Cell Size Lab
Claire Ye, 2A
Problem: Does the surface area to volume ratio of a cell determine how efficiently
outside materials diffuse through it?
Variables
Independent Variable: the surface area to volume ratio of each agar cube
Dependent Variable: the percentage of colored area’s volume in total volume
Control Group
Concentration of sodium hydroxide – Concentration of sodium hydroxide that the
agar cubes are submerged in should be kept as consistent as possible. If the
concentration of sodium hydroxide differs in each solution the cubes are put in, then
the color that determines whether an area is has turned pink or not is also changed.
If a solution with very little sodium hydroxide diffuses through the agar, the color of
the agar would not change as pink as it could’ve been under a stronger solution.
There would be without a clear distinction between what is pink and affected, and
what is not, which would cause inaccuracies in measuring the true volume that have
been diffused through. Re-using the same sodium hydroxide solution for all agar
cubes ensures that all the cubes have been put under the same concentration of
sodium hydroxide, and no mistakes in data recording will be made
Amount of time agar block is submerged in sodium hydroxide – The amount of time
each agar cube is submerged in sodium hydroxide for the liquid to diffuse through
should be the same. If not kept consistent, the results in differences (or lack thereof)
between the percentages of colored areas would not be based on the surface area to
volume ratio, but also the difference in time each agar cube had to let the solution
diffuse through. The amount of time each agar cube is submerged under sodium
hydroxide is kept at 6 minutes so that surface area to volume ratio is the only
independent variable.
Temperature – The temperature should be kept consistent in the experiment
because it is a factor that affects the rate of diffusion. When under higher
temperature, heat gives the particles more energy, and they reach equilibrium faster
- vice versa when the temperature is lower. Given that all agar cubes will be
submerged in sodium hydroxide for the same amount of time, if the liquid diffuses
through in different temperatures, the determining factor of the percentage of area
turned pink by sodium hydroxide would not only be surface area to volume ratio,
but also the rate of diffusion. To assure that the rate of diffusion would not affect the
results, all experiments happened within 2-3 minutes of each other, in the same
classroom at room temperature.
Hypothesis
If the surface area to volume ratio of an agar cube is larger than another, then
that agar cube will have a higher percentage of total volume that the sodium
hydroxide has turned pink. “As a cube gets larger, its volume increases much faster
than its surface area.” (Miller & Stein, 2004) This means the surface area to volume
ratio increases as the volume of a cube decreases. (All agar objects are made cubes
so the shape of the object doesn’t affect the surface area to volume ratio.) Surface
area is important in the process of diffusion because it is the “movement of atoms
and molecules across membranes and within” the cubes. (Miller & Stein, 2004). The
more surface area the cube has in relation to its volume, the more area sodium
hydroxide has to diffuse through and reach the center of the cube. In a larger cell, as
there is less surface area as well as more volume to diffuse through. It is evident that
“it takes much longer for the particles to diffuse throughout the great volume of the
larger cell”, especially with a lower surface area to volume ratio. (Miller & Stein,
2004). With less efficiency than smaller cubes, less percentage of the larger agar
cubes’ volume will be diffused through and turned pink. In this experiment,
phenolphthalein is mixed into the agar. Any phenolphthalein that comes in contact
with sodium hydroxide will turn pink because “phenolphthalein is an indicator of
acids (colorless) and bases (pink)” and “sodium hydroxide is a base.” (Ophardt,
2003). The pink color of where the sodium hydroxide is indicates how far it has
permeated through the cube.
Tables
Total Length, Width, Height, Surface Area, Volume, and Surface Area to Volume Ratio of
Each Agar Cube
Surface
Area to
Agar
Length (±
Width (±
Height (±
Surface
Volume
Volume
2
3
Cubes
0.01 cm)
0.01 cm)
0.01 cm)
Area (cm ) (cm )
Ratio
Large
3.50
3.36
3.51
70.7
41.3 1.71:1
Medium
2.54
2.69
2.45
40.0
16.7 2.4:1
Small
1.48
1.56
1.32
12.9
3.05 4.27:1
Volume = length × width × height
Example: 3.50 × 3.36 × 3.51 = 41.3
Surface Area = 2 × (L × W) + 4 × (W × h)
Example: 2 × (3.50 × 3.36) + 4 × (3.36 × 3.51) = 70.7
Surface Area to Volume Ratio = Surface Area ÷ Volume
Example: 70.7 ÷ 41.3 = 1.71
Length, Width, Height, Volume of Uncolored Area, and Percentage of Colored Area of Agar
Cubes and Volume of Colored Area After Being Submerged in Sodium Hydroxide for 10
Minutes
Colored
Area
Percentage
Agar
Length (±
Width (±
Height (±
Volume
Volume (± of Colored
Cubes
0.01 cm)
0.01 cm)
0.01 cm)
(cm3)
0.01 cm3)
Area (%)
Large
2.74
2.70
2.77
20.5
20.8
50.4
Medium
1.91
1.92
1.61
5.94
10.8
64.7
Small
0.55
0.87
0.81
0.39
2.66
87.2
Colored Area Volume = total volume - uncolored area volume
Example: 41.3 - 20.5 = 20.8
Percentage of Colored Area = colored area volume ÷ total volume × 100
Example: 20.8 / 41.3 × 100 = 50.4
Graph and Analysis
Percentage of Colored Area to Total Volume
of Agar Cubes After Being Submerged in
Sodium Hydroxide for 10 Minutes
100
90
Percentage of Colored Area (%)
80
70
60
50
40
30
20
10
0
Large
Medium
Agar Cube
Small
There is a consistent relationship between the size of the agar cube and the
percentage of colored areas after being soaked in sodium hydroxide for the same
amount of time. It seems the smaller the agar cube, the higher the percentage of it
has turned pink. The smallest percentage is 50.4, while the highest is 87.2. The 5%
error bars indicate that, while the numbers may not be vastly apart, it is highly
unlikely that the other possible values of each percentage overlap each other.
References
Miller, K., & Stein J. (2004). Web Tutorial 41.4 Surface Area/Volume Relationships.
Retrieved April 23rd from
http://www.brown.edu/Courses/BI0020_Miller/week/10/web-1/4-22007_10-20-26/Chapter_41/Present/Animations/41_A01/41_A01s.swf
Ophardt, C. E. (2003). Acid-Base Indicators. Retrieved April 23rd from
http://www.elmhurst.edu/~chm/vchembook/186indicator.html