Project Final Report Cover Page

PROJECT FINAL REPORT COVER PAGE

GROUP NUMBER: ____R2____

PROJECT TITLE:_PERMEABILITY OF DIALYSIS TUBING TO POTASSIUM CHLORIDE

DATE SUBMITTED: ____5-7-01____

ROLE ASSIGNMENTS

ROLE GROUP MEMBER

FACILITATOR………………………..______Edward Hwu______

TIME & TASK KEEPER………………______Amelia Zellander____

SCRIBE………………………………..______Angela Xavier______

PRESENTER………………………….______Anoop Kowshik_____

PLANNER…………………………….._____Kinnari Chandriani____

SUMMARY OF PROJECT

The average permeability constant of potassium chloride through Fisher Scientific #21-152-18 dialysis tubing is found to be 0.00063 ± 7.63E-05 (95% CI). The precision of the seven trials was 13.1%. Because literature values were unavailable, accuracy had to be determined by another method. Given this method, the accuracy was determined to be 2.54%. However, the seven trials conducted yielded significantly different permeability constants. Statistical differences were concluded from t-tests and non-overlapping 95% CI. Although initial concentration of KCl solution inside the membrane was not expected to affect the permeability constant, the results show the contrary. The unexpected results and the presence of no trends between any trials indicate that a complex mechanism must be affecting the diffusion of KCl through the membrane.

Objective:

The objective of the experiment was to determine the permeability constant of potassium chloride through Fisher Scientific #21-152-18 dialysis tubing within a precision of 5%. An aim of this experiment was to observe the affects of varying initial concentrations (0.5 M, 1.0 M, and 3.0 M) of potassium chloride solutions on the permeability constant. Because the permeability constant describes the filtering capabilities of dialysis tubing, the value obtained would provide valuable information for use in dialysis. The permeability constant is directly related to the time needed for purification of a solution, which can be used in various laboratory and medical applications (such as purification of proteins and hemodialysis).

Background:

Before interpreting the data, several information sources were used. To relate concentration to the equivalent conductance of the solution, the CRC Handbook of Chemistry1 was consulted. The handbook lists several concentrations (M) of KCl and their associated conductances (S-cm2/mol). From the provided data, a relationship between conductance and concentration of KCl was determined.

To convert the measured conductance, Physical Chemistry for the Chemical and Biological Sciences2 was used. It provided the necessary equations required to calculate the equivalent conductance, which was then used to calculate the concentration of the solution. In addition, the book presented basic background of the nature of conductance and physical chemistry of solutions.

The Cole-Parmer Model 19101-10 digital conductivity meter manual3 was also consulted to understand how the machine worked. It provided information regarding the cell constant used in calculations. Lastly, Robert Gagnon’s website4 provided the platform to derive equations to solve the cubic equation in converting conductance to concentration.

The permeability constant of a membrane is a quantitative measure of the diffusion rate across a cell boundary. Because it greatly pertains to biological systems, there has been a great deal of research regarding membrane stretching and a consequent increase in permeability. Research on mitochondrial membranes has concluded that swelling is a major contributor to changes in the structuring of the membrane and its permeability.5 Other research in the past has also indicated that swelling of the polymer due to preparation conditions accounts for changes in the permeability constant.6

Theory and Methods of Calculations:

The permeability constant (kp) is a characteristic of a membrane that is measured with respect to the flux and concentration gradient of the two solutions. Given only a conductivity meter, by using Kohlrausch’s relationship and the definition of equivalent conductance a relationship between conductance and concentration can be constructed.

Kohlrausch’s Relationship Λ = Λo –B√c (1)

(2)

For a solution of KCl, the molar conductance is equal to the equivalent conductance. Using values from the CRC Handbook of Chemistry and combining the above two equations, a cubic equation in terms of concentration is derived. Because Microsoft® Excel cannot solve this equation, a formula is supplied in the appendix to help with the conversion from conductance to concentration.

(3)

Where

Λ = Equivalent conductance

Λo = Equivalent conductance at an infinite dilution

B = a constant dependent on the ion

c = concentration

Λm = Molar conductance

C = Conductance

kcell = Cell Constant

By using the definition of flux and the conservation of mass formula, an equation in terms of concentration can be achieved.

(4)

(5)

Where

Kp = Permeability Constant

A = Surface Area

ci(t) = Concentration of the inside compartment

c0(t) = Concentration of the outside compartment

Vo = volume in outside compartment

Vi = volume in inside compartment

Combining these equations together, and then reducing the equation, kp can be determined.

(7)

(8)

Using equation (8), the concentration of KCl can be calculated at any time during the experiment.

