Effect of surface area to volume ratio on the diffusion on sodium chloride from dialysis tubing

Candidate Name: Tony Hong (Seung Mo Hong) IB Biology HL

Candidate Number: __002213-02______

Date: August 15, 2010

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.




Variables

Variable Measured Method of measuring /controlling the variable/reason

of why the variables was categorized in each section

Controlled

Variables

Rate of magnetic stirrer 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.

Once the appropriate rate is measured, do not change it

for other trials.

Volume of distilled water 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.

Distance of conductivity

probe from the visking

tube

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.

Size of 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.

Temperature All trials are experimented in room temperature which is

approximately 28℃

Concentration of sodium

chloride solution

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.

Independent

Variables

Surface area of the

sodium chloride solution

in the visking tube

The surface area of the sodium chloride solution was

changed by increasing the volume of sodium chloride

solution by 5cm3, resulting in 5cm

3, 10cm

3, 15cm

3, 20cm

3

and 25cm3,

Dependent

Variables

Rate of diffusion of NaCl

solution, ΔC/t

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




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 x h

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.

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>.

Rate

of diffu

sion, μS c

m-1

s-1

Surface area, cm2

Rate of diffusion, r/(μS cm-1 s-1) against Surface

area, SA/cm2 of NaCl solution




Apparatus

- Logger Pro

- Conductivity probe

- Sodium chloride solution (NaCl)

- 25.0cm3 pipette (±0.1)cm

3

- Visking tube

- 250.00 cm3 conical flask (±0.15)cm

3

- 100.00 cm3 conical flask (±0.10)cm

3

- 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. Cut approximately 10cm of visking tube.

2. Wet one side of the visking tube and tie a firm knot

3. Wet the other side of the visking tube and open the visking tube.

4. 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 25cm

3 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 cm

3, 20 cm

3, and 25 cm

3 of NaCl solutions.

Figure 2: Diagram for the process of measuring the radius and height of different volumes of NaCl




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 250cm

3 conical flask and a 100cm

3

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 350cm

3 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 cm

3, 20 cm

3, and 25 cm

3 of NaCl solutions.

Figure 3: Diagram for the process of measuring the change of conductivity




Data collection

Table 2: Conductivity measured for every 5 seconds of the triplicate trial of each different NaCl solution volume

Time,

t/s

Conductivity of 5cm3

NaCl solution inside the

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

0 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

5 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

10 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

15 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

20 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

25 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

30 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

35 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

40 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

45 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

50 103.5 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

55 113.0 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

60 119.8 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

65 128.4 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

70 138.6 110.1 128.7 157.6 158.6 192.0 223.8 234.0 241.0 264.6 266.9 357.1 356.1 330.3 411.1

75 143.6 114.4 141.1 170.3 168.1 198.8 233.9 242.6 252.6 282.5 283.2 375.3 372.2 351.1 434.7

80 154.7 122.2 143.9 183.7 175.5 205.2 245.3 251.3 265.7 299.0 299.6 388.3 391.4 367.8 456.4

85 161.5 127.7 148.5 196.4 187.3 219.2 258.4 260.7 280.2 313.7 317.4 407.6 412.0 386.0 476.6

90 170.3 135.1 155.8 211.0 194.6 223.0 270.6 273.5 293.4 326.2 330.6 425.4 428.5 401.2 497.6

Time,

t/s




(±0.1 μS)




(±0.1 μS)




(±0.1 μS)




(±0.1 μS)




(±0.1 μS)




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 – 90s

(a)




Quantitative Data

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

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




Data processing

The following equation is the formula for calculating the surface area of the visking tube:

2 2 + 2 x h

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)

Radius of visking tube, r/cm

(±0.1cm)

Height of NaCl solution, h/cm

(±0.1cm)

5.00 1.0 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)

Calculation of surface area Surface Area of NaCl solution,

SA/cm2

(±0.2cm2)

5.00 2 2 + 2 x 1.1 ≈ 13.1 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




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)

)

