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The Effect of the Molecular Weight of a Substance on Its Rate of Diffusion1
Mark Angelo A. Ordonio
Group 4 Sec. Y – 5L
August 22, 2012
1A scientific paper submitted in partial fulfilment of the requirements in General Biology I Laboratory under Dr. Severina B. Exconde, 1st semester 2012-2013.
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ABSTRACT
The effect of the molecular weight of a substance on its rate of diffusion was determined with two tests, each using a different medium. Using air as medium, ammonia (NH3) and hydrochloric acid (HCl) were made to react inside a glass tube to form ammonium chloride (NH4Cl). The distance travelled by the two reacting gases was measured, with HCl covering the shortest distance (dave = 18.125 cm); thus HCl travelled slower than NH3. Using gel as a medium, a drop each of potassium permanganate (KMnO4), potassium dichromate (K2Cr2O7), and methylene blue was placed on respective wells in an agar-water gel set-up. The diameter of each diffusion zone was measured at three-minute intervals for thirty minutes, with methylene blue having the shortest diameter of diffusion zone (dfinal = 9 mm); thus methylene blue diffused the slowest (rave = 0.199 mm/min). HCl has greater molecular weight compared to NH3 as well as with methylene blue compared with KMnO4 and K2Cr2O7, satisfying the premise that the higher the molecular weight, the slower the rate of diffusion is. In terms of time, the partial rate of diffusion is inversely proportional with the time elapsed.
INTRODUCTION
According to the molecular theory of matter, it states that all matter is
made up of tiny particles called molecules. In gases, the kinetic theory describes
a gas as a large number of molecules in constant, random motion, rapidly
moving and colliding with each other and with the walls of the container.
An assumption of the kinetic theory is that gas molecules travel in straight
lines. Since a molecule frequently collides with other molecules, its actual path is
a series of straight lines connected end to end in no particular pattern. However,
if the concentration of a particular substance is greater in one area of a container
than in another, its molecules will gradually spread out (Smoot, et al, 1990). The
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spread of molecules from a place where they are more abundant per unit of
volume (and, therefore, where collisions are more frequent) to places where they
are less abundant per unit of volume (where collisions are less frequent) is called
diffusion (BSCS, 1963). For example, releasing ammonia in one part of a room
will allow it to disperse it on the entire room, as noted by the odour. Adding a
coloured soluble solid in a water-filled beaker will also spread the colour on the
medium. Diffusion continues until the molecules are evenly distributed throughout
the space available; collisions and rebounds continue, with frequency equal from
one place with another, signifying no net change in the distribution of molecules.
In biology, the diffusion that concerns us the most is diffusion of
substances dissolved in water molecules and of water molecules themselves. All
active, non-dormant cells exist in a water environment; cells of the human body
are no exception. Thus, a living cell in is environment is a mixture of things in
water, separated by the cell membrane from another mixture of things in water
(BSCS, 1963).
Starr and Taggart (2004) pointed several factors that influence the rates of
movement down a concentration gradient: steepness, molecular size,
temperature, and electric or pressure gradients that may be present. The greater
the concentration of a substance in an area of a system entails that the
frequency of particles colliding with each other is higher, causing the particles to
collide at a faster rate. These collisions are due to the high molecular velocities
associated with the thermal energy “powering” the particles (Nave, 2008). At a
given temperature, a smaller particle is said to diffuse at a faster rate than a
larger one. This is because the larger the size of a particle, a greater amount of
force is said to be required to move the particle (Meyertholen, 2007). With the
same amount of energy, a smaller particle can be pushed faster than a larger
particle. Thus, the hypothesis of the study is that the rate of diffusion is inversely
proportional to the size of the particle. That is, a smaller particle will diffuse faster
than a larger one.
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To validate the hypothesis relating the molecular weight of a substance to
its rate of diffusion, two set-ups using different media were used. First, the glass
tube set-up using air as medium was used. Two cotton balls of identical sizes
were moistened with hydrochloric acid, HCl and ammonium hydroxide, NH4OH,
which were then placed concurrently in each end of the glass tubing. The
distance travelled by the two reacting gases (HCl and ammonia, NH3) was
measured – this will indicate the relationship between the molecular weight and
the rate of diffusion. On the other hand, the agar-water gel test, with water as
medium, was then used to assess and verify the effect of the molecular weight
on the rate of diffusion of different substances. A drop each of potassium
permanganate, KMnO4, potassium dichromate, K2Cr2O7, and methylene blue
was placed in three different wells on a petri dish with agar-water gel. Possessing
different colours, the substances are dyes which make them easily identifiable
and suitable for measurement of the diameter of the drops within a period of
thirty minutes.
This study intended to determine the effect the molecular weight of a
substance on its rate of diffusion using different media. The specific objectives
were
1. to identify the factors that could possibly affect the rate of diffusion of
substances; and
2. to explain the effect of molecular weight of a substance on its rate of
diffusion.
The study was conducted at Room C-107, Rafael B. Espino Wing
(Institute of Biological Sciences), Leopoldo B. Uichanco Hall (Biological Sciences
Building) of the College of Arts and Science, University of the Philippines Los
Baños Laguna on August 14, 2012.