Materials/Apparatus:

1.  Potassium Chloride (KCl) provided by Fisher Scientific

2.  DI Water

3.  Cole-Parmer Model 19101-10 Digital Conductivity Meter

4.  Fisher Scientific #21-152-18 Dialysis Tubing

5.  Spectrum dialysis tubing clamps

6.  Fishing Line and swivel apparatus

7.  Fisher Scientific Mini-Pump Variable Flow

8.  Magnetic stirrer, rod, and mouse pad

9.  Bucket large enough to hold the dialysis tubing apparatus. A 2.0 L container was used.

10.  Mettler H72 electronic balance, Mettler BD6000 electronic balance

11.  10 mL plastic pipette, P-1000 air displacement pipette

12.  Suspension Apparatus:

1. Ring stand
2. Fishing Line

Procedure:

Preparation of Solutions

Three potassium chloride solutions (0.5 M, 1.0 M, 3.0 M) were prepared using solid Fisher Scientific KCl. The largest concern was contamination, especially from skin contact, so gloves were worn and all apparatus and materials were always rinsed with deionized water before use. Large volumes of the potassium chloride solutions were made to reduce the effects of mass transfer loss. In addition, DI water was used to rinse all the KCl from the weighing boat into the flask. 18.6375 g KCl were weighed out for the 0.5 M solution, 37.275 g KCl were weighed out for the 1.0 M solution, and 111.8445 g KCl were weighed out for the 3.0 M solution all on the Mettler H72 balance. The salt was added to a 500 mL volumetric flask and deionized water was added to the mark. The flasks were covered with Parafilm to prevent evaporation of the solution and the solution was allowed to equilibrate to room temperature.

Preparation of Dialysis Tubing and Bucket

The dialysis tubing was cut into approximately 12 cm pieces. The tubing lengths were soaked in DI water and stored in the refrigerator until the morning when they were to be used. For each trial, the inside of the tubing was rinsed with KCl solution of the same concentration to be used for that trial. The tubing was then clamped on one end and 10.0 mL of KCl solution was transferred in using a 10 mL plastic pipette. The tubing was then clamped on the top as close to the solution as possible with minimal loss of solution, where usually one air bubble remained. Fishing line was tied to the top clamp so that its free end could hang from the hook on the ring stand. This allows for the free rotation of the dialysis tubing suspension. The entire tubing setup, which includes the tubing filled with solution, the clamps, and the fishing line were then weighed on the Mettler H72 electronic balance. Finally, the entire setup was rinsed with DI water. The tubing setup was reweighed after the completion of the trial to check for any volume change. In addition, the volume of the KCl solution inside of the tubing at the end of the trial was measured by removing it with a 10mL plastic pipette.

A 2.0 L bucket was placed on the Mettler BD6000 electronic balance and the balance was tared. 1.5 L of DI water was added by mass to the bucket. A stirrer bar was placed at the bottom of the bucket and the entire bucket was placed on the magnetic stirrer with a mouse pad separating the two, serving as insulation from heat. Before the onset of the trials, the DI water in the bucket was allowed to equilibrate to room temperature. Again, the bucket was reweighed after the trial was completed to check for volume change.

Preparation of the Flow Pump, Conductivity Meter and Calibration Curve

The Model 19101-10 Digital Conductivity Meter Operations Manual was consulted for determining the cell constant and calibrating the meter. The meter was always kept in “ATC ON” mode during the trials. A solution of known concentration and conductivity for the same cell constant should be used to calibrate the meter. The supplied wires were used to connect the recorder port on the back of the conductivity meter to the analog-to-digital converter on the board.

The flow pump and conductivity cell were cleaned before each trial by running DI water through the tubing while the pump was on. The electrode was placed in the solution with the flow pump tubing attached to it above. The speed of the flow pump was set to 8.0 on “fast” mode.

Since the CRC handbook data was used in calculations, a calibration curve was produced using our conductivity meter and solutions to make sure it correlated with that of the CRC handbook. Dilutions from the 1.0 M KCl solution as prepared above were made ranging from 0.001 M to 0.01 M in increments of 0.001 M. Dilutions of such low concentrations were prepared because the concentrations in the trials would only reach small values in this range. A P-1000 air displacement pipette and 100 mL volumetric flask were used for the 0.006 M - 0.01 M dilutions, while the same pipette and a 200 mL volumetric flask were used for the 0.001-0.005 M dilutions.

RESULTS:

In order to relate conductance to concentration, seven sample solutions were made to correlate concentration with conductance. The results deviated from the CRC values by 5%. Because of the small error of 5%, the relationship from the CRC values was applied. Figure 1, below, relates concentration with conductance.

