St.

Paul College, Pasig

High School Department
SY 2019-2020

Names: MEJIA, Kezia, PASCO, Juliana Score:

Grade and Section: 12-6 St. Ignatius de Loyola Date Submitted: August 16, 2019

EXPERIMENTAL DESIGN: THE EFFECT OF SURFACE TO VOLUME RATIO IN

GELATIN DIFFUSION OF VINEGAR

I. OBJECTIVES
At the end of the experiment, the students should be able to:
● identify the relationship between surface area-volume ratio and the amount of
material diffused into a semi-permeable membrane by submerging into vinegar
colored gelatin cubes of varying sizes; and
● correlate their findings to the importance of cell size and efficiency of material
exchange
II. VARIABLES
The controlled variables in the experiment were the amount of time the cubes were
submerged in vinegar (10 minutes) and the type and amount of vinegar used (5% acetic
acid). For the independent variable, the size (volume) of gelatin cubes varied (27 cm 3, 8
cm3, and 1 cm3). The dependent variable (depends on the independent variable), on the
other hand, was the amount of vinegar diffused into the cubes.

III. METHODOLOGY
A. Materials
To make the gelatin, one sachet of unsweetened, clear gelatin to be used as the
“cell”, 1183 mL of water, a metal bowl, hot plate, stirring rod, and 15 cm x 9 cm
x 5 cm tray serving as the “mold” were used. Creating the different sets of “cells“
required the use of a ruler and a knife. The materials utilized in the actual
experiment’s testing include around 450 mL of vinegar, blue food coloring, and
yellow food coloring to help in identifying the volume penetrated by the vinegar.

B. Procedure
Before the diffusion test was conducted, the gelatin was first created. To do this,
1183 mL of water was placed in a metal bowl, along with 25g of gelatin powder.
The mixture was then stirred using a stirring rod until there were no visible
clumps of powder. After, 5 drops of blue food coloring was added to the gelatin
mixture, which was stirred until a (medium) blue color was achieved. Placing the
bowl on the hot plate, the mixture was heated at an average of 250 (degrees) C
while stirring and brought to a near-boil state for 20.5 minutes. Special care was
taken during this procedure so as to avoid mishandling hot objects -- a safe
distance was placed between the students and the bowl, and pot holders were
used. After which the mixture was poured onto the 15 cm x 9 cm x 5 cm tray and
left to cool in a refrigerator for 6 days.
 Figure 1. Cooled gelatin to be used in the experiment.

The succeeding step involved measuring and slicing the now-solidified gelatin
with the ruler and knife according to the required sizes: 3 sets of 2cm x 2.9cm x
3cm cubes, 3 sets of 2cm x 2cm x 2cm cubes, and 3 sets of 1cm x 1cm x 1cm
cubes.

Figure 2. Gelatin cut into 3cm x 3cm x 3cm cubes.

Figure 3. Gelatin cut into 2cm x 2cm x 2 cm cubes.

Figure 4. Gelatin cut into 1cm x 1cm x 1cm cubes.

To test the amount of diffusion of vinegar into each cube, 9 small containers, each
containing vinegar mixed with 3 drops of yellow food coloring, were prepared.
 Then, the first set of cubes were placed in separate containers and submerged in
the vinegar completely.

Figure 5. Gelatin cubes submerged in colored vinegar.

Reactions were observed, and after 10 minutes, the cubes were taken out of the
vinegar, cut in half, and placed over a white surface in order to see the coloring
more clearly. The volume of the remaining blue area of each cube was measured
and subtracted from the original volume to get the volume penetrated by the
vinegar. This was repeated for all trials and cubes.

After conducting the experiment, the used gelatin was disposed of in the proper
waste disposal sites, and all materials used were thoroughly cleaned.

IV. DATA AND CALCULATIONS

The following are the results of submerging differently-sized blue gelatin cubes in
yellow-colored vinegar, producing a green border (blue color + yellow color) over parts
that the vinegar penetrated:

Figure 6. 3cm x 3cm x 3cm cubes removed from the vinegar after 10 minutes, cut in half.

