How Does the Shape of a Cell Affect the Rate of Diffusion?

Modified: 18th May 2020
Wordcount: 4701 words

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1.0   Rationale

In this experiment, the rate of diffusion of hydrochloric acid into different agar shapes will be recorded in order to ultimately determine whether the shape of a cell affects the rate of diffusion. Human observation will be used to decide when there is no remaining pink agar. In theory, the relatively less surface area available for substances to diffuse through a cell results in a slower the rate of diffusion. (BBC, n.d.).

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The cell membrane controls the movement of substances in and out of the cell. This is done through the process of active or passive transport. In this instance, passive transport, and in particular, diffusion, is the movement occurring. Diffusion is a physical process that refers to the net movement of molecules from a region of high concentration to one of lower concentration in order to be at a state of equilibrium (biology dictionary, 2017). Diffusion is vital for the uptake of substances needed by cells, and also the removal of waste products produced by the cells. However, for this to occur, the cell membrane must be partially permeable. That is, the structure of these membranes is such that they allow certain particles to pass through membranes, hence into or out of the cell (IvyRose Holistic, n.d.). In terms of mathematical measurements, the important point is that the surface area to the volume ratio gets smaller as the cell gets larger. Thus, if the cell grows beyond a certain limit, not enough material will be able to cross the membrane fast enough to accommodate the increased cellular volume (Blamire, 2001). In this experiment, the hydrochloric acid was used to diffuse through the cell, which is represented by the pink agar shapes which were made of phenolphthalein and sodium hydroxide. As hydrochloric acid diffuses into the cell, it neutralises the base and the indicator disappears.


2.0   Research question – How does the shape of a cell affect the rate of diffusion?

Independent variable – Shape (surface area) of agar

Dependent variable – The time for the pink to disappear

Controlled variables – Concentration of acid, temperature of acid, the size of the dish the experiments are tested in, amount of stirring, volume of agar.


3.0   Methodology

3.1 Original method

The original method focused on diffusion of sulfuric acid through three pink agar cubes of a different volume. After 10 minutes, the remaining volume of pink agar was measured to determine the impact the surface to volume ratio had on diffusion.

3.2 Modifications to method

3.2.1 Refined by

The original experiment was modified in order to improve accuracy. Rather thanmeasuring the volume remaining after 10 minutes, we measured the time it took for the acid to completely diffuse into the agar. This is because by changing the shape of the agar, it would have been difficult to record accurate measurements of the volume for the remaining pink agar. The initial experiment was altered due to the excessive time it took for the act of diffusion to occur. In response to this, the concentration was increased from 0.1M to 1M.

3.2.2 Extended by

The modifications that were made to the original experiment based on the research question was the shape of the agar. This was changed from cubes to five different shapes in order to have varied surface area to volume ratios and determine its impact on diffusion rate. The volume for each shape was the same at 7ml.

3.3 Risk Management

Before conducting the experiment, potential hazards were identified as well as ways to minimise these risks. Hazards include breakage of beaker, cuts from chipped rims, easily flammable paper towels, heating of the plastic spoon resulting in the release of toxic vapours, irresponsible use of rulers as well as potential burning and splinters, and the blade or plastic handle from the Stanley knife causing hand and eye injuries. However, these can be managed and prevented by inspecting and discarding chipped or cracked breakers, avoid use of paper towels, spoons and rulers near naked flames and heat sources, checking for splinters and avoid using Stanley knife where possible.

4.0   Results

Table 1


This table is the original data from the experiment containing the time it took for the acid to diffuse through each shape. These results show the rate of diffusion for five tests.

Table 2


This table represents the relevant data from the five conducted experiments. The mathematical concepts involved assist provide information on the reliability and validity of the experiment and ultimately assist in answering the research question.


P(T<=t) two-tail

Rectangular Prism / Pineapple


Rectangular Prism / Tree


Rectangular Prism / Disk


Rectangular Prism / Oval


Pineapple / Tree


Pineapple / Disk


Pineapple / Oval


Tree / Disk


Tree / Oval


Disk / Oval


 Table 3










This table indicates the comparison of the shapes and the P value outcomes to determine any statistical differences between shapes.

Table 4

Surface Area (mm)


Rectangular Prism















This table shows the comparison of the surface area for each shaped versus the mean time it took for hydrochloric acid to diffuse into the agar. This is used to identify any patterns or trends and to determine if the shape or surface area of a cell affects the rate of diffusion.

Graph 1


This graph shows the mean rate of diffusion for each shape as well as the standard deviation.

