Liquid Diffusion

ABSTRACT The objective of liquid diffusion experiment was to determine the diffusivity of sodium chloride solution in distilled water. This experiment was also conducted to determine the conductivity of the solution when sodium chloride solution (NaCl) was diffused into the distilled water. The graph of conductivity against time was plotted to get the rate of diffusion. Liquid diffusion coefficient apparatus was used to determine the conductivity value when the NaCl solution was diffused into distilled water. The diffusion vessel was filled with approximately 1.2 L of distilled water. Next, the conductivity probe BNC connector was connected to the diffusion vessel to determine the conductivity values and the magnetic stirrer was also connected to increase the rate of diffusion. Two concentrations of NaCl were used for this experiment which was 1 M and 4 M. The NaCl solution was added in capillary tube and then was immersed into the distilled water right below the water level surface. Then, the conductivity meter was switched on to calculate the conductivity values of the solution. Based on this experiment, the results showed that at 4 M NaCl solution, the conductivity of the solution was increased by time. The conductivity value was started with 37.3 μs then ended with 95.7 μs in 40 minute. For 1 M NaCl solution, the result was also increased by time. The conductivity was started with the value of 34.9 μs and ended with the value of 54.3 μs. The slope gradient for 4 M NaCl solution was higher than the slope gradient for 1 M NaCl solution, thus the diffusivity value was higher for 4 M NaCl solution which was 3.045 x 10⁻⁸ m²/min while for 1M has value 1.218 x 10⁻⁷ m²/min. The increasing conductivity by time proved that the hypothesis was accepted in which the longer the time, the higher the conductivity. Next, the result for calculation of rate of diffusivity proved that the higher the concentration, the higher the rate of diffusion. Automatically, the diffusivity of the solution was higher with higher concentration of the solution.

TABLE OF CONTENT

ABSTRACT.................................................................................................................................................. 1 TABLE OF CONTENT ................................................................................................................................ 2 1.0

INTRODUCTION ............................................................................................................................ 3

2.0

OBJECTIVES ................................................................................................................................... 3

3.0 THEORY ................................................................................................................................................ 4 4.0 DESCRIPTIONS OF APPARATUS ...................................................................................................... 5 5.0 PROCEDURES....................................................................................................................................... 6 5.1OPERATING PROCEDURE .............................................................................................................. 6 5.2 EXPERIMENTAL PROCEDURE ..................................................................................................... 7 6.0 RESULTS ............................................................................................................................................... 8 6.1 DISCUSSIONS ................................................................................................................................... 9 7.0 SAMPLE CALCULATIONS ............................................................................................................... 11 8.0 CONCLUSIONS................................................................................................................................... 12 10.0

RECOMMEDATIONS ................................................................................................................... 13

11.0 REFERENCES ................................................................................................................................... 13 12.0 APPENDICES .................................................................................................................................... 14

1.0

INTRODUCTION The processes involved in chemical engineering field are divided by two; mass transfer

and heat transfer. Yet problems in this field are often lie in mass transfer field. By mass transfer is meant the tendency of a component in a mixture to travel from a region of high concentration to one of low concentration [1]. By this definition, liquid diffusion is one of the mass transfer processes as a component(s) is diffused from high concentration to low concentration. Diffusion process is usually applied in liquid-liquid extraction, gas absorption, distillation process and others. There are two types of diffusion; equimolar counterdiffusion and diffusion of a component through a stagnant, nondiffusing component. In this experiment, equimolar counterdiffusion is applied in which NaCl solution with two different concentrations is diffused into distilled water. The SOLTEQ Liquid Diffusion Coefficient Apparatus (Model: BP 09) is the apparatus used in this experiment to determine the diffusivity of NaCl in distilled water. This experiment is done twice with two different concentrations of NaCl solution. The NaCl solution is placed in the diffusion cell, which is then immersed right below the distilled water surface. A magnetic stirrer and a conductivity meter are provided to determine the conductivity value. The diffusivity value is not calculated directly from this experiment, yet it will be evaluated based on the conductivity value. A graph of conductivity value against time is used to determine the diffusivity of NaCl in distilled water.

2.0

OBJECTIVES

This experiment is conducted to evaluate the value of diffusivity of sodium chloride. It is done by using two different concentrations of sodium chloride solution to observe the difference in

diffusivity value. The diffusivity value can be calculated using the slope of the graph of conductivity value against time and the formula given.

