17.09.2014 1
Irena Sionek 2IB
DIFUSSION IN AGAR CUBES – LAB REPORT
Research question
What is the effect of surface area on volume ratio on the rate of diffusion of pigment
from the agar cube measured by percentage volume of diffusion over time?
Background
Diffusion is a process of spontaneous spreading of particles in an environment (e.g.
a cell), which is a consequence of chaotic collisions of molecules of the diffusing
substances with each other or with the molecules of the surrounding environment.
It can be observed in cells when substances e.g. water, oxygen, nutrients, cellular
waste are transported inside, outside the cell or to different cellular organelles.
It is easy to observe diffusion by gently pouring a coloured liquid into water. In this
experiment I will examine diffusion of a solution in a jelly-like substance - agar.
Because both the solution and the agar are colourless I will use agar that had before
been mixed with phenolphthalein. This also colourless substance is a commonly
used indicator that changes its colour into pink with the presence of a base. It will
turn pink immediately when mixed with a NaOH solution. When the agarphenolphthalein cubes will be put into the sodium hydroxide solution, NaOH will
start diffusing through the agar cubes and turn the inside of the cube pink gradually.
We want to examine whether ad how the rate of diffusion over time is dependent on
the cubes surface area to volume ratio (SA:V). Smaller cubes have bigger SA:V than
big cubes. We know that e.g. cells seek to have the biggest surface area possible and
a small volume. We will therefore see, whether one of the reasons they do it is the
rate of diffusion.
Hypothesis
If a big surface area to volume ratio is something very desired by cells that need
efficient and fast diffusion for their functioning (transporting nutrients, oxygen,
water, waste), then the greater the SA:V, the greater is the rate of diffusion of
pigment from the agar tube measured by the percentage volume of diffusion over
time.
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Variables:
dependent:

independent:

controlled:







the distance from the core of the
pigment to the border of the agar
cube
the size of the agar cube (edge
length) , this will be: 1 cm, 1.5 cm,
2 cm, 2.5 cm
time
type of solution in which we
submerge – 4% sodium hydroxide
Temperature of the solution: 21 °
C
Time we keep the cubes in the
solution: 10 minutes
Volume of the solution – 100 cm3
(± 0.5 cm3)
The material used to prepare agar
cubes
The method of measuring the
length of cube edges
Controlling the variables
Type of solution
The solution temperature
Time we keep the cubes in the solution
Volume of the solution
The material used to prepare the cubes
The method of measuring the length of
cube edges
We put exactly 4g of sodium hydroxide
in 96 cm3 of water. We measure the
NaOH with a weight and the volume of
water with a measuring cylinder.
We measure it with a thermometer with
a proper error and control it with a
water bath set at that exact temperature
(21 ° C). We put the beakers in the bath.
We measure this with a timer (± 0.5 s)
We use a measuring cylinder (one of a
corresponding but bigger volume), (± 0.5
cm3)
We use the same package of agar and
same of the phenolphthalein. It was
bought at a chemical store and the
package was labelled.
We use the same ruler for all
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Apparatus and materials (one of each for a group)






