Candidate Name: Tony Hong (Seung Mo Hong) Candidate Number: __002213-02______ Date: August 15, 2010
IB Biology HL
How will changing the surface area by changing the volume, affect the rate of diffusion of sodium chloride across a visking tube, measured using a conductivity probe? Aim
To investigate the relationship between surface area and the rate of diffusion of sodium chloride across a visking tube, measured using a conductivity probe. Introduction Diffusion is the process of which particles spread through random regions of higher concentration to regions of lower concentration. The rate of diffusion is the measure of how fast the particles from a region of higher concentration diffuse into the region of lower concentration or the change of concentration over a period of time. The rate of diffusion is affected by the following: a) Surface Area – as the surface area increases, more particles can spread as there is more area to travel. b) Temperature – as temperature rises, molecules will have a greater kinetic energy and hence, more molecules will have a greater energy than the activation energy, leading to more formations of products. c) Concentration Gradient – as the concentration gradient increases, more amounts of particles (in the same amount of volume) would be able to travel through from the higher concentrated region to the lower concentrated region. Hence, if any of these three variables are changed, the rate of diffusion would change as well.
Candidate Name: Tony Hong (Seung Mo Hong) Candidate Number: __002213-02______ Date: August 15, 2010
IB Biology HL
Variables Variable Measured Rate of magnetic stirrer
Method of measuring /controlling the variable/reason of why the variables was categorized in each section The rate of magnetic stirrer shouldn’t be too slow as it would take a longer time to gather information as well as due to the fact that the particles won’t spread throughout the regions fast enough. The rate of magnetic stirrer shouldn’t be too fast either as the magnetic can lose its balance and spin out causing the experiment to not work properly.
Volume of distilled water
Controlled Variables
Distance of conductivity probe from the visking tube
Size of visking tube
Temperature Concentration of sodium chloride solution
Independent Surface area of the sodium chloride solution Variables in the visking tube Dependent Variables
Rate of diffusion of NaCl solution, ΔC/t
Once the appropriate rate is measured, do not change it for other trials. The volume of distilled water needed to be appropriate. If the sodium chloride solution was put inside too much water. The rate of diffusion would have been difficult to measure as the concentration of the water wouldn’t changed much and wouldn’t occur fast enough. Also, the height of the volume needs to large enough for the whole visking tube to fit. Hence, 350cm3 of distilled water was used for all the trials by using conical flasks. This is a controlled variable as the rate of diffusion would vary if it changed throughout the experiment. The distance of conductivity probe from the visking tube is a controlled variable because the amount of concentration would be higher as it is closer to the visking tube and lower as it is further away from the visking tube. The size of visking tube is controlled by using the same sized visking tube. It is a controlled variable because if the size differed the surface area would have also changed. All trials are experimented in room temperature which is approximately 28℃ All trials are experimented with the same concentration as it can change the rate of diffusion if it isn’t controlled. The experiment is conducted by 1.0M of sodium chloride solution. The surface area of the sodium chloride solution was changed by increasing the volume of sodium chloride solution by 5cm3, resulting in 5cm3, 10cm3, 15cm3, 20cm3 and 25cm3, As the volume and surface area changes the rate of diffusion would change as well as more particles can diffuse across the visking tube. Change of conductivity (over time) was measured through Logger Pro by using a conductivity probe to calculate the rate of diffusion.
Table 1: List of Variables
Candidate Name: Tony Hong (Seung Mo Hong) Candidate Number: __002213-02______ Date: August 15, 2010
IB Biology HL
Hypothesis The rate of diffusion is the measure of how fast the particles from a region of higher concentration diffuse into the region of lower concentration or the change of concentration over a period of time. Three variables that could change the rate of diffusion is shown in the introduction. However, as the concentration and temperature is a controlled variable in the experiment, the surface area variable is the variable that will be changed to determine the change of rate of diffusion. Hence, by changing the surface area (by changing the volume) of the 1.0M of sodium chloride solution, the change of rate of diffusion would be measurable. The following equation is the formula for calculating the surface area of the visking tube:
2
2
+2
xh
Where: r = the radius of the visking tube h = the height of the visking tube The radius of the visking tube would be constant as the size of the visking tube is a controlled variable. Hence, the height of the sodium chloride solution inside the visking tube would be the determining factor that would change the surface area for diffusion. Therefore, by changing the volume, the height of the sodium chloride solution would change, leading to the difference of the surface areas. When looking at the equation, as the volume increases, the height also increases, leading to a greater surface area. And when the surface area increases, the area for the number of particles to spread through the regions increases as well. Hence, more numbers of particles are able to diffuse from the higher concentrated region to the lower concentrated region during the same amount of time.1 As such, the hypothesis for this experiment is that as the surface area of 1.0M sodium chloride solution increases, the rate of diffusion would linearly increase. Therefore, as the surface area of the 1.0M sodium chloride solution increases, the rate of diffusion would increase as well.
