Surface Area to Volume Ratio and the Relation to the Rate of Diffusion
Aim and Background This is a
n experiment to examine how the Surface Area / Volume Ratio affects the rate of diffusion and how th
is relates to the size and shape of living organisms. The surface area to volume ratio in living org
anisms is very important. Nutrients and oxygen need to diffuse through the cell membrane and into th
e cells. Most cells are no longer than 1mm in diameter because small cells enable nutrients and oxyg
en to diffuse into the cell quickly and allow waste to diffuse out of the cell quickly. If the cells
were any bigger than this then it would take too long for the nutrients and oxygen to diffuse into
the cell so the cell would probably not survive. Single celled organisms can survive as they have a
large enough surface area to allow all the oxygen and nutrients they need to diffuse through. Larger
multi-celled organisms need organs to respire such as lungs or gills.
Method
The reason I chose t
o do this particular experiment is because I found it very interesting and also because the aim, met
hod, results- basically the whole experiment would be easily understood by the average person who kn
ew nothing about Surface Area/Volume Ratio. The variable being tested in this experiment is the rate
of diffusion in relation to the size of the gelatin cube. Another experiment one could do to determ
ine the surface area to volume ratio is to construct a set of cubes out of construction paper- 1 x 1
, 2 x 2, 3 x 3 and 4 x 4 (cm).Then use this formula to determine the surface area- L x W x 6 and com
pare it with the volumes. The formula to determine volumes of cubes is L x W x H. Although that type
of experiment will show no insight into SA/V ratio in relation to the rate of diffusion.
Equipment
1.
Agar-phenolphthalein - sodium hydroxide jelly 2.
O.1 M
hydrochloric acid 3.
Ruler (cm and mm) 4.
Razor blade 5.
Pape
r towel 6.
Beaker
Method 1. A block of gelatin which has been dyed with phenolphthalei
n should be cut into blocks of the following sizes (mm). 5 x 5 x 5 10 x 10 x 10 15 x 15 x 15 20 x 20
x 20 30 x 30 x 30 20 x 5 x 5 Phenolphthalein is an acid/alkali indicator dye. In the alkali conditi
ons of the gelatin it is red or purple but when it gets exposed to acid it turns almost colorless. G
elatin is used for these tests because it is permeable which means it acts like a cell. It is easy t
o cut into the required sizes and the hydrochloric acid can diffuse at an even rate through it. 2. A
small beaker was filled with about 400ml of 0.1 molar Hydrochloric acid. This is a sufficient amoun
t of acid to ensure that all the block sizes are fully covered in acid when dropped into the beaker.
3. One of the blocks is dropped into this beaker, left for 10 minutes, then removed, dried, and cut
in two to measure the depth of penetration. This test should be repeated for all the sizes of block
s three times to ensure an accurate test. Fresh acid should be used for each block to make sure that
this does not affect the experiment's results. 4. The Surface Area/Volume Ratio and an average of t
he results can then be worked out. A graph of Surface Area to Volume Ratio can then be plotted along
with percentages left colored and uncolored . From this graph we will be able to see how surface ar
ea affects the rate of diffusion of materials into the cubes.
Results
I carried out
the above experiment and these results were obtained. Dimensions (mm)
Surface Area
Volume (V) (mm)
Surface Area / Volume Ratio
Test 1
T
est 2
Test 3 5 x 5 x 5
150
125
1.2:1
1mm
1mm
1mm 10 x 10 x 10
600
1,000
0.6:1
1mm
1mm
1mm 20 x 20 x 20
2,400
8,000
0.3:1
1mm
1mm
1mm 30 x 30 x 30
5,400
27,000
0.2:1
1mm
1mm
1m
m
The Surface Area to Volume Ratio is calculated by SA = cm
From these results I was able to make
a graph of the volume still coloured along with the percentages left coloured and uncoloured. Dimens
ions (mm)
Volume left coloured
3(mm )
Percentage coloured compared
to original volume
Percentage penetratedby the acid 5 x 5 x 5
3mm
60%
40% 10 x 10 x 10
8mm
80%
20% 20 x 20 x
20
18mm
90%
10% 30 x 30 x 30
28mm
93.3%
6.7%
Length of side not penetrated = (s - 2x)
3 Volume left coloured (Vc) = (s - 2x)
Percentage
still coloured (C%) = Vc x 100
V
1 Percentage of cube penetrated = 100 - C%
Interpretation
In all the blocks of gelatin
the rate of penetration of the hydrochloric acid from each side would have been the same but all th
e cubes have different percentages still coloured because they are different sizes. As the blocks ge
t bigger the hydrochloric acid to diffuses smaller percentages of the cubes. It would take longer to
totally diffuse the largest cube even though the rate of diffusion is the same for all the cubes. A
s the volume of the blocks goes up the Surface Area/Volume ratio goes down. The larger blocks have a
smaller surface area than the smaller blocks. The smallest block has 1.2mm squared of surface area
for every 1mm cubed of volume. The largest block only has 0.2mm squared of surface area for each 1mm
cubed of volume. This means that the hydrochloric acid is able to diffuse the smallest block much f
aster than the largest block. When the Surface Area/Volume Ratio goes down it takes longer for the h
ydrochloric acid to diffuse into the cube but if the ratio goes up then the hydrochloric acid diffus
es more quickly into the block of gelatin. Some shapes have a larger surface area to volume ratio so
the shape of the object can have an effect on the rate of diffusion. The single error or limitation
I encountered was the impossiblity to precisely measure the size of gelatin block. I measured the s
izes to the nearest mm so the sizes of block that I used should be correct to the nearest mm.
