investigate the effect of changing surface area to volume ratio on diffusion using agar blocks of different sizes

Movement into and out of Cells

Objective

To investigate how changing the surface area‑to‑volume (SA:V) ratio of agar blocks influences the rate of diffusion of a solute into the block.

Background Theory

Diffusion is the net movement of particles from an area of higher concentration to an area of lower concentration. The rate of diffusion across a membrane (or into a solid) is proportional to the surface area available for exchange and inversely proportional to the distance particles must travel, which is related to the volume of the material.

The relationship can be expressed as:

\$\text{Rate of diffusion} \propto \frac{\text{Surface Area}}{\text{Distance}} \approx \frac{A}{V^{1/3}}\$

For a cube of side length l:

\$A = 6l^{2}\$

\$V = l^{3}\$

\$\frac{A}{V} = \frac{6}{l}\$

Thus, as the side length decreases, the SA:V ratio increases, leading to a faster diffusion rate.

Hypothesis

If the SA:V ratio of the agar blocks is increased (by using smaller blocks), then the diffusion of the solute into the blocks will occur more rapidly, resulting in a greater change in colour/intensity over a fixed time period.

Materials

• Agar powder
• Distilled water
• Food‑colouring or potassium permanganate solution (as a diffusible solute)
• Four sets of moulds to produce cubes of side lengths 1 cm, 2 cm, 3 cm and 4 cm
• Ruler or caliper
• Stopwatch
• Clear plastic cuvettes or beakers
• Digital camera (optional for recording colour change)

Method

1. Prepare a 1 % agar solution, pour into moulds, and allow to set, producing cubes of the four specified sizes.
2. Measure and record the exact side length of each cube (to the nearest 0.1 mm).
3. Place each cube in a separate cuvette containing an equal volume (e.g., 50 mL) of the solute solution.
4. Start the stopwatch as soon as the cubes are immersed.
5. At 5‑minute intervals, remove each cube, gently blot the surface, and record the depth of colour penetration (e.g., using a ruler or by photographing against a white background).
6. Return the cube to the solution after each measurement.
7. Continue observations for 30 minutes or until colour has reached the centre of the smallest cube.

Variables

• Independent variable: Surface area‑to‑volume ratio (changed by varying cube size).
• Dependent variable: Rate of diffusion, measured as depth of colour penetration per unit time.
• Controlled variables: Agar concentration, temperature, solute concentration, volume of solution, and observation time intervals.

Data Collection Table

Calculations

For each cube, calculate the surface area, volume and SA:V ratio using the measured side length l:

\$A = 6l^{2}\$

\$V = l^{3}\$

\$\frac{A}{V} = \frac{6}{l}\$

Plot a graph of SA:V ratio (x‑axis) against depth of colour penetration after a fixed time (y‑axis) to visualise the relationship.

Safety Considerations

• Handle hot agar solution with heat‑resistant gloves.
• Wear goggles and lab coat when working with chemical dyes or potassium permanganate.
• Dispose of dye solutions according to school waste‑disposal guidelines.

Analysis and Discussion

Interpret the graph to determine whether a higher SA:V ratio correlates with a faster diffusion rate. Discuss any deviations and possible experimental errors such as:

• Inaccurate measurement of side lengths.
• Uneven temperature across cuvettes.
• Diffusion through the sides of the cuvette rather than solely through the agar surface.

Conclusion

Summarise whether the experimental data support the hypothesis. Relate findings to biological contexts, e.g., why cells such as red blood cells are small and have a high SA:V ratio to facilitate efficient gas exchange.

Extension Activities

• Repeat the experiment using spherical agar beads and compare the SA:V ratios with those of cubes.
• Investigate the effect of temperature on diffusion rate while keeping SA:V constant.
• Model diffusion in living cells using computer simulations and compare with experimental results.