The Relationship Between the Rate of Diffusion and Molecular Weight as Observed in Postassium manganate, Potassium dichromate, and Methylene Blue

The Relationship Between the Rate of Diffusion and Molecular Weight as Observed in Postassium manganate, Potassium dichromate, and Methylene Blue

Elisha Padilla
Group 3 Sec. X – 8L

March 26, 20151

ABSTRACT

The relationship between the rate of diffusion and the molecular weight of a substance was determined by introducing three substances (KMnO₄, K₂Cr₂O₇, C₁₆H₁₈N₃SCl) of different molecular weight to agar-water gel, and measuring the distance of diffusion every three minutes for 30 minutes. Ideally the lighter substance would spread at a faster rate. However, C₁₆H₁₈N₃SC, the one with highest molecular weight, had a highest rate of diffusion. It is either (1) the hypothesis is wrong and thus rejected, or (2) parts of the experiment 's conduct was incorrectly done, such as the amount of the substance droped into the agar-water gel.

INTRODUCTION

Diffusion is defined by Mader (1999) as a process wherein “molecules move from higher to lower concentration” which commonly occurs in liquids, gases, and more rarely in solids. This movement is made possible by the internel kinetic energy of the substance, which means there is no arrangement as to the manner of the movement of molecules and that this leads to their collision (Velasquez & Villamor-Assis, 1993). Furthermore, Velasquez & Villamor-Assis (1993) discuss that diffusion is possible if the substances “normally mix and do not repel each other.” Diffusion occurs until the concentration of molecules is equal althroughout the mixture of substances. For the purpose of illustration, the class observed the diffusion of hydrocholoric acid (HCl) and ammonium hydroxide (NH4OH) by simultaneously dipping separate cotton buds into the mentioned solutions. These were then immediatley used to plug the ends of a two-feet glass tube. Gaseous diffusion is observed using this set-up. A ring of white smoke was later seen, and the students have marked and tabulated the distance in centimeters. According to this set-up, the white smoke was closer to HCl (12.80 cm) compared to NH4OH (24.80), which leads to the question as to why this is so, when the plugging of the cotton balls was done simultaneously. Ideally, the white smoke would occur at the middle of the glass tube, but repeated trials have constantly shown the distance of the smoke closer to HCl (Table 1).

Table 1. The distance of NH3 relative to Hcl during a simultaneous diffusion in a glass tube.
Trial
Distance (cm)
(d)

dHCl dNH3 1
12.0
24.0
2
11.4
24.3
3
12.8
24.8
4
14.0
26.5

One seen factor is the difference in molecular weight of the two substance; while HCl has a molecular weight of 36 g/mole, NH3 has 17 g/mole. According to Graham 's Law of effusion, given a temperature and pressure, a gas will diffuse faster if its molecular weight is ligther, otherwise, the diffusion would be slower (chemistry book). This set-up, however, is not sufficient to further study this possible phenomenon. There is a need for an experimental set-up that could be easily monitored. In this experiment it is hypothesized, given the results of the preliminary investigation and the Graham 's law, that a substance with a low molecular weight would diffuse faster, while a substance with a high molecular weight would diffuse slower. The experiment conducted at Room 127, Wing C of the Institute of Biological Sciences in UP Los Banos, then aims to:
1. measure the distance of diffusion of three different substances with varrying molecular weight at regular time intervals;
2. determine the partial rates of diffusion of the three substances; and
3. explain the relationship among time, rate of diffusion, and molecular weight.

