Research Question: How does the surface area and volume ratio affect the cell’s effectiveness and ability to diffuse substances?Background Information: Why are cells so small? Diffusion is the net passive movement of particles from a region in which they are in higher concentration to regions of lower concentration. This can be observed in cells when substances such as water, oxygen, nutrients, cellular waste are transported inside or outside the cell or to different cellular organelles. Moreover, both the solution and the agar are colourless, so agar will be mixed with phenolphthalein. Phenolphthalein is also a colourless substance and an indicator that changes its colour to pink with the presence of a base. The phenolphthalein will turn pink immediately when it comes into contact with the NaOH solution. The NaOH will start diffusing through the agar cubes and turn the inside of the cube pink when the agar-phenolphthalein cubes are put into a sodium hydroxide solution. Lastly, smaller cubes have bigger SA:V than big cubes. Hypothesis: The agar cubes with a smaller volume will have better diffusion rate due to its size and less volume the sodium hydroxide must diffuse through.Variables:Table 1:Independentthe size of the agar cubeDependent the distance from the core of the pigment to the border of the agar cubeControlledtype of solution in which we submerge: 0.1 M sodium hydroxide Time of the cubes left in the solution: 10 minutesVolume of solution The material used to prepare agar cubesThe method of measuring the length of cube edgesControlling the variables: Table 2Type of solutionUse the same batch of sodium hydroxide each trialTime the cubes are in waterUse a timer Volume of solutionUse the same graduated cylinderMaterials used to prepare the cubesUse the same package of agar and same batch of the phenolphthalein.Method to measure lengthUse the same ruler for allMaterials and Apparatus:Nutrient agar500 mL beakers0.5 % Phenolphthalein0.1 M NaOHHot plateStirring rodsThermometerContainer (4 x 4 x 4)Procedure: Part 1: Making the agar cubes (Day 1)Add 5.75 g of agar powder into a beaker filled with 250 mL water. Heat the mixture just below boiling.When agar mixture cools down to about 55 degrees, add 2.5 mL phenolphthaleinPut the agar mixture into a container that will give a height, length, and width of 4 cm or larger.Let the agar rest for a day and use it the next dayPart 2: Cutting the agar into cubes and immersing into the NaOH solution (Day 2)The agar batch will have dimensions that are 4 cm or largerCut the agar into cubes that will have the dimensions: 0.5 cm, 1 cm, 1.5 cm, 2 cm, 2.5 cm, 3 cm, 3.5 cm. Add 200 mL of 0.5 M NaOH into a 500 mL beaker.Set the timer to 10 minutes.Add the cubes into the beaker and start the timer. Leave the cubes in the solution for 10 minutes.After 10 minutes, take out the cubes onto a flat surface.With paper towel, blot the cubes so there is remnants of the sodium hydroxide.Cut each of the cubes in half.Using a ruler, measure how far the NaOH has diffused. In the diagram (figure 1) below, measure the length of “x”. Measure the width of the white cube.Figure 1: Agar cube when immersed in the NaOH solutionData Collection:Quantitative Data:Table 3Dimension (cm)Surface area (cm2)Initial volume of agar cube (cm3)Trial Length of the white area (cm)0.5 x 0.5 x 0.51.50.12510.020.130.01 x 1 x 16110.420.530.51.5 x 1.5 x 1.513.53.37510.820.730.82 x 2 x 224811.322.214.171.124 x 2.5 x 2.537.515.62511.721.731.73 x 3 x 3542712.121.932.13.5 x 3.5 x 3.573.542.87512.822.632.8Table 4: Diffusion of NaOHDimension (cm)Surface area (cm2)Initial volume of agar cube (cm3)Trial Length of the white area (cm)Volume of area not diffused by NaOH (cm3)Volume of area diffused by NaOH(cm3)0.5 x 0.5 x 0.51.50.12510.00.00.12520.10.0010.12430.00.00.1251 x 1 x 16110.40.0640.93620.50.1250.87530.50.1250.8751.5 x 1.5 x 1.513.53.37510.80.5122.86320.70.3433.03230.80.5122.8632 x 2 x 224811.32.1975.80321.11.3316.66931.21.7286.2722.5 x 2.5 x 2.537.515.62511.74.91310.71221.74.91310.71231.74.91310.7123 x 3 x 3542712.19.26117.73921.96.85920.14132.19.26117.7393.5 x 3.5 x 3.573.542.87512.821.95220.92322.617.57625.29932.821.95220.923Table 5: Average Volume Diffused by NaOHDimension (cm)Surface area (cm2)Initial volume of agar cube (cm3)Trial Volume of area not diffused by NaOH (cm3)Volume of area diffused by NaOH(cm3)Average volume of area diffused by NaOH (cm3)0.5 x 0.5 x 0.51.50.12510.00.1250.12520.0010.12430.00.1251 x 1 x 16110.0640.9360.89520.1250.87530.1250.8751.5 x 1.5 x 1.513.53.37510.5122.8632.91920.3433.03230.5122.8632 x 2 x 224812.1975.8035.24821.3316.66931.7286.2722.5 x 2.5 x 2.537.515.62514.91310.71210.71224.91310.71234.91310.7123 x 3 x 3542719.26117.73918.54026.85920.14139.26117.7393.5 x 3.5 x 3.573.542.875121.95220.92322.382217.57625.299321.95220.923Table 6: Diffusion Percentage and RateDimension (cm)Surface area (cm2)Initial volume of agar cube (cm3)Surface area to volume ratioAverage volume of area diffused by NaOH (cm3)Percentage of diffusion (%)Rate of diffusion (%/min)0.5 x 0.5 x 0.51.50.12512:10.125100.00101 x 1 x 1616:10.89589.508.951.5 x 1.5 x 1.513.53.3754:12.91986.498.6492 x 2 x 22483:15.24865.606.562.5 x 2.5 x 2.537.515.6252.4:110.71268.566.8563 x 3 x 354272:118.54068.676.8673.5 x 3.5 x 3.573.542.8751.7:122.38252.205.22Qualitative Observations:In like manner, the agar blocks were tinged with light yellow and were slightly opalescent (it has a milky iridescence). When the agar cubes were placed in the sodium hydroxide solution, the colour immediately changed from light yellow to pink. Regardless of the volume size, all of the agar blocks changed colour immediately when immersed in the solution. However, the volume size of the agar cubes had an