Discu
ssion
It is important that cells have a large surface area to volume ratio so that they can get eno
ugh nutrients into the cell. Single celled organisms have a large surface area to volume ratio becau
se they are so small. They are able to get all the oxygen and nutrients they need by diffusion throu
gh the cell membrane. Here is a diagram of a standard leaf:
Their are openings within a leaf called
stomata. These allow for the gases to flow in and out of the leaf. Leaves of plants have a large su
rface area, and the irregular-shaped, spongy cells increase the area even more meaning a larger amou
nt of gas exchange. An example of surface area to volume ratio in a real world context would be some
thing such as the example that was just explained.
Therefore, by increasing the surface area the ra
te of diffusion will go up.
Appendices
(2002) Biology: The Surface Area to Volume Ratio of a Cell
[Web document] http://www.geocities.com/CapeCanaveral/Hall/1410/lab-B-24.html
This piece of informa
tion was a good start for the investigation of Surface Area to Volume Ratio investigation. Even thou
gh it has no mention about rate of diffusion in relation to SA/V ratios, its relevance to my investi
gation was crucial.
(2002) Encyclopedia Britannica: Biology- Surface Area to Volume Ratio [CD-ROM]
I found this source of information to be very reliable. The Encyclopedia Britannica is a popular an
d credible way to gain information. It covers the whole range of factors relating to SA/V ratios as
well as the rate of diffusion. It was very appropriate for my investigation.
(2000) Sizes of Organi
sm's: Surface area to Volume ratio [Web document] http://www.tiem.utk.edu/~mbeals/area_volume.html
This document had an in depth discussion about the relation between Surface Area and Volume Ratio's.
It used plenty of examples to get the point across more clearly. It also touched on Surface Area to
Volume Ratio's of sphere's.
surface area volume ratio relation rate diffusion background this expe
riment examine surface area volume ratio affects rate diffusion this relates size shape living organ
isms surface area volume ratio living organisms very important nutrients oxygen need diffuse through
cell membrane into cells most cells longer than diameter because small cells enable nutrients oxyge
n diffuse into cell quickly allow waste diffuse cell quickly were bigger than this then would take l
ong nutrients oxygen into would probably survive single celled organisms survive they have large eno
ugh allow they need through larger multi celled need organs respire such lungs gills method reason c
hose particular experiment because found very interesting also because method results basically whol
e experiment would easily understood average person knew nothing about variable being tested rate di
ffusion relation size gelatin cube another could determine construct cubes construction paper then f
ormula determine compare with volumes formula determine volumes cubes although that type will show i
nsight relation equipment agar phenolphthalein sodium hydroxide jelly hydrochloric acid ruler razor
blade paper towel beaker method block gelatin which been dyed with phenolphthalein should blocks fol
lowing sizes phenolphthalein acid alkali indicator alkali conditions gelatin purple when gets expose
d acid turns almost colorless used these tests permeable which means acts like easy required sizes h
ydrochloric even through small beaker filled with about molar hydrochloric sufficient amount ensure
that block sizes fully covered when dropped beaker blocks dropped left minutes then removed dried me
asure depth penetration test should repeated blocks three times ensure accurate test fresh should us
ed each block make sure that does affect results average results worked graph plotted along percenta
ges left colored uncolored from graph will able affects materials cubes carried above these were obt
ained dimensions test calculated from these able make graph still coloured along percentages left co
loured uncoloured dimensions coloured percentage compared original percentage penetratedby length si
de penetrated percentage still cube penetrated interpretation penetration from each side have been s
ame have different percentages still they different bigger diffuses smaller take longer totally larg
est cube even though same goes goes down larger smaller than smaller smallest squared every cubed la
rgest only squared each cubed means able smallest much faster largest when goes down takes longer di
ffuses more quickly some shapes larger shape object effect single error limitation encountered impos
siblity precisely measure size measured nearest used correct nearest discussion important large enou
gh single celled large small membrane here diagram standard leaf their openings within leaf called s
tomata allow gases flow leaf leaves plants irregular shaped spongy increase even more meaning amount
exchange example real world context something such example just explained therefore increasing will
appendices biology document http geocities capecanaveral hall html piece information good start inv
estigation investigation though mention about ratios relevance investigation crucial encyclopedia br
itannica biology found source information very reliable encyclopedia britannica popular credible gai
n information covers whole range factors relating ratios well appropriate organism document http tie
m mbeals html document depth discussion between plenty examples point across more clearly also touch
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