Rate of diffusion, r/(ÎźS cm-1 s-1) against Surface
Rate of diffusion, ÎźS cm-1 s-1
area, SA/cm2 of NaCl solution
Surface area, cm2
Figure 1: graph showing the predicted trend mentioned in the hypothesis 1
"Surface-area-to-volume ratio." Wikipedia. 13 Feb 2011. Wikipedia Foundation. 15 Feb 2011 <http://en.wikipedia.org/wiki/Surface-area-to-volume_ratio>.
Candidate Name: Tony Hong (Seung Mo Hong) Candidate Number: __002213-02______ Date: August 15, 2010
IB Biology HL
Apparatus -
Logger Pro Conductivity probe Sodium chloride solution (NaCl) 25.0cm3 pipette (±0.1)cm3 Visking tube 250.00 cm3 conical flask (±0.15)cm3 100.00 cm3 conical flask (±0.10)cm3 Distilled Water Magnetic stirrer 30cm Ruler (±0.1)cm Beaker
Procedure Preparation of making 1M of NaCl solution 1. Measure 14.61g of sodium chloride (NaCl) using an electric weighing machine. 2. Measure 250cm3 of distilled water using a conical flask and put the 14.61g of NaCl inside it 3. Stir well until all the NaCl is completely dissolved. Preparation of preparing visking tube 1. 2. 3. 4.
Cut approximately 10cm of visking tube. Wet one side of the visking tube and tie a firm knot Wet the other side of the visking tube and open the visking tube. Put water inside the visking tube and check for leakage.
Measurement of the radius and the height of different volumes of 1.0M NaCl solution 1. Transfer 5cm3 of NaCl solution into a visking tube with a 25cm3 pipette. 2. Put pressure on the visking tube so that it would be shaped as a cylinder and measure its radius using a 30cm ruler. 3. After finding its radius, measure the height of the NaCl solution in the visking tube using a 30cm ruler. 4. Repeat steps 1-3 with 10 cm3, 15 cm3, 20 cm3, and 25 cm3 of NaCl solutions.
Figure 2: Diagram for the process of measuring the radius and height of different volumes of NaCl
Candidate Name: Tony Hong (Seung Mo Hong) Candidate Number: __002213-02______ Date: August 15, 2010
IB Biology HL
Process of measuring the conductivity of the different volume of 1.0M of NaCl solution 1. Measure 350cm3 of distilled water in a beaker by using a 250cm3 conical flask and a 100cm3 conical flask. 2. Place the beaker on top of a magnetic stirrer, and put the magnetic stirrer at a constant rate of power. 3. Place the visking tube with 5cm3 of NaCl solution inside the beaker filled with 350cm3 of distilled water and measure the change of conductivity through logger pro using a conductivity probe. 4. Repeat steps 1-3 three times in order to collect triplicate data. 5. Repeat steps 1-4 with 10 cm3, 15 cm3, 20 cm3, and 25 cm3 of NaCl solutions.