influence on the rate and depth of the penetration of the sodium hydroxide solution. For instance, the agar blocks with the volume of 0.125 cm3, had the fastest rate of the sodium hydroxide penetrating the agar cube, as well, it also had the most region that the pink colour has tainted. Correspondingly, the agar block with the biggest volume of 42.875 cm3 had the slowest rate of the pink colour penetrating the block, and it had the biggest sector where the pink colour had not penetrated. In other words, the cube with the biggest dimension and volume had the smallest area of the pink stain. Moreover, when the agar cubes were cut in half, the area where the sodium hydroxide did not penetrate could be visibly identified. The region where the sodium hydroxide did not permeate was white and it also followed the shape of the agar cube.Data Processing: Calculating surface area of the agar cubes: Table 2Dimension (cm)Surface area (cm2)0.5 x 0.5 x 0.51.51 x 1 x 161.5 x 1.5 x 1.513.52 x 2 x 2242.5 x 2.5 x 2.537.53 x 3 x 3543.5 x 3.5 x 3.573.5SA – surface areae – edge of the cubeSA = 6e2Eg: to calculate the SA of the agar cube with the dimensions of 2 cm SA = 6 x 22 = 24 cm2Calculating initial volume of the agar cubes: Table 2Dimension (cm)Initial volume of agar cube (cm3)0.5 x 0.5 x 0.50.1251 x 1 x 111.5 x 1.5 x 1.53.3752 x 2 x 282.5 x 2.5 x 2.515.6253 x 3 x 3273.5 x 3.5 x 3.542.875V – volumeV = e3Eg: to calculate the volume of the agar cube with dimensions of 2 cmV = 23 = 8 cm3 From this graph, it can be identified that the volume of diffusion decreases as the surface area to volume ratio gets lower. The diffusion percentage does not decrease at a constant rate. In addition, at the SA:V of 4:1, the value is lower than the values of the SA:V ratios of 5:1 and 6:1. This is an indication to where a source of error may have taken place. This graph is similar to Graph 1; it presents the same information. However this graph was intended to demonstrate how the rate of diffusion went down as the volume of the agar cubes got bigger. This helps to enhance the understanding that the agar cubes with a larger volume has a lower SA:V ratio, while the smaller cubes have a higher SA:V ratio. Moreover it can be seen from the points from the agar cubes with the volume of 8 cm3 to 27 cm3, there is a plateau to be present, instead of a steady decrease. Once again, this could be an indication of a source of error.Conclusion:From the collected data, it can be inferred that the SA:V ratio has an influence on diffusion and therefore the hypothesis that was stated can be supported. In addition, it is also important to notice from the data that the agar blocks with a smaller volume had a high SA:V ratio, while the cubes with a larger volume correspondingly had a low SA:V ratio.The agar blocks with a high SA:V ratio had a faster rate of diffusion, as well as a higher percentage of diffusion. Moreover, the results from the data demonstrates how cells are more efficient when they have a high SA:V ratio. When a cell has a bigger surface area to volume ratio, it means that the cell has a greater surface for substances to pass through and less volume that the substance have to diffuse through . More importantly, in this case, the sodium hydroxide is the substance trying to diffuse through to the center of the agar cube. Essentially, when the agar block has a high SA:V ratio, it means that the sodium hydroxide has a greater surface and less volume to diffuse through which ultimately means that the sodium hydroxide has less work and therefore can diffuse through the agar cubes within a faster rate. Nextly, a cell needs to absorb nutrients and remove waste through their cell membrane. However, when there is not enough surface area for the cell to carry out the functions such absorbing nutrients and removing waste, the cell dies, since the volume is greater, there must be more intake of nutrients and removing of waste. When the cell has a greater surface area to volume ratio, there is more cell membrane to carry out the necessary functions for the cell to survive.Evaluation: There were errors present within the lab that may have influenced the data that was obtained and an example is the not precisely measuring and cutting the agar cube into its designated dimensions. It was very difficult to cut accurately, and as a result, some of the sides of the agar blocks were not smooth or straight. Moreover, when the agar cubes were placed into the sodium hydroxide solution, some agar cubes were put into the solution first as a result of putting many cubes into one beaker. This means that some agar cubes were immersed in the solution for a longer period of time than the others. Additionally, not all of the cubes were taken out at the same time, as it was difficult to drain the solution from the beaker and there were remnants of the solution within the beaker which could have influenced the data. Many improvements can be made within this lab. There should be more trials held and a strainer can be used to remove the solution from the beaker which can help to remove the agar blocks at the same time. Despite these weaknesses, the strength of this lab was that the same batch was used for the same trial and disposed of, and a new batch of agar was made every other day in order for the agar to not get moldy and grow bacteria as nutrient agar is mostly used for that purpose. Another strength was that throughout this experiment, the same ruler and knife was used to get the measurements. An extension to the experiment can include a variation of shapes. Instead of observing the diffusion of only the shape of a cube, perhaps in the future, the diffusion of agar in the form of a rectangle or triangle should be done.