Diffusion and Surface Area to Volume Ratio

Every cell must take in the substances it needs — oxygen, glucose, water — and get rid of its waste, such as carbon dioxide. The simplest way substances move in and out of cells is by diffusion. But diffusion only works over short distances, and this creates a problem as organisms get bigger: a large body cannot supply all its cells by diffusion alone. This lesson, the heart of Topic B2 of OCR Gateway Science A, explains diffusion, the factors that affect its rate, and the all-important surface area to volume ratio that explains why large organisms need special exchange surfaces and transport systems. The cube calculation here is one of the most reliable sources of marks in B2.

By the end of this lesson you should be able to define diffusion, list the factors affecting its rate, calculate and compare surface area to volume ratios, and explain why larger organisms need exchange surfaces and transport systems.

What Is Diffusion?

Diffusion is the net movement of particles from a region of higher concentration to a region of lower concentration — that is, down a concentration gradient. It happens because particles are always moving randomly; over time this random movement spreads them out until they are evenly spread.

A few key points:

Diffusion is a passive process — it needs no energy from the cell.
It moves substances down the concentration gradient (high → low).
The word net matters: particles move both ways, but more move from high to low, so the overall (net) movement is high → low.

Substances that move in and out of cells by diffusion include oxygen and carbon dioxide (in gas exchange) and small soluble molecules. They diffuse across the cell membrane, which is partially permeable.

Exam Tip: Always use the word net and the phrase down a concentration gradient (high to low). State that diffusion needs no energy — this is what distinguishes it from active transport later in the topic.

Factors Affecting the Rate of Diffusion

OCR expects you to know what makes diffusion faster or slower. There are four main factors:

Factor	Effect on rate of diffusion
Concentration gradient (difference)	The steeper the gradient (bigger difference), the faster the diffusion
Temperature	Higher temperature → particles have more energy and move faster → faster diffusion
Surface area	A larger surface area allows more diffusion at once → faster overall
Diffusion distance (membrane thickness)	A shorter distance / thinner membrane → faster diffusion

Higher tier only: these factors can be combined into a relationship. The rate of diffusion is proportional to the surface area multiplied by the concentration difference, divided by the diffusion distance: $\text{rate of diffusion} \propto \frac{\text{surface area} \times \text{concentration difference}}{\text{diffusion distance}}$ This single expression captures all three of the key factors at once: increasing the surface area or concentration difference speeds diffusion up, while increasing the diffusion distance slows it down.

Exam Tip: When a question asks how to increase the rate of diffusion across a surface, the strong answers are: increase the surface area, increase the concentration gradient, decrease the diffusion distance (make it thinner), or raise the temperature.

Surface Area to Volume Ratio

Here is the central idea of "scaling up". A cell or organism exchanges substances across its surface, but it uses those substances throughout its volume. So what matters is the surface area to volume ratio (SA:V) — how much surface is available for each unit of volume.

The crucial fact is this: as an object gets bigger, its volume increases faster than its surface area, so its surface area to volume ratio falls. A small object has a large SA:V (lots of surface for its size); a large object has a small SA:V (relatively little surface for its size).

Worked Example — Comparing cubes

Cubes are a simple model of cells because the formulae are easy:

Surface area of a cube $= 6 \times (\text{side} \times \text{side}) = 6 \times \text{side}^{2}$ (a cube has 6 square faces).
Volume of a cube $= \text{side} \times \text{side} \times \text{side} = \text{side}^{3}$ .

Let us work out the SA:V for cubes of side $1$ , $2$ and $3$ units.

Cube of side 1 unit:

$\text{surface area} = 6 \times 1^{2} = 6 \qquad \text{volume} = 1^{3} = 1$ $\text{SA:V} = \frac{6}{1} = 6 : 1$

Cube of side 2 units:

$\text{surface area} = 6 \times 2^{2} = 6 \times 4 = 24 \qquad \text{volume} = 2^{3} = 8$ $\text{SA:V} = \frac{24}{8} = 3 : 1$

Cube of side 3 units:

$\text{surface area} = 6 \times 3^{2} = 6 \times 9 = 54 \qquad \text{volume} = 3^{3} = 27$ $\text{SA:V} = \frac{54}{27} = 2 : 1$

Collecting the results:

Cube side	Surface area	Volume	SA:V ratio
1 unit	6	1	6 : 1
2 units	24	8	3 : 1
3 units	54	27	2 : 1

The pattern is clear: as the cube gets bigger, the SA:V ratio falls (from 6:1 down to 2:1). The volume (which needs supplying) grows much faster than the surface area (which does the supplying). This is exactly why a single large cell, or a large solid animal, could not survive on diffusion across its outer surface alone — there simply would not be enough surface for its volume.

Common error: calculating surface area as $\text{side}^{2}$ (one face) instead of $6 \times \text{side}^{2}$ (six faces), or writing the ratio the wrong way round. SA:V puts surface area first, and for a cube the surface area uses the factor of 6.

Exam Tip: Learn the two cube formulae cold: surface area $= 6 \times \text{side}^{2}$ and volume $= \text{side}^{3}$ . Then SA:V $= \dfrac{\text{surface area}}{\text{volume}}$ . Show every step — examiners award method marks for the working even if the final division slips.

Worked Example — Why shape matters too

It is not only size that affects the surface area to volume ratio — shape matters as well. Compare two objects with the same volume of $8$ cubic units:

A cube of side $2$ : surface area $= 6 \times 2^{2} = 24$ ; volume $= 8$ ; SA:V $= \dfrac{24}{8} = 3 : 1$ .
A flat slab measuring $8 \times 1 \times 1$ : volume $= 8 \times 1 \times 1 = 8$ ; surface area $= 2(8\times1) + 2(8\times1) + 2(1\times1) = 16 + 16 + 2 = 34$ ; SA:V $= \dfrac{34}{8} = 4.25 : 1$ .

Even though both have the same volume, the flatter, thinner slab has a larger surface area to volume ratio ( $4.25{:}1$ versus $3{:}1$ ). This is exactly why many exchange surfaces in living things are flat or thin rather than compact — a flat shape squeezes more surface around the same volume. It is one reason a leaf is broad and thin, and why the lining of the gut is folded into flat villi.

Diffusion and Surface Area to Volume Ratio

Diffusion and Surface Area to Volume Ratio

What Is Diffusion?

Factors Affecting the Rate of Diffusion

Surface Area to Volume Ratio

Worked Example — Comparing cubes

Worked Example — Why shape matters too

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