Figure 3: Diagram for the process of measuring the change of conductivity
Candidate Name: Tony Hong (Seung Mo Hong) Candidate Number: __002213-02______ Date: August 15, 2010 Data collection Time, t/s
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90
IB Biology HL
Conductivity of 5cm3 Conductivity of 10cm3 Conductivity of 15cm3 Conductivity of 20cm3 Conductivity of 25cm3 NaCl solution inside the NaCl solution inside the NaCl solution inside the NaCl solution inside the NaCl solution inside the distilled water, C/μS distilled water, C/μS distilled water, C/μS distilled water, C/μS distilled water, C/μS (±0.1 μS) (±0.1 μS) (±0.1 μS) (±0.1 μS) (±0.1 μS) Trial 1 Trial 2 Trial 3 Trial 1 Trial 2 Trial 3 Trial 1 Trial 2 Trial 3 Trial 1 Trial 2 Trial 3 Trial 1 Trial 2 Trial 3 14.4 9.8 17.0 21.2 17.8 8.7 17.1 26.8 7.6 24.9 19.9 16.3 16.2 23.4 20.7 14.5 8.8 11.2 14.4 11.4 13.8 17.1 37.1 12.8 21.8 34.0 29.7 39.4 19.4 44.4 29.3 17.4 17.8 24.6 20.7 31.1 38.9 65.9 38.7 55.3 59.8 66.1 75.9 60.6 90.2 42.0 26.0 32.3 33.4 34.3 49.6 59.1 85.5 64.7 79.7 99.6 111.1 101.0 97.6 133.8 53.0 34.5 41.2 44.6 48.1 68.5 72.5 108.2 87.3 96.1 124.5 141.4 150.3 139.0 160.4 63.0 41.4 50.9 57.0 57.4 78.9 90.6 122.0 114.7 116.5 143.8 161.9 180.7 164.9 187.2 71.2 48.4 60.5 69.4 69.5 95.5 118.1 138.6 133.7 133.8 166.1 183.1 201.3 182.0 218.1 79.3 57.4 71.6 84.2 82.6 114.8 131.1 158.6 149.7 154.4 181.5 204.3 218.5 205.9 248.9 91.5 63.6 77.2 95.7 92.4 127.2 147.1 168.6 167.1 173.4 191.9 223.2 236.3 219.5 269.5 97.7 70.6 88.6 105.5 101.0 138.0 162.6 185.3 183.1 187.3 205.3 243.0 253.6 237.1 300.0 103.5 79.3 96.2 118.5 112.7 151.8 175.4 194.2 197.3 204.6 217.7 264.8 271.6 258.7 324.9 113.0 84.5 103.7 129.9 121.0 164.8 188.9 201.8 208.4 218.4 227.8 283.3 294.4 273.2 351.1 119.8 92.7 113.2 141.2 135.6 173.9 201.7 214.0 218.2 233.7 246.3 310.3 315.9 289.1 370.5 128.4 99.7 118.5 148.1 144.5 182.5 215.9 225.5 230.2 247.4 258.7 328.6 335.5 308.6 389.6 138.6 110.1 128.7 157.6 158.6 192.0 223.8 234.0 241.0 264.6 266.9 357.1 356.1 330.3 411.1 143.6 114.4 141.1 170.3 168.1 198.8 233.9 242.6 252.6 282.5 283.2 375.3 372.2 351.1 434.7 154.7 122.2 143.9 183.7 175.5 205.2 245.3 251.3 265.7 299.0 299.6 388.3 391.4 367.8 456.4 161.5 127.7 148.5 196.4 187.3 219.2 258.4 260.7 280.2 313.7 317.4 407.6 412.0 386.0 476.6 170.3 135.1 155.8 211.0 194.6 223.0 270.6 273.5 293.4 326.2 330.6 425.4 428.5 401.2 497.6 Table 2: Conductivity measured for every 5 seconds of the triplicate trial of each different NaCl solution volume
Candidate Name: Tony Hong (Seung Mo Hong) Candidate Number: __002213-02______ Date: August 15, 2010
IB Biology HL
(a)
Figure 4: Graph showing the change of conductivity against time for every trial of five different volume of sodium chloride solution (a)
Rate of diffusion for each trial was measured by calculating the gradient of the change of diffusion from the time interval, 0 â&#x20AC;&#x201C; 90s
Candidate Name: Tony Hong (Seung Mo Hong) Candidate Number: __002213-02______ Date: August 15, 2010
IB Biology HL
Quantitative Data Volume of NaCl, v/cm3 (±0.03cm3)
Rate of diffusion of NaCl solution, r/(μS cm-1 s-1) Trial 1
Trial 2
Trial 3
5.00
1.459 ± 0.0065
1.707 ± 0.01364
1.730 ± 0.01088
10.00
2.163 ± 0.01298
2.467 ± 0.03717
2.245 ± 0.01594
15.00
2.653 ± 0.04803
3.156 ± 0.05409
2.921 ± 0.03254
20.00
3.268 ± 0.05539
4.488 ± 0.04651 (-) (a)
3.436 ± 0.02606
25.00
4.204 ± 0.5900
5.195 ± 0.06209 (-)
4.439 ± 0.05810
Table 3: Rate of diffusion of triplicate trial of each different NaCl solution volume
(a)
Data that is an outlier and hence is not used to calculate the average rate of diffusion
Qualitative Data -