Knife
Ruler
Beaker
Measuring cylinder
Timer
Spoon






Petri dish
Weight
Paper towels (optional)
96 cm3 water
4 g NaOH
Tray of agar with phenolphthalein
Method
We have 6 groups making the very same experiment, so we have 6 trials. This gives the
experiment reliability.
We already have a tray of agar with phenolphthalein. The instructions are for one group.
1) Measuring out with a ruler cut out 4 agar cubes with the following edge
lengths: 1cm; 1.5 cm; 2 cm; 2.5 cm. Cut as accurately as possible.
2) Pour 96 cm3 of water into the beaker.
3) Weight out 4g of sodium hydroxide and add it to the water in the beaker.
4) Put the four cubes into the solution.
5) Immediately turn on the timer.
6) Leave the cubes in the solution for 10 minutes; remember to check on the
temperature.
7) After the 10 minutes had passed, take out the cubes onto the petri dish using
a spoon.
8) If necessary blot the cubes with a paper towel, so no sodium hydroxide is left
on them.
9) Cut each of the cubes in half and collect measurements using a ruler.
Safety
As NaOH is a corrosive acid that can cause chemical burns on skin and permanent
blindness when contacted with eyes. Be sure to wear gloves all of the time and do not touch
your eyes.
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Collecting raw data
I will use this table to record the collected data:
DIMENSION
(cm ± 1 mm)
SURFACE
AREA
(Cm2)
INITIAL
VOLUME
without
the violet
colour
(Cm3)
FINAL
VOLUME
Without
the violet
colour
(Cm3 ± 0.5
mm3)
DIFFUSED
VOLUME
- With
violet
colour
(Cm3)
Group
number
1
2
3
4
5
6
1
2
3
4
5
6
1
2
3
4
5
6
1
2
3
4
5
6
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Data processing
To do all the mathematical operations and draw graphs I used a simple calculator and
Microsoft Excel 2011. These are the used formulas and example operations.
Calculating the surface area of cubes
e – edge of the cube
SA – surface area
𝑺𝑨 = 𝟔 𝒆𝟐
E.g. �� (1)1 = 6 × 12 = 6
Calculating the initial volume
V- volume
𝑽 = 𝒆𝟑
e.g. 𝑉(1) = 13 = 1
Calculating the final volume
fV – final volume
w – edge of the little uncoloured cube in the centre of the whole agar cube
𝒇𝑽 = 𝒘𝟑
e.g. 𝑓𝑉 (1) = 03 = 0
Calculating the diffused volume
dV – diffused volume
dV = V – fV
e.g. dV (1) = 1 – 0 = 1
by (1) i will mark the smallest cube (1cm x1cm x1cm) and the biggest one will
respectively be marked (4)
1
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DIMENSION
(cm ± 1 mm)
1x1x1
1.5x1.5 x1.5
2x2x2
2.5x2.5x2.5
SURFACE
AREA
(cm2)
6
13.5
24
37.5
INITIAL
VOLUME
without
the violet
colour
(cm3)
1
3.375
8
15.625
FINAL
VOLUME
Without
the violet
colour
(cm3 ± 0.5
mm3)
DIFFUSED
VOLUME
- with
violet
colour
(cm3)
0
1
12
0
1
2
0
1
3
0
1
4
0
1
5
0.216
0.784
6
0
3.375
1
0
3.375
2
0
3.375
3
0
3.375
4
0
3.375
5
0.729
2.646
6
0.064
7.936
1
0.125
7.875
2
0.008
7.992
3
0.512
7.488
4
0
8
5
4.096
3.904
6
1.331
14.294
1
0.343
15.282
2
0.216
15.409
3
1.728
13.897
4
1.331
14.294
5
12.167
3.458
6
Anomalies
2
group 1 is the group in which I personally worked.
group
number
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The highlighted and bolded data (collected by group 6) seems to be anomalous. It visibly
differs from the data collected by other groups (from which most are very similar).
For example let’s look at the data collected from the biggest cube – the diffused volume.
While data collected by the groups 1-5 stays in the interval 13.897 – 15.409 [cm3], the
number collected by group 6 is 3.458 cm3, which is significantly deviating.
It is most probable that the reason of such an inconsistency is an incorrect conduct of the
method. We can presume that the time the cubes stayed in the solution wasn’t exactly 10
minutes (maybe because of a broken timer) or the ruler used to take measurements was
much different from the ones used by other groups. The time between taking out the cubes
from the solution and measuring can impact the results.
Therefore, for the good of the experiment’s result I decided to skip the data collected by
group 6 in the data processing.
Calculating the surface area to volume ratio and diffusion rate in each of the groups
(excluding group no. 6)
SA:V – surface area to volume ratio
𝑺𝑨: 𝑽 =
𝑺𝑨
𝑽
e.g. 𝑆𝐴: 𝑉 (1) =
6
1
=6
%Vd – percent volume of diffusion
%𝑽𝒅 =
𝒅𝑽
× 𝟏𝟎𝟎
𝑽
e.g. %𝑉𝑑 (1) =
1
1
× 100 = 100
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DIMENSION
(cm ± 1 mm)
1x1x1
1.5x1.5 x1.5
2x2x2
2.5x2.5x2.5
SURFACE AREA
TO VOLUME
RATIO
6
4
3
2.4
PERCENT
VOLUME OF
DIFUSION
over 10 minutes
[%]
group number
100
1
100
2
100
3
100
4
100
5
100
1
100
2
100
3
100
4
100
5
99.2
1
98.4
2
99.9
3
93.6
4
100
5
91.5
1
97.8
2
98.62
3
88.94
4
91.48
5
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Irena Sionek 2IB
correlation between SA:V and % volume of
diffusion
% volume of diffusion [%]
102
100
98
group 1
96
group 2
94
group 3
group 4
92
group 5
90
88
0
1
2
3
4
5
6
7
SA:V
Calculating the average from % volume of diffusion in each of the cube sizes.
A – average %Vd in this cube size
Σ𝑥 - sum of all the %Vd in all of the groups
n – number of the groups
𝑨=
A (1) =
𝚺𝒙
𝒏
100 + 100 + 100 + 100 + 100
= 100
5
A (2) = 100
A (3) = 98.22
A (4) = 93.668
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Calculating the standard deviation of mean % volume of diffusion in each of the cube
sizes
σ – standard deviation
x – each value of A in each of the cube sizes
n – number of values of A in this cube size
𝑥̅ – mean of all values of A in this cube size
𝝈=
𝚺 (𝒙 − 𝒙̅ )𝟐
𝒏−𝟏
σ (1) = 0
σ (2) = 0
σ (3) = 2.661203
σ (4) = 4.284777707
Correlation between SA:V and average % volume of diffusion in each of the cube sizes
Correlation between SA:V and mean % volume
of diffusion
mean % volume of diffusion
102
100
98
96
94
92
90
88
0
1
2
3
4
SA:V
5
6
7
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Irena Sionek 2IB
