The Effect of Surface Area to Volume Ratio on the Rate of Diffusion (VCE SSCE Biology): Revision Notes

The Effect of Surface Area to Volume Ratio on the Rate of Diffusion

Introduction

Cells must continuously exchange materials with their surroundings to survive. These materials include water, oxygen, nutrients, and waste products. The efficiency of this exchange is crucial for cell survival and depends largely on the cell's surface area to volume ratio (SA:V ratio).

The SA:V ratio is affected by both the size and shape of a cell. Understanding this relationship helps explain why cells remain small and why certain cell shapes are more efficient than others for particular functions.

What is this investigation about?

This practical investigation uses agar jelly cubes of different sizes to demonstrate how SA:V ratio affects the rate of diffusion. The experiment provides a visual model of what happens inside cells when substances move across their membranes.

The chemistry behind the colour change

The agar cubes contain two important chemicals:

• Phenolphthalein: A pH indicator that changes colour depending on acidity
  • In alkaline (low-acid) conditions: turns pink
  • In acidic conditions: turns clear
• Sodium hydroxide: An alkaline solution that makes the indicator (and therefore the cubes) appear pink

When sulphuric acid is added to the beakers, it gradually diffuses into the cubes. As the acid moves inward, it increases the acidity inside the cube, causing the phenolphthalein to change from pink to clear. This colour change allows us to measure how far the acid has diffused into each cube.

Aim

To observe and record the effect of surface area to volume ratio on the rate of diffusion.

Materials

• Pre-prepared agar jelly containing phenolphthalein indicator and sodium hydroxide
• 0.1 M sulphuric acid
• 4 × 250 mL beakers
• Tongs
• 1 × scalpel or knife
• 1 × stirring rod
• Paper towel
• 1 × ruler
• 1 × timer

Safety equipment

• Lab coat
• Safety glasses
• Gloves

Method

Follow these steps carefully to ensure accurate results:

Step 1: Use the scalpel or knife to cut the agar jelly into four cubes with sides measuring 10 mm, 30 mm, 50 mm, and 70 mm in length. Take care to make accurate cuts, as precise measurements are essential for reliable results.

Step 2: Pour 125 mL of sulphuric acid into each of the four beakers, or until approximately half full.

Step 3: Set the timer for 10 minutes.

Step 4: Carefully add one cube to each beaker of sulphuric acid. Be very careful not to splash the acid. Start the timer immediately after adding all cubes.

Step 5: Gently stir the acid in each beaker every few minutes using the stirring rod. This ensures even distribution of acid around each cube.

Step 6: When 10 minutes have elapsed, use tongs to carefully remove each cube from its beaker. Place the cubes onto paper towel to absorb excess acid.

Step 7: Cut each cube in half using the scalpel or knife. This reveals the interior and allows you to see how far the acid has diffused.

Step 8: Use a ruler to measure the distance of the clear region from the edge of each cube. This measurement represents how far the acid has diffused into the cube. Record your measurements in Table 2.

Results

Part A: Surface area to volume ratio

Before analysing your diffusion results, you need to calculate the SA:V ratio for each cube size. Complete the following calculations:

For a cube:

• Surface area = $6 \times \text{(side length)}^2$
• Volume = $\text{(side length)}^3$
• SA:V ratio = $\frac{\text{surface area}}{\text{volume}}$

Cube size (mm)	Surface area (mm²)	Initial volume (mm³)	SA:V ratio
10 × 10 × 10
30 × 30 × 30
50 × 50 × 50
70 × 70 × 70

Part B: Percentage of diffusion

To determine how effectively the acid diffused into each cube, complete the following calculations for each cube size:

Step 1: Record the initial side length of the cube (already provided in Table 2).

Step 2: Measure and record the length of the clear region in each cube (the distance from the edge to where the pink colour begins).

Step 3: Calculate the inner pink cube's side length: $\text{Inner cube side length} = \text{total side length} - (2 \times \text{distance diffused})$

Step 4: Calculate the inner pink cube's volume: $\text{Inner cube volume} = \text{(inner cube side length)}^3$

Step 5: Calculate the diffusion volume (the volume that has turned clear): $\text{Diffusion volume} = \text{initial total volume} - \text{inner cube volume}$

Step 6: Calculate the percentage of volume diffusion: $\text{Percentage volume diffusion} = 100\% \times \frac{\text{diffusion volume}}{\text{initial cube volume}}$

Measurement	Cube 1	Cube 2	Cube 3	Cube 4
1. Side length (mm)	10	30	50	70
2. Distance diffused by sulphuric acid (mm)
3. Inner cube side length (mm)
4. Inner cube volume (mm³)
5. Diffusion volume (mm³)
6. Percentage of volume diffusion (%)

Understanding the results

Key observations

After completing your calculations, you should notice an important pattern:

The clear region shows where acid has diffused into the cube, neutralising the alkaline sodium hydroxide and changing the indicator from pink to clear. This visual change makes it easy to measure the extent of diffusion.

Why does this happen?

The relationship between SA:V ratio and diffusion rate can be explained as follows:

Lower SA:V ratio = Less efficient diffusion

In larger cubes:

• Substances must travel further to reach the centre
• The volume increases faster than the surface area (volume increases with the cube of the length, whilst surface area only increases with the square of the length)
• A smaller proportion of the total volume receives materials within the same time period

The mathematical relationship

As a cube increases in size:

• Its volume increases much faster than its surface area
• This causes the SA:V ratio to decrease
• The efficiency of diffusion decreases accordingly

Real-world applications

Why are cells so small?

This investigation helps explain a fundamental principle of cell biology: cells must remain small to function efficiently.

If cells were too large, they would face several problems:

1. Insufficient nutrient supply

Nutrients diffusing in from the surface would take too long to reach the centre of the cell. The cell's interior would be starved of essential materials.

2. Waste accumulation

Waste products produced in the centre of the cell would take too long to diffuse out to the surface for removal, potentially becoming toxic.

3. Slow response times

Signals and regulatory molecules would take longer to spread throughout the cell, reducing the cell's ability to respond quickly to changes.

4. Inefficient gas exchange

Oxygen would struggle to reach all parts of the cell, and carbon dioxide would accumulate in the centre.

Strategies to increase SA:V ratio

Some cells and organisms have evolved special adaptations to increase their effective SA:V ratio:

Exam tips

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