NaCl solution was colourless Visking tube containing the NaCl solution became slightly bigger after diffusion
Candidate Name: Tony Hong (Seung Mo Hong) Candidate Number: __002213-02______ Date: August 15, 2010
IB Biology HL
Data processing The following equation is the formula for calculating the surface area of the visking tube:
2
2
+2
xh
Where: r = the radius of the visking tube h = the height of the visking tube To calculate the surface area, the following measurements were required: Volume of NaCl solution, v/cm3 (±0.03cm3) 5.00
Radius of visking tube, r/cm (±0.1cm) 1.0
Height of NaCl solution, h/cm (±0.1cm) 1.1
10.00
1.0
2.7
15.00
1.0
4.3
20.00
1.0
5.9
25.00
1.0
7.4
Table 4: Measurement of the radius and height of different volume of sodium chloride solution
Volume of NaCl solution, v/cm3 (±0.03cm3) 5.00
Calculation of surface area
2
2
+2
x 1.1 ≈ 13.1
Surface Area of NaCl solution, SA/cm2 (±0.2cm2) 13.1
10.00
2
2
+2
x 2.7 ≈ 23.2
23.2
15.00
2
2
+2
x 4.3 ≈ 33.3
33.3
20.00
2
2
+2
x 5.9 ≈ 43.2
43.2
25.00
2
2
+2
x 7.4 ≈ 52.7
52.7
Table 5: Calculation of surface area
Candidate Name: Tony Hong (Seung Mo Hong) Candidate Number: __002213-02______ Date: August 15, 2010
IB Biology HL
The average rates of diffusion of the three trials were calculated by the following equation:
Surface Area of NaCl solution, SA/cm2 (±0.2cm3)
Calculation
Average rate of diffusion of NaCl solution, r/(μS cm-1 s-1) (μS cm-1 s-1± s.d(b)) 1.63 ± 0.1503
12.6
≈ 1.632
22.6
≈ 2.295
2.30 ± 0.1623
32.7
≈ 2.910
2.91 ± 0.2517
42.7 52.8
c
≈ 3.352
3.35 ± 0.1188
≈ 4.322
4.32 ± 0.1662
Table 6: Calculation of average rate of diffusion (b) (c)
s.d - Abbreviated form of Standard Deviation Data contained an outlier and hence was not put into the calculation of average rate of diffusion
Candidate Name: Tony Hong (Seung Mo Hong) Candidate Number: __002213-02______ Date: August 15, 2010 Data Presentation
IB Biology HL
Rate of diffusion, r/(μS cm-1 s-1) against Surface Area, SA/cm2 of NaCl solution
5
Rate of Diffusion, (μS cm-1 s-1)
4.5
y = 0.0649x + 0.7541 R² = 0.9843
4 3.5 3 (a)
2.5 2 1.5 1 0.5 0 0
10
20
30
40
50
Surface Area, (cm2)
Figure 5:Graph showing the average rate of diffusion against the surface area of NaCl solution (a)
Error bar representing the standard deviation of the average rate of diffusion
60
Candidate Name: Tony Hong (Seung Mo Hong) Candidate Number: __002213-02______ Date: August 15, 2010 Uncertainty/ Error Analysis
Surface Area of NaCl solution, SA/cm2 13.1 23.2 33.3 43.2 52.7
Surface Area of NaCl solution, SA/cm2 13.1 23.2 33.3 43.2 52.7
IB Biology HL
% uncertainty for length use Length of radius % uncertainty of Length of height % uncertainty of of visking tube, Length ( % ) of NaCl solution, Length ( % ) using a 30cm ruler using a 30cm ruler (Δr = ± 0.1) cm (Δ = ± 0.1) cm 1.0 ± 0.1 (0.1/1.0) x 100 1.1 ± 0.1 (0.1/1.1) x 100 = 10.0% = 9.1% 1.0 ± 0.1 (0.1/1.0) x 100 2.7 ± 0.1 (0.1/2.7) x 100 = 10.0% = 3.7% 1.0 ± 0.1 (0.1/1.0) x 100 4.3 ± 0.1 (0.1/4.3) x 100 = 10.0% = 2.3% 1.0 ± 0.1 (0.1/1.0) x 100 5.9 ± 0.1 (0.1/5.9) x 100 = 10.0% = 1.7% 1.0 ± 0.1 (0.1/1.0) x 100 7.4 ± 0.1 (0.1/7.4) x 100 = 10.0% = 1.4% Table 7: Uncertainty of the measurements of lengths due to the ruler
Total % of Uncertainty
Surface Area with uncertainty
10.0% + 9.1% = 19.1% 10.0% + 3.7% = 13.7% 10.0% + 2.3% = 12.3% 10.0% + 1.7% = 11.7% 10.0% + 1.4% = 11.4%
13.1 ± 19.1% 23.2 ± 13.7% 33.3 ± 12.3% 43.2 ± 11.7% 52.7 ± 11.4%
% uncertainty in surface area, SA/cm2 ΔSA (%)
Surface Area, SA/cm2 and uncertainty ΔSA (cm2)
19.1 13.7 12.3 11.7 11.4
13.1 ± 2.5 23.2 ± 3.2 33.3 ± 4.1 43.2 ± 5.1 52.7 ± 6.0