Conclusion
From the data obtained it can be concluded that there is some relationship between SA:V
and the rate of diffusion. The experiment results seen on the graph (trend line) show that
the bigger is the surface area to volume ratio, the bigger is the percentage volume of
diffusion, so the rate of diffusion of pigment from the agar cube.
Looking at the data we can notice that smaller cubes (of smaller volume) have bigger SA:V.
We can than state that the results of the experiment have also shown, that the smaller is
the cube, the bigger is the rate of diffusion.
We can see that differences in the diffusion rate are much bigger in bigger 3 cubes (4 %
difference in the % volume of diffusion with the difference of only 0.6 in their SA:V).
There was no noticeable difference in the diffusion rate of the smaller4 cubes ( 0%
difference in the diffusion rate with the difference of 2 in their SA:V).
The graph appears to flatten off at the point of the cube with the dimensions 1,5cm x 1,5 cm
x 1,5 cm and SA:V = 4 and stays at the same level to the smallest cube (1 cm x 1 cm x 1cm,
SA:V = 6). The visible trend is called decelerating increase.
The relationship between the variables has its explanation. Bigger surface area to volume
ratio means that there is more surface through which the substance (NaOH in this case) has
to pass , so more compounds can do it at once and less volume that they have to diffuse
through in order to reach the cube’s centre. There are more of the compounds and also
each of them has much less to do, so they do their “work” faster.
The obtained results have a reflection in the biological world. As said in the “background”
section” cells seek to have the biggest SA:V they can. Cells need to take in nutrients from
their surroundings and expel waste through their cell membrane. If there is a large surface
area to volume ratio, there is more cellular membrane to take care of both of these
functions. If a cell gets too large, it’s SA:V gets smaller and there is not enough surface area
to expel wastes or intake nutrients (the cell has bigger volume so needs more of them) fast
enough and the cell shrinks or dies.
by bigger I mean the ones with SA:V = 2,4 and 3 (2.5cm x2.5cm x2.5cm and 2cm x2cm
x2cm)
4 by smaller I mean the ones with SA:V = 4 and 6 (1.5cm x1.5cm x1.5cm and 1cm x1cm
x1cm)
3
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Evaluation
Overall I am not very confident about the conclusion I made, as there were certain points in
this experiment that may cause objections. I don’t find any mistakes in the chosen
apparatus and materials.
The first thing, which contributed to the low reliability of these experiment is a small,
insufficient number of trials. With only 6 groups conducting the experiment, when one of
them makes an error it has a significant impact on the final results of the whole experiment
as the group’s result states 1/6 (about 17 %) of the final result.
Second of all, it was already mentioned that the data collected by group number 6 is very
different from the data collected by the other groups. It is very probable that this group has
misunderstood the method.
Having calculated the standard deviation of mean % volume of diffusion we can see (it’s
shown on the graph – standard deviation error bars) that the value of standard deviation is
very big in two of the biggest cubes, even more than 4 in the case of the biggest cube.
Both the odd results of group 6 and the high value of standard deviation can be the result of
other human errors. Keeping the cubes in the solution much more or much less than 10
minutes has probably affected the results most significantly – the diffusion would be at a
different stage. The same happens with waiting too much between removing the cubes
from the solution and taking measurements.
Thirdly, what can have some effect on the low reliability is that different people were
taking measurements using rulers with different errors.
Uncertainties themselves might have affected the results only on a very small scale as they
all had a small range.
Considering the weaknesses of this experiment we should avoid repeating the same
mistakes next time. First of all, it is better when much more trials are conducted
(preferably tens), but the same person, using only one ruler with a specific error, does
them all. In this case the error would have the same impact on all of the data, so wouldn’t
have a significant meaning in the outcomes. What should also be improved is the accuracy
in the adherence to the time the cubes should stay in the solution. The measurements are
to be taken immediately after removing the cubes – it will prevent any undesired processes
to start and change the results.
A good idea to extent the experiment is to examine more cubes with more different sizes.
This will give us an image on how does the correlation between SA:V and diffusion rate
look in a full spectrum, does it stay in the same trend as this experiment has shown or not.
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Bibliography:
1. Katarzyna Zaremba, „IB DIPLOMA PROGRAMME BIOLOGY SL AND HL STUDENT
HANDBOOK”
2. „Writing a good biology lab report”,
http://signatureibbiology.wikispaces.com/file/view/The+Perfect+Biology+Lab+Re
port.doc, , Web, 11.09.2014
3. „How to write a good biology lab report”, http://www.ibsurvival.com/topic/13178how-to-write-a-good-biology-lab-report/, 21.02.2014, Web, 11.09.2014
4. „Diffusion”, http://en.wikipedia.org/wiki/Diffusion , 07.09.2014, Web, 12.09.2014
5. „Sodium hydroxide”, http://en.wikipedia.org/wiki/Sodium_hydroxide, 21.08.2014,
Web, 13.09.2014
6. „What does stansard deviation show us about our data”,
http://science.halleyhosting.com/sci/soph/inquiry/standdev2.htm, Web,
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