Surface area to Volume ratio
Aim: To model/investigate:
 The change in the surface area to volume ratio with ‘cell’ size.
 The effect of a change in the surface area to volume ratio on the rate of diffusion.
Materials:
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Agar-phenolphthalein-sodium hydroxide cubes (gelatin blocks)
0.1M hydrochloric acid (approximately 150mL)
30cm ruler
Scalpel
Paper towels
250mL beaker
100mL beaker
Plastic spoon
stopwatch
Introduction/Background:
Understanding the relationship between the size of cells (volume) and their surface area helps us to realise
how the physical limitation of the size of cells is important if they are to function effectively. In order to
carry out necessary chemical activities (metabolism) cells need to absorb substances that they require
from their surroundings. This uptake is often dependent on the process of diffusion. Diffusion is a slow
process and so to be more effective, the number of molecules that can be taken in a particular space of
time should be increased.
The hypothesis to be tested is that by increasing the surface area over which uptake occurs (for an object
of a particular volume), diffusion can be increased and molecules can reach the centre of an object sooner
than if the object has a lower surface area to volume ratio. Therefore, although the rate of diffusion is still
the same, by increasing the amount of diffusion occurring, the overall rate of movement increases.
This investigation makes use of a model to investigate the effect of the surface area to volume ratio on
cellular diffusion. Cells of different sizes are represented by gelatin cubes, a simplification to try to
increase understanding of the concept and to allow predictions to be made. When interpreting the
behaviour of substances in the model (in this instance, the movement of the chemicals by diffusion) the
limitations of the model must be taken into account. For example one limitation is that the jelly cubes do
not have a selectively permeable boundary such as a cell membrane. The validity of the model should also
be assessed. For example, the lack of a cell membrane and an energy source suggests that no active
transport can take place, indicating that only diffusion is being investigated.
Safety:
Phenolphthalein can stain clothing. Wear safety glasses and take care not to get HCl on skin or in eyes. If
acid comes in contact with any part of the body irrigate well with water. Turn the gelatin blocks with a
spoon and do not handle the chemicals.
Procedures:
1. Cut agar cubes into sizes of 1cm, 2cm and 3cm using a scalpel or razor blade.
2. Calculate the surface are to volume ratio of each of the cubes (see table below). Assume the cubes
have exactly 3cm, 2cm or 1cm sides. Due to the indicator (phenolphthalein) and the presence of the
base (NaOH, sodium hydroxide) in the cubes they will appear pink.
3. Place one of each size cube (1cm³, 2cm³ and 3cm³) into each 250mL beaker making sure that each
cube is not touching the others.
4. Cover the cubes with the hydrochloric acid and leave for 10 minutes. Turn the cubes over every 2
minutes with a plastic spoon.
5. Remove the cubes from the acid after 10 minutes, quickly blotting dry the surface of the cubes
using paper towel.
6. Cut each cube into 2 using the scalpel blade. Measure the depth of penetration of the acid into
each cube in millimetres and record it in the table below.
7. Complete the remaining calculations in the table, determining the volume of each cube that
remains coloured and calculating the percentage penetration in the last column as a measure of the
proportion of the cube affected by diffusion, in cubes of different sizes.
Results:
Table 1: Investigating the effects of changing the surface area to volume ratio on the percentage acid penetration in agar blocks of NaOH and phenolphthalein indicator
when placed into HCl.
Cube size
l
(mm ±
0.5mm
Surface
area SA
(6xl²)
mm²
Volume V
(l³)mm³
𝑆𝐴
𝑉
= 𝑆𝐴: 𝑉
Trial
1
2
10
3
4
1
2
20
3
4
1
2
30
3
4
Volume left
Depth of
penetration coloured
𝑉𝑐 =(l-2x)³
(x) mm
% left
coloured
𝑉
( 𝑐)x100
𝑉
% acid
penetration
= 100-𝑉𝑐 %
Average %
acid
penetration
Standard
deviation
Discussion:
1.
2.
3.
4.
Identify the trend in the change in surface area to volume ratio as the volume of the cube increases.
Assess the accuracy of any measurements and calculations made and their relative importance in this practical.
Describe the evidence that indicates that diffusion in the cube has occurred.
Identify which cube (cell) showed the greatest depth of penetration of acid and which showed the least. Was this what you would
have expected? Explain.
5. Explain why it was necessary to calculate the percentage acid penetration for each cube.
6. When a cell divides, it produces two identical cells that at first, are half the size of the original cell. Describe the change to the:
a. Total surface area: _________________________________________________
b. Total volume: ____________________________________________________
c. Surface area to volume ratio for each cell: ________________________________________________________________
7. These cells will then grow, but to a limited size. Clarify the significance of the results of this investigation for multicellular living
organisms.
8. Discuss the limitations of the jelly cubes representing cells (hint: see Intro/background)