Figure 1: Calibrations

Regression Statistics for Figure 1

Coefficients / Standard Error / t Stat / P-value / Lower 95% / Upper 95%
Intercept / 149749.1 / 41.63883 / 3596.38 / 7.73E-08 / 149569.9 / 149928.2
X Variable 1 / -89067.9 / 1032.932 / -86.2282 / 0.000134 / -93512.2 / -84623.5

Because the values of concentrations expected during the experiment were at most 0.003 ± 0.001M, only the CRC values below 0.005M were used. The linear regression for those points is shown above. The slope was found to deviate by 4.9% of the mean, while the y-intercept deviated by 0.1% of the mean.

To calculate the kp values and observe trends, many measurements were taken before and after each trial was conducted. Table 1, below, displays the measurements that were taken for each trial.

Table 1: Initial and Final Measurements.

Results / Molarity / Vout (L)
Initial / Vout (L)
Final / % change of volume
of tank / Vin (L)
Initial / Vin (L)
Final / % change of volume in tubing / Tubing Length Final (cm) / SA (cm2)
Trial 1 / 1.0 / 1.588 / 1.55 / -2.39 / 0.006 / 0.0060 / 0.00 / 5.9 / 29.5
Trial 2 / 0.5 / 1.500 / 1.483 / -1.13 / 0.010 / 0.0110 / 10.00 / 7.4 / 37.0
Trial 3 / 1.0 / 1.500 / 1.449 / -3.40 / 0.010 / 0.0097 / -3.00 / 7.4 / 37.0
Trial 4 / 3.0 / 1.500 / 1.494 / -0.40 / 0.010 / 0.0107 / 7.00 / 7.0 / 35.0
Trial 6 / 3.0 / 1.500 / 1.502 / 0.13 / 0.010 / 0.0118 / 18.00 / 6.9 / 34.5
Trial 7 / 0.5 / 1.500 / 1.493 / -0.47 / 0.010 / 0.0096 / -4.00 / 7.3 / 36.5
Trial 9 / 0.5 / 1.500 / 1.495 / -0.33 / 0.010 / 0.0120 / 20.00 / 8.0 / 40.0

Table 1 shows that there was a decrease in the outside volume over time, with an accompanied increase of internal volume over time. The average percent change for the outside volume is 1.14% and 6.86% for the inside volume. The percent change in volume also differs for each trial, showing that there were no trends, even between trials of similar concentration. Further note should be made that during the course of each trial, less than 3.2% of the total water mass was lost over time. Because the mass loss and change in volume are insignificant, calculations were done assuming that the volume did not change over time.

Using equation 8, a graph was constructed where the slope was defined to be kp. Figure 2 displays the graphs of the permeability constants for all the trials.

Figure 2: Graph for Permeability Constant for the 7 Trials

Figure 2, above, displays the change in the permeability constant over time. The permeability constant (the slope) is linear only within the first hour. After the first hour the permeability constant gradually decreases. After 10 hours, the permeability constant for trial 3 has been reduced by a factor of 80. The chart also shows that the starting points for the trials are clustered by concentration.

Table 2: Permeability Constants

Permeability Constants / Descriptive Statistics for Kp
Molarity / Kp / 95% CI / Mean / 0.00063
Trial 1 / 1.0 / 5.56E-04 / 1.60E-05 / Standard Error / 3.12E-05
Trial 2 / 0.5 / 7.19E-04 / 3.30E-06 / Median / 0.000646
Trial 3 / 1.0 / 5.27E-04 / 3.30E-06 / Standard Deviation / 8.25E-05
Trial 4 / 3.0 / 6.86E-04 / 4.40E-06 / Sample Variance / 6.8E-09
Trial 6 / 3.0 / 7.19E-04 / 1.90E-06 / Range / 0.000192
Trial 7 / 0.5 / 6.46E-04 / 1.60E-06 / Minimum / 0.000527
Trial 9 / 0.5 / 5.56E-04 / 2.30E-06 / Maximum / 0.000719
Confidence Level(95.0%) / 7.63E-05

Table 2, shows the experimental permeability constants for each trial with their 95% CI. The table clearly shows that the 95% CI values do not consistently overlap one another. A precision of 13.1% was calculated for the 7 trials.

Table 3: Y-intercepts

Molarity / Y-intercept* / Y-intercept / 95%CI / % error
(theoretical) / (experimental)
Trial 1 / 1.0 / -5.11600 / -5.2515 / 0.02273 / 2.65
Trial 2 / 0.5 / -5.29832 / -5.4222 / 0.004798 / 2.34
Trial 3 / 1.0 / -4.60517 / -4.7463 / 0.004814 / 3.06
Trial 4 / 3.0 / -3.50656 / -3.5709 / 0.003022 / 1.83
Trial 6 / 3.0 / -3.50656 / -3.5992 / 0.002732 / 2.64
Trial 7 / 0.5 / -5.29832 / -5.4122 / 0.003049 / 2.15
Trial 9 / 0.5 / -5.29832 / -5.4637 / 0.004883 / 3.12
Average / 2.54

*Y-intercept = ln(Vi*Ci(0))