MATERIALS AND METHODS

The inadequacy of a gaseous set-up in observing diffusion closely led to the use of an agar-water gel. The agar-water gel permits the diffusion of liquids at a slower rate, and is therefore good for the purpose of the experiment. Three substances, Potassium permanganate (KmnO₄), Potassium dichromate (K₂Cr₂O₇), and Methylen blue (C₁₆H₁₈N₃SCl) are used as variables. KmnO₄ has a molecular weight of 158 g/mole, K₂Cr₂O₇ has 294 g/mole, and C₁₆H₁₈N₃SCl has 374 g/mole. One drop of each of the mentioned substances was placed in three separated wells inside a petri dish with agar-water gel. The initial diameter of each drop was then measured in millimeters (mm) using a ruler. After three (3) minutes, the diameters are again measured and recorded. This process should go on for thirty (30) minutes. However, due to mishandling, the students had to repeat the set up. Another petri dish was acquired and the process of droping the substances was repeated. The second set-up was accidentally spilled, causing the liquid inside to spread irregularly throughout the gel. Because of these circumstances, the data from another group of students was borrowed for the purpose of saving time and for interpretation of data. The data of the diameters from the other group were then tabulated according to time and the kind of substance. The students also had to illustrate the diameter of the substances at zero minute, and compare it to the result after 30 minutes. Using the data gathered, the partial rate of diffusion of each substance was computed according to each time interval. The partial rate of diffusion is computed as:
Partial rate (rp) = di – di-1

ti – ti-1

Where: di = diameter of colored area at a given time di-1 = diameter of colored area immediately before di ti = time when di was measured ti-1 = time immediately before ti After computing the partial rates of diffusion, the avegae rate of diffusion (mm/min.) was indicated below the table.

Figure 1. Comparison of the diffusion of substances between zero and thirty minutes.

RESULTS AND DISCUSSION

Table 2 shows the data collected repeatedly in three-minute intervals for 30 minutes. This shows the diameter in millimeters of each substance. It could be observed that there was an increase in the diameter of each specified area. However, the Potassium permanganate set-up stoped diffusing after nine minutes. As for Potassium dichromate and Methylene blue, it could be observed that their diameters have increased through time. After 30 minutes, Potassium permanganate 's diameter remained at 8 mm, while the Potassium dichromate and Methylene blue got 13 mm and 23 mm, respectively. This table shows the definition of population as described by Reece, et. al. (2011) as “the movement of particles of any substance so that they spread out into the available space.” Table 2. Diffusion of KMnO₄, K₂Cr₂O₇ and C₁₆H₁₈N₃SC as measured by diameters in three-minute intervals for thirty minutes.
Time
(minute)
Diameter (mm)

Potassium permanganate
(MW 158 g/mole)
Potassium dichromate
(MW 294 g/mole)
Methylene blue
(MW 374 g/mole)
0
5
5
4
3
5
5
4
6
7
6
6
9
8
8
8
12
8
9
10
15
8
9
13
18
8
9
14
21
8
10
15
24
8
11
20
27
8
12
22
30
8
13
23

Table 3 shows the partial rates of diffusion of the three substances for each time interval. These were based on the data gathered on Table 1. The avarage rate of Potassium permanganate is relatively lower at 0.10 mm/min compared to Potassium dichromate and Methylene blue, at 0.27 mm/min and 0.63 mm/min, respectively. However, it could be observed that the rate of diffusion for Methylene blue is significantly higher compared to the other two. It could be racalled that the molecular weight of Methylene blue is the heaviest at 374 g/mole, compared to Potassium permanganate and Potassium dichromate at 158 g/mole and 294 g/mole, respectively. The relationship between the molecular weight and average rate of diffusion could be further examined using Figure 1. From here, the Potassium manganate could be seen as the substance having the slowest rate of diffusion, while the Methylene blue is significantly faster than both Potassium manganate and Potassium dichromate.

Table 3. Partial and avergae rates of diffusion of KMnO₄, K₂Cr₂O₇ and C₁₆H₁₈N₃SC three-minute intervals for thirty minutes.
Time elapsed
(minute)
Diameter (mm)

Potassium permanganate
(MW 158 g/mole)
Potassium dichromate
(MW 294 g/mole)
Methylene blue
(MW 374 g/mole)
3
0.00
0.00
0.00
6
0.67
0.33
0.67
9
0.33
0.67
0.67
12
0.00
0.33
0.67
15
0.00
0.00
1.00
18
0.00
0.00
0.33
21
0.00
0.33
0.33
24
0.00
0.33
1.67
27
0.00
0.33
0.67
30
0.00
0.33
0.33
Average rate of diffusion
(mm/min)
0.10
0.27
0.63

