface area-to-volume (SA) ratio on diffusion, we can use agar blocks of different sizes infused with a pH indicator (such as phenolphthalein) and immerse them in a diffusion agent (e.g., dilute hydrochloric acid). By measuring how far the acid diffuses into each block, we can observe the relationship between SA
ratio and diffusion efficiency.
Materials
- Agar blocks infused with a pH indicator (e.g., phenolphthalein, which is pink in basic solutions and turns colorless in acidic solutions)
- Dilute hydrochloric acid
- Ruler or caliper
- Timer
- Knife for cutting the agar
Method
- Prepare Agar Blocks: Create agar blocks of different sizes, such as 1 cm31 \, \text{cm}^3, 2 cm32 \, \text{cm}^3, and 3 cm33 \, \text{cm}^3 cubes.
- Immerse in Acid: Place the blocks in a container with dilute hydrochloric acid. The acid will begin to diffuse into the blocks.
- Measure Diffusion: After a set period (e.g., 5–10 minutes), remove the blocks from the acid.
- Record Results: Measure the depth of diffusion (the colorless region) into each block.
Calculations and Observations
Calculate the SA
ratio for each block.
For a cube with side length ss:
\text{Surface Area (SA)} = 6s^2 \text{Volume (V)} = s^3 \text{SA Ratio} = \frac{\text{SA}}{\text{V}} = \frac{6s^2}{s^3} = \frac{6}{s}Example Calculations
- For a 1 cm cube:
\text{SA Ratio} = \frac{6}{1} = 6
- For a 2 cm cube:
\text{SA Ratio} = \frac{6}{2} = 3
- For a 3 cm cube:
\text{SA Ratio} = \frac{6}{3} = 2
Expected Results
Smaller blocks with higher SA ratios should show greater diffusion depth (i.e., a larger colorless region) than larger blocks with lower SA ratios. This demonstrates that smaller cells or objects, with a high SA ratio, allow materials to diffuse more efficiently throughout their volume.
Explanation
The high SA ratio in smaller blocks provides more surface area relative to volume, which facilitates faster diffusion rates. As block size increases, the diffusion distance to the center also increases, resulting in a slower rate of diffusion for larger blocks with a lower SA ratio.
BNO Team