Absolute % uncertainty in surface area, SA/cm2 ΔSA (cm2) (19.1/100) x 13.1 = 2.5 (13.7/100) x 23.2 = 3.2 (12.3/100) x 33.3 = 4.1 (11.7/100) x 43.2 = 5.1 (11.4/100) x 52.7 = 6.0 Table 8: The absolute uncertainty for each surface area
Candidate Name: Tony Hong (Seung Mo Hong) Candidate Number: __002213-02______ Date: August 15, 2010 Surface Area, SA/cm2 Solution ΔSA (cm2)
NaCl
IB Biology HL Average rate of diffusion of NaCl solution,r/(μS cm-1 s-1) (μS cm-1 s-1 ± s.d)
13.1 ± 2.5
1.63 ± 0.15
23.2 ± 3.2
2.30 ± 0.16
33.3 ± 4.1
2.91 ± 0.25
43.2 ± 5.1
3.35 ± 0.12
52.7 ± 6.0
4.32 ± 0.17
Table 9: Relationship between the surfaces areas with absolute uncertainty and the average rate of diffusion
Candidate Name: Tony Hong (Seung Mo Hong) Candidate Number: __002213-02______ Date: August 15, 2010 Conclusion
IB Biology HL
The exact relationship between the average rate of diffusion and the surface areas can be seen on table 6. As it can been seen on table 6, the surface areas increase approximately by 10.0 cm2 per variable and the difference between the average rate of diffusion of the variables (of the one after it) is 0.67, 0.61, 0.44, 0.97 respectively. The difference between the average rates of diffusion of 3rd – 4th is relatively small and 4th – 5th is relatively big when comparing it to the previous difference values. Hence, when taking a linear perspective towards the data it can be said that the value of the average rate of diffusion of the fourth SA variable (42.7cm2) is smaller than the theoretical value. This can also be seen through figure 5 which show the overall relationship between the average rate of diffusion and the surface areas. Therefore as it can been seen on both table 6 and figure 5, as the surface area increases, the average rate of diffusion also increases; hence having a positive correlation. Although the average rate of diffusion value (3.352 μS cm-1 s-1) of the fourth SA variable (42.7cm2) is small, making the differences between the average rate of diffusion not constant, I believe that the trend increases in a linear manner as we have to take the relatively big error bars in consideration. The linear relationship states that the average rate of diffusion is directly proportional to the constant change of the surface areas of the reactant. As it can be seen on table 6, 7 and 8, the experiment contained high uncertainties due to the fact that the apparatus (especially the ruler) was not as accurate. However, to improve on the accuracy of the experiment each variable was run 3 times, hence giving a triplicate data. Despite the high uncertainties, the data was fairly constant and was reliable enough to confirm the trend. As such, the hypothesis is valid and accepted. Evaluation Weaknesses Improvements Uncertainty of the surface area was too high due Can use an apparatus which has a lower to the relative high uncertainty of the 30cm ruler uncertainty than the 30cm ruler (±0.1cm) to reduce the uncertainty, which allows the experiment to become more accurate and reliable The fluctuation of the initial collection of data Let the logger pro run before putting in the NaCl made the gradient (the rate of diffusion) less solution. After seeing constant/ straight data accurate. Look at Figure 4. collection, put in the NaCl solution so that the fluctuation of the initial data collection would be smaller. A visking tube is not a perfect cylinder. Hence, Can use a more skinny visking tube (which has a the calculation of the surface area of the visking smaller radius) as it would be easier to put tube is not exactly accurate. pressure on it, in order to make a more accurate cylindrical shape