4.2 Processing data

The statistical methods that were used to process the data consisted of mean, standard error, standard deviation, range, minimum, maximum, sum, count, confidence levels and P values.

4.3 Processed data

The collected processed data demonstrates comparable mathematical outcomes. The mean shows the average rate of diffusion. Relating to this is standard deviation which quantifies the dispersion of the set data values. Similarly, the standard error determines if most of the data is around our mean and the confidence level is how accurate the mean is based on the data and its representatives of it. The P values indicates if there is a statistical difference between the samples. If the P value is less than 0.05, there is a difference between these two shapes. The range is the difference between the lowest and highest values and can also assist in determining if outliers are apparent. The sum shows the total of the results when added together. The count states the number of tests that were conducted. These results were all calculate using data analysis in Excel and incorporating detailed statistics.

4.4 Interpretation

There were various trends noticed throughout the data tables and graphs. It is visible in table 2 and graph 1 that the rectangular prism had the fastest mean rate of diffusion at 11.488 minutes. This was followed by the tree at 12.69 minutes, the disk at 16.776 minutes, the oval at 21.064 minutes and the pineapple with a mean time of 22.222 minutes. However, when analysing the line representing standard deviation, the disk had the most widespread data. For example, the standard deviation for the disk was 6.74. This means that the replicants were not similar, with a range of 16.79 minutes. According to graph 1, the diffusion rate of test number 5 for the disk was 28.12 minutes. This is a major outlier being roughly double the average of the other four tests. Therefore, the confidence levels for the disk data is poor. This is compared to the rectangular prism which had the smallest standard deviation with just 0.96, and a range of 2.56 minutes to support this. In addition to this, the pineapple, oval and tree shared similar two standard deviations. However, the individual tests for the pineapple were pushing a state of being unreasonable with a range of 7.19 minutes. The P values shown on table 2 indicate that the cube had a faster rate than the pineapple, the pineapple had a quicker time than the tree and the tree had a faster time than the oval. Thus, means that these shapes are more efficient at diffusion. As for the remaining comparable shapes, there is no real statistical difference and using either shape would not have a high impact on the rate of diffusion.

After analysing the data and comparing the surface area of each shape to its mean rate of diffusion, it was identified that the shapes had no particular pattern despite the theory stating that the smaller surface area meant a slower diffusion time. Therefore, in theory, the shape with the fastest time should have been the pineapple, however, in this case it was the opposite with the pineapple having the slowest rate of diffusion. This was followed by the rectangular prism which contains the second largest surface area yet had the quickest time. These results may be due to the actual shape itself. For example, the rectangular prism and tree resembled a geometric shape more so than the pineapple and the oval as both of these shapes had faster diffusion rates.

4.5 Analysis

During the experimental method, five tests were conducted for each shape to minimise the limitations. By doing so, this ensures higher accuracy for the results and enhances reliability. The calculation of the surface area did appear to have an impact on the ability to compare surface area to time of diffusion. The key outliers in the disk and pineapple test also Outlier mention – in two tests


5.0   Evaluation

5.1 Sources of error

5.1.1 Affecting reliability

Throughout the experiment, there were numerous factors that affected the reliability of the data. When conducting the experiments, it was difficult to keep track of the diffusion rate and record the time for all shapes. This was because some shapes had similar diffusion rates. For example, we had only two people observing when the pink had disappeared for all five rectangular tests as well as 4/5 tests for the tree and 2/5 tests for the disk, all at an approximate diffusion rate of 11-13 minutes. This affects the reliability as the times that were recorded were not exact, but however, were very close to it. The low standard deviation of 0.96 for the rectangular prism shows that the rate of diffusion for each replicant were similar and therefore is accurate and reliable. In contrast to this, the disk and pineapple results were quite varied and unreasonable. However, the disk did maintain some consistency with two tests having an approximate time of 12 minutes and two others being at around 116 minutes. The outliers for the pineapple and disk majorly affected the range, this is either because it is hard to observe or simply not a good shape to consider. Due to not using geometric shapes, the surface area was difficult to calculate. To work a way around this, we had to use geometric shape surface area formulas that were similar to the shapes of the agar used. However, this didn’t account for the patterns on the agar shapes and therefore our results for this weren’t completely accurate. The only source of determining when the pink had disappeared was through human observation and thus may have impacted the validity of the experiment if the recorded times were inaccurate. If this test was repeated, the likelihood that they would obtain similar results is low. This is because many experiments have been done to prove the theory that the smaller the surface area of a cell, the slower the rate of diffusion. Although the conducted experiment did not support this, the chance of these outcomes occurring again are unlikely and the possibility that human error had a relative impact on the results is high.

