Effect of size on uptake by diffusion
We used blocks of Agar as models for different-sized cells. We wanted to investigate why cells are so small, in the context of diffusion. Diffusion is passive transport - substances are transported across cell membranes without energy being used.
Angie made up blocks of firm agar with 0.01M (ie very,. very weak) sodium hydroxide and a squirt (technical term there) of phenolphthalein indicator, which made the alkaline blocks turn pink. We cut these blocks into cubes of three different sizes - with sides 2cm, 1cm, and 5mm.
 |
| Leo cutting cubes to size. |
We worked out the surface area, volume, and surface area to volume ratio of these cubes:
A
Length of side (cm) |
B=A2
Area of one side (cm) |
C
=6B
Total surface area
of cube (cm2) |
D
=A3
Volume of cube (cm3) |
E
=C/D
Surface area to
volume ratio |
| 2 |
4cm2 | 24cm2 |
8cm3 |
3 |
| 1 |
1cm2 |
6cm2 | 1cm3 |
6 |
| 0.5 |
0.25 cm2 |
1.5cm2 |
0.125cm3 |
12 |
If you are a bit unsure about how to calculate volume and surface area, this diagram may help:
 |
| Surface area and volume diagram from BBC Bitesize (link at foot of page) |
We dropped our cubes in very dilute (0.1M) hydrochloric acid . We removed them after 5 minutes, patted them dry with paper towels, then cut them in half and measured how far the colour had changed.
As soon as we dropped the cubes into the acid solution, the pink colour started to disappear from the outside, leaving it colourless. We could see the amount of pink shrinking before our eyes as the acid diffused into the agar block.
The surprising thing about this was that the diffusion rate really was so exact and precise - the coloured area of the blocks shrank at the same rate all round and they looked really symmetrical when sliced in half. The rate of colour change was consistent.
After 5 minutes, the smallest block had lost all its pink colour - but the largest one still had a substantial pink area unchanged in the middle.
We measured the distance from the outside of the cube to the start of the remaining pink area. T
he most common result was that the acid diffused 4mm into each block in 5 minutes - so, for the cube with sides of 0.5mm, it diffused right into the centre. The rate of diffusion was approximately 0.8mm/minute. We would need to run more tests before we had enough data to be reliable.
Discussion
If we think of oxygen diffusing into a cell, we can see that a large surface area to volume ratio means that it takes longer for substances to reach the centre of the cell.
From a useful handout -
No Brain Too Small:
Cells need to be small because they rely on diffusion for getting many substances into and out of their centres. When a cell grows, there is relatively less membrane for the substances to diffuse through, resulting in the centre of the cell not receiving the substances that it needs. Diffusion is less efficient, cell processes slow down, and the cell stops growing. The cell then needs to divide into two smaller cells, which each have a larger surface area: volume ratio, and can diffuse materials more efficiently again.
This is why large organisms can't rely on diffusion to meet their needs for oxygen and nutrient transport. They need specialised organ systems (and also something called active transport, which uses energy to move substances - that that's another topic).
From BBC Bitesize on
Organ Systems:
All living organisms rely on exchanges with the environment to survive. However, diffusion only works efficiently if the distance over which the substances have to diffuse is small and the organism has a large surface areacompared to its volume. This is the case for small organisms.
For larger, more complex organisms – which have a small surface area:volume ratio and a bigger distance from the surface to the cells inside the body - diffusion alone is insufficient to meet the needs of all cells.
As larger organisms evolved, specialised organ systems - with surfaces across which substances could be exchanged efficiently - also evolved. These specialised organ systems were needed in order to transport substances around the organisms.
Apart from keeping cells small, what else can change to increase the surface area to volume ratio of a tissue?
Some of us cut different shapes, to see what happened if we increased the ratio of surface area to volume by cutting a wavy or convoluted surface:
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| These convoluted shapes quickly lost their colour. |
This is one of the ways that exchange surfaces in organisms have adapted - by developing folded surfaces which increase the surface area relative to the volume. Examples are the alveoli in the lungs, and villi in the intestines.
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| Alveoli in lungs |
Further Reading
Our activity was based on the classic
"Effect on size of uptake by diffusion " from the Nuffield Foundation
BBC Bitesize:
Organ Systems
BBC Bitesize on Diffusion
Sourcing Materials :
I used food grade agar powder, which is cheaper than laboratory-grade. For activities at this level, you don't necessarily need expensive specialist materials.
The agar powder cost £5.95 for 100g,which was plenty -as you use only 2g per 100ml of water to make up approx 100ml of agar jelly.
See Special Ingredients Agar Agar Premium Quality Powder 100 g https://www.amazon.co.uk/dp/B00EZMPMNE/ref=cm_sw_r_other_apa_MGgjybJMNG576
Phenolphthalein indicator can be bought on eBay or Amazon.
Sodium Hydroxide is caustic soda. It can be bought from the high street, eg Poundland or any large supermarket . We wanted very dilute solution (0.1M) so that it was low-hazard; dilute to one-hundredth of the strength suggested for cleaning drains etc..
CLEAPSS Student Safety Sheet for sodium hydroxide : http://www.cleapss.org.uk/attachments/article/0/SSS31.pdf
CLEAPSS Recipe Book : guidance on safety in science education.
http://www.cleapss.org.uk/attachments/article/0/RBPrint.pdf