Figure 7. 2cm x 2cm x 2cm cubes removed from the vinegar, cut in half.

Figure 8. 1cm x 1cm x 1cm cubes removed from the vinegar, cut in half.
 It was observed that the distance traveled by the vinegar (as seen in the green border) is
the same for each cube size (2mm or 0.2 cm). The measurements taken regarding the
amount of vinegar diffused into each cube and percentage of the cube penetrated by the
vinegar are shown in the following tables:

Table 1. Properties of 3x3x3 cubes and the volume penetrated by the vinegar.
VOLUME OF
SURFACE AREA VOLUME CUBE THAT DIFFUSED VOLUME
2
[6 × ( sidelength ) ] (side length)3 REMAINED BLUE ( volumetotal−volume ¿remaining )
(side length)3
TRIAL
1
TRIAL 6 x (3 cm)2 = (3 cm)3 = 27
(2.6 cm)3 = 17.6 cm3 27 cm3 – 17.6 cm3 = 9.4 cm3
2 54 cm2 cm3
TRIAL
3

Table 2. Properties of 2x2x2 cubes and the volume penetrated by the vinegar.
VOLUME OF
SURFACE AREA VOLUME CUBE THAT DIFFUSED VOLUME
2
[6 × ( sidelength ) ] (side length)3 REMAINED BLUE ( volumetotal−volume ¿remaining )
(side length)3
TRIAL
1
TRIAL
6 x (2 cm)2 = 24 cm2 (2 cm)3 = 8 cm3 (1.6 cm)3 = 4.1 cm3 8 cm3 – 4.1 cm3 = 3.9 cm3
2
TRIAL
3

Table 3. Properties of 1x1x1 cubes and the volume penetrated by the vinegar.
VOLUME OF
SURFACE AREA VOLUME CUBE THAT DIFFUSED VOLUME
[6 × ( sidelength )2 ] (side length)3 REMAINED BLUE ( volumetotal−volume ¿remaining )
(side length)3
TRIAL
1
TRIAL
6 x (1 cm)2 = 6 cm2 (1 cm)3 = 1 cm3 (0.6 cm)3 = 0.22 cm3 1 cm3 – 0.22 cm3 = 0.78 cm3
2
TRIAL
3

Table 4. Surface to volume ratio and percentage penetration of vinegar per cube size.
SURFACE AREA TO VOLUME
surface area PERCENTAGE PENETRATION
CUBE SIZE
RATIO ( ¿ ¿)
volume
54 9.4
3 cm x 3 cm x 3 cm =2 ×100 %=34.81 %
27 27
24 3.9
2 cm x 2 cm x 2 cm =3 ×100 %=48.75 %
8 8
6 0.78
1 cm x 1 cm x 1 cm =6 ×100 %=78 %
1 1
V. PREDICTED RESULTS AND ANALYSIS
The hypothesis of the experiment is that the smaller the size of the gelatin cube,
the higher the surface area to volume ratio, and the higher the percentage of the cube
diffused into by the vinegar. The smallest size of the cube is thus expected to have the
highest percentage penetration of vinegar. Although the relationship between the surface
area and volume is direct, the change is not proportional. So, when the volume of the
cube increases, the surface area also increases but at a smaller rate. This causes bigger
gelatin cubes to absorb a smaller percent of vinegar out of its total volume, compared to
smaller sizes (as seen in Figures 6, 7, and 8). Thus, as the size of the cube decreases, its
surface area to volume ratio increases, along with the amount of vinegar diffused into the
material. This is supported by the results of the experiment as shown in Table 4.

Regarding material exchange efficiency considering the size of cubes, it was

found that, given that gelatin served as the model for a cell, the smaller cell size, the
better. This is supported by the fact that the vinegar reached/diffused into a higher
percentage of the small “cell” (78%) compared to the other, larger sizes (which reached
only 34.81% and 48.75% of the cell, respectively). Based on this, it can be concluded that
the exchange of materials by the surface of a cube is more efficient when the cell is
smaller, and the surface area to volume ratio is large. This is also the reason for the
presence of many organelles within in the cells, which increases the surface area of the
cell, and consequently, maximizes the exchange of materials.