5.1.2         Affecting validity

There were many obstacles that had an impact on the experiment’s validity. Although, the surface area measurements weren’t exact, this still provides an indication for the surface area to volume ratio and answers the research question to a certain extent. The disk with the outstanding outlier also created questionable results. To determine how much of an effect this had on the calculations, the mean was recalculated based on the first four tests. It was concluded that even if the outlier was removed, the disk would still have the third fastest ranking rate of diffusion and would not support our research question, but however, would make the test more reliable. Ultimately, the research question was answered but is not supported by secondary evidence or data. However, it does need to be considered that it is an experiment and doesn’t always go to theory. Couldn’t measure sa accurately, any reference to sa is questionable – shapes weren’t consistant thickness, showed anomilies had thick and thin as opposed to those who had even thickness. Geometric or consistent thickness to have a valid consideration.


5.2 Improvements and extensions

5.2.1 Suggested improvements

If this experiment were to be conducted again, various areas of improvement could be made in order to improve the reliability and validity of the results. To ensure accurate surface area calculations, replacing the current agar moulds with geometric shaped agar would be ideal. Specifically, shapes with straight edges to ease the difficulty when measuring. In regard to conducting the experiment, adjustments can be made based on the apparatus, and in particular, the placement of the agar in the beakers. Rather than having one of each shape in five different jars, grouping the same shapes into each jar would be more efficient when observing. This would be more so effective for the cube test as they have similar diffusion rates. In addition to this, allocating more people of the group to observe a jar each would allow more focus and attention to detail on your allocated shapes when determining the remaining pink agar. Is there some way to determine absence of colour. Mention reducing human error in relation to identify the remaining pink colour To increase the reliability of the results, any significant outliers should be removed, for instance, disk test number 5,

Even thickness

5.2.2 Suggested extensions

There are minimal extensions that can be made to this experiment. However, adding onto the poor accuracy issue, any major outliers, or remarkably varied times, that occur throughout the first trial of the experiment could be conducted again in hope to retrieve a more reasonable outcome. ADD


6.0   Conclusion

The experiment focusing on analysing surface area to volume ratio was conducted in order to answer the research question of; How does the shape of a cell affect the rate of diffusion? Through research, it was found that theoretically, the smaller the cell is the slower the rate of diffusion and vice versa. Despite the numerous factors that impacted the final results, such as the difficulty to calculate and the approximation of surface area, human errors through observation and lack of people controlling the results, a conclusion was able to be made to answer our research question; the shape of the cell does not affect the rate of diffusion. In spite of that contradicting the theory, it is an experiment which can arise many complications or unexpected outcomes. In this case, there was a key outlier in the experiment which prosed unrealistic data to present. However, removing this outlier from the five tests would not have assisted in answering the question and rather was recommended to conduct the test again if this were to occur in the future in order to produce more reliable and valid results.



          Change to third person

          Emphasise surface area and thickness

          Change cube to rectangular prism


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7.0   References

Works Cited

  • BBC. (n.d.). Retrieved from Bitesize:
  • biology dictionary. (2017, April 28). Diffusion definiton. Retrieved from biology dictionary:
  • Blamire, P. J. (2001). Cell Biology. Retrieved from Exploring Life @ BIO dot EDU:
  • Diffusion. (n.d.). Retrieved from Cassio Education:
  • IvyRose Holistic. (n.d.). Functions of the Cell Membrane. Retrieved from IvyRose Holistic:



  • BBC. (n.d.). Retrieved from Bitesize:
  • biology dictionary. (2017, April 28). Diffusion definiton. Retrieved from biology dictionary:
  • Blamire, P. J. (2001). Cell Biology. Retrieved from Exploring Life @ BIO dot EDU:
  • Diffusion. (n.d.). Retrieved from Cassio Education:
  • IvyRose Holistic. (n.d.). Functions of the Cell Membrane. Retrieved from IvyRose Holistic:
  • Regina, U. o., & Science, P. I. (n.d.). Quandaries & Queries. Retrieved from Math Central:
  • V, S. (2016, January 28). What is the formula for the surface area of a triangular prism? Retrieved from SOCRATIC:
  • Z., E. (2015, June 20). How does surface area to volume ratio relate to cell division? Retrieved from socratic:
  • Zghaib, I. (2018, August 25). How is the surface area of a half cylinder calculated? Retrieved from Quora:




















8.0  Appendices



















































Standard Deviation

Rectangular Prism























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