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MATERIALS AND METHODS
For the glass tube test, the set-up (Figure 4.1) was initially prepared. Two
equally-sized cotton balls each soaked in HCl and NH4OH were plugged
simultaneously at each end of the glass tube. The white smoke forming a ring
inside the tube was observed and marked. The distance (in cm) between the
cotton and at the marked position was then measured and recorded.
For the agar-water gel test, a petri dish containing water-agar gel with
three wells was initially prepared. A drop of the following coloured solutions,
substances which differed in their molecular weights was placed on their
respective wells: potassium permanganate (KMnO4), potassium dichromate
(K2Cr2O7), and methylene blue. The diameter (in mm) of each diffusion zone was
measured and recorded in regular three-minute intervals for thirty minutes. The
average rate of diffusion (in mm/min) was computed using the following formula:
푝푎푟푡푖푎푙푟푎푡푒 푟 = (1)
where di = diameter of diffusion zone at a given time
di-1 = diameter of diffusion zone immediately before di
ti = time when di was measured
ti-1 = time immediately before ti
All computed values were tabulated and the mean of the computed partial
rates as well as the average rate of diffusion of each substance was calculated.
Partial rates of each substance at a specific time were plotted for analysis.
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Figure 4.1. The glass tube set-up.
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RESULTS AND DISCUSSION
To be able to develop a hypothesis that relates the molecular weight of a
substance and its rate of diffusion, the glass tube test was utilized. It uses air as
medium of diffusion for the gases NH3 and HCl. The reaction involved, the
formation of NH4Cl, is described by the following mechanisms:
HCl(l) → HCl(g) (2)
NH4OH(l) → NH3 (g) + H2O(l) (3)
HCl(g) + NH3 (g) → NH4Cl(g) (4)
Table 4.1. Distances travelled by the diffusion of ammonia gas and hydrochloric acid gas and ratios of the distances to the total distance.
Trial
Distance (cm)
(d) Total
distance
(D)
Ratio
dHCl dNH3 dHCl
D dNH3
D NH3
HCl
1 25.0 15.5 40.5 0.6173 0.3827 0.6200
2 25.0 23.0 48.0 0.5258 0.4792 0.9201
3 24.0 17.0 41.0 0.5854 0.4146 0.7082
4 21.5 17.0 38.5 0.5584 0.4416 0.7908
Average 23.875 18.125 42.0 0.5717 0.4295 0.7598
The white smoke that formed inside the tube is ammonium chloride,
NH4Cl, the product of the reaction between HCl and NH3 by diffusion, as seen in
(4). Based on the presented data, we could deduce that the measured rates of
diffusion of a series of molecules are proportional to the molecular weights of
diffusing substances. As seen in Table 4.1, it shows that HCl travelled at a longer
distance (dave = 23.875 cm) as compared to NH3 (dave = 18.125 cm), which tells
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us that the site of the initial reaction occurred near NH3. Hydrochloric acid (MM =
36 g/mol) has a relatively larger molecular weight compared to ammonia (MM =
17 g/mol). Since HCl travelled faster, the hypothesis “the higher the molecular
weight, the faster the diffusion” is developed.
Gases do not diffuse at the same rate, with the assumption that the rate of
diffusion varies directly with the velocity of molecules. At constant temperature,
molecules of low mass diffuse faster than molecules of large mass because they
travel faster, which will also pass a small hole (effuse) more rapidly than the
molecules of higher mass. Given two substances in constant temperature, the
average kinetic energies must also be constant. From this, Graham’s Law was
derived,
= (5)
which shows that the relative rates of diffusion of two gases vary inversely as the
square root of their molecular masses (Smoot, et al, 1990).
Theoretically, since NH3 has a smaller molecular weight, it must also
diffuse at a higher rate; thus, NH3 must travel faster and must reach the other
end with a longer distance compared to HCl. However, the initial part of the
experiment showed the opposite.
Re-testing the hypothesis using the agar-water gel test was done. As the
difficulty arises from measuring unseen moving molecules in fluids (i.e. gases
and liquids), substances that can be seen to diffuse as well as a medium that
permits diffusion should be considered. Moving media affects the rate of
diffusion, so incorporating water into a gel still allows diffusion in the same
medium (water) but is not moving and will not influence the rate of diffusion. This
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(a)
(b)
Figure 4.2. (a) Initial and (b) final agar water-gel set-up with three wells, each
containing a drop of potassium permanganate (purple), potassium dichromate
(yellow), and methylene blue (dark blue).
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is because a gel is made up of a framework of solid particles (chains) which trap
water in their interstices, causing its immobilization.
The measured diameters in Table 4.2 show that KMnO4, after the thirty-
minute period, exhibited the largest diffusion zone among the three, while
methylene blue has the smallest. Comparing their molecular weights, KMnO4
(MM = 158 g/mol) has the least against K2Cr2O7 (MM = 294 g/mol) and
methylene blue (MM = 374 g/mol). Table 4.3 shows the average rate of diffusion,
with KMnO4 having the fastest rate of diffusion (rave = 0.465 mm/min) among the
three.