12.6

≈ 1.632

1.63 ± 0.1503

22.6

≈ 2.295

2.30 ± 0.1623

32.7

≈ 2.910

2.91 ± 0.2517

42.7 c

≈ 3.352

3.35 ± 0.1188

52.8

≈ 4.322

4.32 ± 0.1662

Table 6: Calculation of average rate of diffusion (b)

s.d - Abbreviated form of Standard Deviation (c)

Data contained an outlier and hence was not put into the calculation of average rate of diffusion




Data Presentation

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

y = 0.0649x + 0.7541

R² = 0.9843

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 10 20 30 40 50 60

Rate

of

Diffu

sion, (μ

S c

m-1

s-1)

Surface Area, (cm2)

Rate of diffusion, r/(μS cm-1 s-1) against Surface Area,

SA/cm2 of NaCl solution

(a)




Uncertainty/ Error Analysis

Table 7: Uncertainty of the measurements of lengths due to the ruler

Surface Area of

NaCl solution,

SA/cm2

% uncertainty in surface area, SA/cm2

ΔSA (%)

Absolute % uncertainty in surface area,

SA/cm2

ΔSA (cm2)

Surface Area, SA/cm2 and uncertainty

ΔSA (cm2)

13.1 19.1 (19.1/100) x 13.1 = 2.5 13.1 ± 2.5

23.2 13.7 (13.7/100) x 23.2 = 3.2 23.2 ± 3.2

33.3 12.3 (12.3/100) x 33.3 = 4.1 33.3 ± 4.1

43.2 11.7 (11.7/100) x 43.2 = 5.1 43.2 ± 5.1

52.7 11.4 (11.4/100) x 52.7 = 6.0 52.7 ± 6.0

Table 8: The absolute uncertainty for each surface area

Surface Area of

NaCl solution,

SA/cm2

% uncertainty for length use

Total % of

Uncertainty

Surface Area with

uncertainty Length of radius

of visking tube,

using a 30cm ruler

(Δr = ± 0.1) cm

% uncertainty of

Length ( % )

Length of height

of NaCl solution,

using a 30cm ruler

(Δ = ± 0.1) cm

% uncertainty of

Length ( % )

13.1 1.0 ± 0.1 (0.1/1.0) x 100

= 10.0%

1.1 ± 0.1 (0.1/1.1) x 100

= 9.1%

10.0% + 9.1%

= 19.1%

13.1 ± 19.1%

23.2 1.0 ± 0.1 (0.1/1.0) x 100

= 10.0%

2.7 ± 0.1 (0.1/2.7) x 100

= 3.7%

10.0% + 3.7%

= 13.7%

23.2 ± 13.7%

33.3 1.0 ± 0.1 (0.1/1.0) x 100

= 10.0%

4.3 ± 0.1 (0.1/4.3) x 100

= 2.3%

10.0% + 2.3%

= 12.3%

33.3 ± 12.3%

43.2 1.0 ± 0.1 (0.1/1.0) x 100

= 10.0%

5.9 ± 0.1 (0.1/5.9) x 100

= 1.7%

10.0% + 1.7%

= 11.7%

43.2 ± 11.7%

52.7 1.0 ± 0.1 (0.1/1.0) x 100

= 10.0%

7.4 ± 0.1 (0.1/7.4) x 100

= 1.4%

10.0% + 1.4%

= 11.4%

52.7 ± 11.4%




Solution

Surface Area, SA/cm2

ΔSA (cm2)

Average rate of diffusion of NaCl solution,r/(μS cm-1

s-1

)

(μS cm-1

s-1

± s.d)

NaCl

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




Conclusion

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 – 5

th 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

to the relative high uncertainty of the 30cm ruler

Can use an apparatus which has a lower

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

made the gradient (the rate of diffusion) less

accurate. Look at Figure 4.

Let the logger pro run before putting in the NaCl

solution. After seeing constant/ straight data

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,

the calculation of the surface area of the visking

tube is not exactly accurate.

Can use a more skinny visking tube (which has a

smaller radius) as it would be easier to put

pressure on it, in order to make a more accurate

cylindrical shape

Effect of surface area to volume ratio on the diffusion on sodium chloride from dialysis tubing

Education

Transcript of Effect of surface area to volume ratio on the diffusion on sodium chloride from dialysis tubing