These results as shown in Table 1 and 2, and Figures 2 and 3, are in contrast with Graham 's Law of effusion which states, “the rate of effusion of gas molecules from a particular hole is inversely proportional to the square root of the molecular weight of the gas at constant temperature and pressure (Ebbing and Gammon, 2007).”
Figure 2. Average rate of diffusion of KMnO₄, K₂Cr₂O₇ and C₁₆H₁₈N₃SC relative to their molecular weight.
Figure 3. Partial rates of diffusion of KMnO₄, K₂Cr₂O₇ and C₁₆H₁₈N₃SC in three-minute time intervals for 30 minutes.

SUMMARY AND CONCLUSION

The data obtained from the experiment is in contrast with Graham 's Law of effusion. This could mean that either (1) the hypothesis is wrong and thus should be rejected, or (2) parts of the experiment 's conduct was incorrectly done. One cause of error may be the amount of substances droped into the wells of the agar-water gel. It was observable that the liquid poured using the dropper of the Methylyne blue was significantly greater than the Potassium permanganate and Potassium dichromate. Another cause of error may be unsimoultaneous application of the substances into the petri dish. However, the bulk of error may be more based on the first reason. Due to these contrasts, the Methylene blue obtained the fastest rate of diffusion, while the Potassium permanganate was slowest. The experiment conducted is most likely faulty and it is therefore suggested that the it be repeated. All variables must be constant, including the dropper, time, and amount of substance; except for the substances used and the rate of diffusion, which is the dependent variable. If on the next trials the Potassium permanganate shows the fastest rate of diffusion, then it may be said that the initial hypothesis that substances of lighter molecular weight would diffuse the fastest. Otherwise, if the results persists to be of the same rate even at repeated trials, it may be said that the hypothesis is wrong. This is however unlikely since it would be difficult to refute the well-established Graham 's Law of Effusion.

LITERATURE CITED
Duka, I.A., M.Q. Diaz, N.O. Villa. 2009. Biology I Laboratory Manual: An Investigative Approach. 9th ed. Laguna: Genetics and Molecular Biology Division, Institute of Biological SciencesUniversity of the Philippines Los Baños. pp. 35-36
Ebbing, D.D. and Gammon S.D. 2007. General Chemistry.9th ed. Boston, USA: Houghton Mifflin Company. pp. 204-205
Mader, S.S. 1999. Biology. 6Th ed. USA: McGraw-Hill Companies, Inc. p. 87
Reece, J.B., Urry, L.A., Cain, M.L., Wasserman, S.A., Minorvsky P.V., and Jackson, R.B. 2011. Campbell Biology. 10Th ed. USA: Pearson Education, Inc.
Velasquez, C. and Villamor-Asis, C. 1993. Modern Biology: Philippine Version. Revised ed. Caloocan, Ph: Phiilippine Graphic Arts, Inc. pp. 67-68

Cited: Duka, I.A., M.Q. Diaz, N.O. Villa. 2009. Biology I Laboratory Manual: An Investigative Approach. 9th ed. Laguna: Genetics and Molecular Biology Division, Institute of Biological SciencesUniversity of the Philippines Los Baños. pp. 35-36 Ebbing, D.D. and Gammon S.D. 2007. General Chemistry.9th ed. Boston, USA: Houghton Mifflin Company. pp. 204-205 Mader, S.S. 1999. Biology. 6Th ed. USA: McGraw-Hill Companies, Inc. p. 87 Reece, J.B., Urry, L.A., Cain, M.L., Wasserman, S.A., Minorvsky P.V., and Jackson, R.B. 2011. Campbell Biology. 10Th ed. USA: Pearson Education, Inc. Velasquez, C. and Villamor-Asis, C. 1993. Modern Biology: Philippine Version. Revised ed. Caloocan, Ph: Phiilippine Graphic Arts, Inc. pp. 67-68