Table 4.2. Diameters of the diffusion zones made by drops of potassium permanganate, potassium dichromate, and methylene blue measured at three-minute intervals for thirty minutes.
Time
(min)
Diameter (mm)
Potassium
permanganate
Potassium
dichromate
Methylene
blue
0 5 5 3
3 11 8 7
6 12 9 7
9 14 10 7
12 15 10 7
15 16 11 7
18 17 11 8
21 17 12 9
24 18 12 9
27 18 12 9
30 19 12 9
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Table 4.3. Partial rates of diffusion of potassium permanganate, potassium dichromate, and methylene blue measured at three-minute intervals for thirty minutes.
Time
elapsed
(min)
Partial rates of diffusion (mm/min)
Potassium
permanganate
Potassium
dichromate
Methylene
blue
3 2.00 1.00 1.33
6 0.33 0.33 0.00
9 0.67 0.33 0.00
12 0.33 0.00 0.00
15 0.33 0.33 0.00
18 0.33 0.00 0.33
21 0.00 0.33 0.33
24 0.33 0.00 0.00
27 0.00 0.00 0.00
30 0.33 0.00 0.00
Average rate
of diffusion
(mm/min)
0.465 0.232 0.199
Figures 4.3 and 4.4 show graphs of the average rate of diffusion with
respect to the factors molecular weight and time, respectively, to further display
the trend and pattern with this phenomenon. From Figure 4.3, it can be observed
that potassium permanganate, being the lightest, had the largest diameter
covered after 30 minutes. Meanwhile, methylene blue, being the heaviest, had
the smallest diameter covered. The expansion of the diffusion zones measured
by the diameters show the diffusion of the substances. Graham’s law proves
these results; however, it does not support the hypothesis that the higher the
molecular weight, the faster the rate of diffusion, but support the theoretical claim
that the higher the molecular weight, the slower the rate of diffusion.
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Figure 4.3. Average rate of diffusion of three coloured solutions with respect to
molecular weight.
Figure 4.4 Partial rates of diffusion of various coloured solutions in an agar-water
gel with respect to time.
0
0.1
0.2
0.3
0.4
0.5
158 294 374
Aver
age
rate
of d
iffus
ion
(mm
/min
)
Molecular weight (g/mol)
0
0.5
1
1.5
2
3 6 9 12 15 18 21 24 27 30
Part
ial r
ate
of d
iffus
ion
(mm
/min
)
Time elapsed (min)
KMnO4
K2Cr2O7
methylene blue
Linear (KMnO4)
Linear (K2Cr2O7)
Linear (methylene blue)
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Figure 4.4 shows the relationship between the partial rates of diffusion
with respect to time elapsed. It indicates that as time proceeds, the rate of
diffusion tends to decrease, as suggested by the lines of best fit for each
coloured solution. The negative slope indicates that time is inversely proportional
to the rate of diffusion.
The inconsistency of the results shown in the first test with theoretical
basis is possibly caused by human errors. Non-spontaneity in plugging the cotton
balls can cause the gas on the first plugged cotton ball to diffuse first before the
other. For better results regarding the second experiment, the wells must be
equal in size and shape to provide better basis of comparison.
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SUMMARY AND CONCLUSION
The effect of molecular weight on the rate of diffusion was determined
using the glass tube set-up and the water-agar gel set-up. These set-ups differ in
the medium used: air on the glass tube set-up and water on the water-agar gel
set-up.
On the first experiment, results showed that HCl, the heavier substance
(MM= 36 g/mol; dave = 23.875 cm) diffused at a faster rate than NH3, the
substance with the lighter molecular weight value (MM= 17 g/mol; dave = 18.125
cm). Contrary to the previous results, the second experiment showed that
methylene blue (MM= 374 g/mol) the substance with heavier molecular value had
diffused the slowest (rave = 0.199 mm/min) than the other two substances.
However, since the first experiment was found to be inconsistent with theory, the
hypothesis was considered void, as verified by the second experiment.
Thus, the higher the molecular weight of a substance, the slower the rate
of diffusion. Also, as time proceeds, the rate of diffusion also decreases.
It is recommended that, to be able to arrive with results that can be easily
based with scientific claims, the experiment be strictly observed in terms of
handling and execution. Several factors such as irregularities in temperature and
concentration may affect the results.
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LITERATURE CITED
Biological Sciences Curriculum Study (BSCS). 1963. High School Biology. Chicago: Rand McNally & Company. p. 384-385.
Meyertholen, E. 2007. Diffusion. Retrieved Aug. 16, 2012 from http://www.austincc.edu/~emeyerth/diffuse1.htm
Nave, R. 2008. Diffusion. Retrieved Aug. 16, 2012 from http://hyperphysics.phyastr.gsu.edu/hbase/kinetic/diffus.html
Starr, C. and R. Taggart. 2004. Biology: The Unity and Diversity of Life. 10th ed. Belmont, California: Thomson Brooks/Cole. P. 87.
Smoot, R.C., R.G. Smith, and J. Price. 1990. Chemistry: A Modern Course. 2nd ed. Columbus, Ohio: Merrill Publishin Company. p. 365-366.
