Biology 11–12 · Year 11

Surface-area-to-volume ratio and diffusion into agar cubes

Module 1: Cells as the Basis of Life (Cell Function)

Practical, model not builtLow risk

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The idea

Diffusion supplies a cube only from its surface, so a larger cube has proportionally less surface for each unit of volume and its centre is reached later.

What you need

Agar containing 0.01 mol/L sodium hydroxide, the concentration the source specifies, with phenolphthalein (pink) or universal indicator, set in a tray about 3 cm deep; prepared by the technician
Hydrochloric acid 0.1 mol/L, 200 mL per group
Scalpel on a white tile; ruler; agar cubes of 2.0, 1.0 and 0.5 cm sides, 3 of each
250 mL beakers, 3; stop clock; paper towel; plastic spoon

How to do it

Cut three cubes of each size from the indicator agar and calculate surface area, volume and their ratio for each size.
Place each set of cubes in 0.1 mol/L hydrochloric acid at the same moment and start the clock.
After 5 minutes remove the cubes with a spoon, blot, cut each in half and measure the depth to which the colour has changed from the surface inward.
Record the time at which the smallest cube loses colour to its centre and predict the larger cubes' times from it: the diffusion length grows with the square root of time (2 x sqrt(D t)), so the time to reach the centre grows with the square of the half-side, 4 times as long for the 1 cm cube and 16 times for the 2 cm cube (computed).
Calculate the fraction of each cube's volume reached: 1 minus ((side minus 2 x depth) divided by side) cubed.
Plot fraction reached against surface-area-to-volume ratio.

What you should see

Surface-area-to-volume ratios are 3, 6 and 12 per centimetre for the 2, 1 and 0.5 cm cubes (computed). The acid front advances the same distance from every face in the same time, slowing as it goes deeper because the diffusion length grows with the square root of time, so after 5 minutes the same depth is decolourised in every cube, but that depth reaches a different fraction of each: with a depth of 0.25 cm, an illustrative figure that each class measures because the front speed depends on the alkali concentration in the agar and the acid strength, the 0.5 cm cube is changed throughout, the 1 cm cube is 87.5 percent reached and the 2 cm cube only 57.8 percent, leaving a pink core (computed). The learner knows it worked when the small cubes are uniformly changed while the large cube shows a coloured centre.

What changes

What you change: cube side length (cm)
What you measure: depth of colour change after a fixed time, and fraction of volume reached
What you keep the same: acid concentration
time
temperature
agar batch and indicator
volume of acid

Common misconceptions

Each of these ideas is wrong, and the activity is a chance to test it.

Larger cubes absorb acid faster because they have more surface; the front reaches the same depth in every cube in the same time, and the larger cube has more volume per unit surface.
The acid moves faster in small cubes; at any moment the front has reached the same depth in every cube and the smaller cube's centre is nearer, and because depth grows with the square root of time, the time to reach the centre grows with the square of the half-side.
Cells are small because of some limit on how much material they can hold rather than because of exchange across the surface.

Safety card

Low riskLearners carry it out

Hazards

Hydrochloric acid 0.1 mol/L and sodium hydroxide in the agar: irritant to eyes
Scalpel cuts

Controls

Wear eye protection
Rinse splashes with water
Cut on a tile away from the body

Note

Acid and alkali handling per the NSW Department of Education Chemical Safety in Schools package (https://education.nsw.gov.au/content/dam/main-education/asset-management/chemical-safety/1._Section_1_-_General_information_for_all_staff.pdf) and RiskAssess (https://www.riskassess.com.au/).

Curriculum references

The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.

Biology Stage 6 Syllabus (2017), current: Year 11 taught to the end of 2026 and Year 12 to Term 3 2027BIO11-8 BIO11/12-3 BIO11/12-4
Biology 11–12 Syllabus (2025), Year 11 focus area Cells to systems; new syllabus not yet taught: Year 11 from Term 1 2027, Year 12 from Term 4 2027BI-11-02
Biology 11–12 Syllabus (2025), Year 11 Working scientifically; new syllabus not yet taught: Year 11 from Term 1 2027, Year 12 from Term 4 2027BI-11WS-03 BI-11WS-04
Australian Curriculum v9No Australian Curriculum v9 code is listed.

Sources

The pages the author read to write this activity.

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