3.0 THEORY As stated in the introduction before, diffusion process are divided into two types; equimolar counterdiffusion and diffusion of a component through a stagnant, nondiffusing component. Different formulas are used to determine the diffusivity value for both cases. For equimolar counterdiffusion which is conducted in this experiment, the formula used is

where J is the diffusion rate, D is the value of diffusivity and dC/dx is the concentration gradient. The negative sign in the formula indicates that the flow is from high concentration to low concentration. During the experiment, the concentration at the lower ends is taken to be constant and the concentration at the top end is zero. Thus,

in which V is the volume of distilled water in diffusion vessel, M is molar concentration of the solution, C is conductivity change per unit molar concentration change and x, d and N is the

length of capillaries, the diameter of capillaries and the number of capillaries respectively. The value of conductivity change per unit molar concentration, C, is 4.1 x 10⁵ μS.L/mol. Then the slope gained from the graph can be used to evaluate the diffusivity value.

4.0 DESCRIPTIONS OF APPARATUS

Diffusion Cell

Capillaries Conductivity Meter

Diffusion Vessel Conductivity Probe Stirrer Bar Magnetic Stirrer

Diagram 1: Liquid Diffusion Coefficient Apparatus

The SOLTEQ Liquid Diffusion Coefficient Apparatus (Model: BP 09) is used to determine the diffusivity of NaCl solution in distilled water. A known concentration of NaCl solution is placed in a diffusion cell, which is then immersed in distilled water. A magnetic stirrer and a conductivity meter are provided to monitor the progress of the diffusion process over time. A plot of conductivity value against time will allow for the determination of the liquid diffusivity.

5.0 PROCEDURES 5.1OPERATING PROCEDURE General Start-up procedures 1. The diffusion vessel was filled with approximate 1.2 liter of distilled water. The conductivity probe protector was ensured that there was no air trap inside it. 2. The conductivity probe BNC connector was connected into the socket on the conductivity meter. The mini phono jack of temperature sensor was inserted into the socket on the conductivity meter. 3. The magnetic stirrer mains cable was plugged to the electrical supply. The voltage of the supply was ensured that it was correctly suit the equipment. 4. The ON button on the conductivity meter was pressed. 5. The magnetic stirrer was switched on and the speed knob had been set to 500 rpm. 6. The conductivity value was taken. The distilled water gave a very low reading. 7. The equipment was ready for student experiment. General Shut-down Procedure 1. The magnetic stirrer and conductivity meter were switched off.

2. Both the BNC connector and the mini phono jack from the conductivity meter were disconnected. 3. The solution in the diffusion vessel and cell was drained. 4. The diffusion vessel and cell was rinsed.

5.2 EXPERIMENTAL PROCEDURE 1. The start-up procedure was performed. 2. The type of NaCl concentration had been given by the instructor to be used in the experiment. 3. The diffusion cell was filled with the solution prepared in step 2. The capillary tubes were ensured to be in place. The cell was completely filled and excess solution was wiped off to ensure that there was no air trap inside the capillary tube. 4. The cell was carefully immersed into the distilled water and the cell had been positioned until the top of the capillaries was right below the water level. 5. The conductivity meter and the magnetic stirrer were switched on. The stop watch was started. 6. The conductivity reading was recorded after 10 minutes. For every 5 minutes intervals the reading had been taken until 40 minutes. 7. Step 1 to 6 was repeated using different molarity of NaCl solutions.

6.0 RESULTS Volume of water, V

: 1.193 L

Length of capillaries, X

: 5 mm

Diameter of capillaries, d

: 1 mm

Number of capillaries, N

: 97

Time, t (min)

1 M NaCl Solution

4 M NaCl Solution

Conductivity, k (μS)

Conductivity, k (μS)

10

34.9

37.3

15

39.2

46.7

20

42.1

56.0

25

45.4

65.8

30

48.4

75.8

35

51.6

85.8

40

54.3

95.7

Table 1: Conductivity values of 1 M and 4 M of NaCl solutions

Conductivity, k (μS) against Time, t (min) 120

Conductivity, k (μS)

100

y = 1.9514x + 17.371

80 1M NaCl Solution

60

y = 0.6379x + 29.182

4M NaCl Solution Linear (1M NaCl Solution)

40

Linear (4M NaCl Solution)

20 0 0

10

20

30

40

50

Time, t (min)

Diagram 2: Graph of Conductivity, k (μS) against Time, t (min)

6.1 DISCUSSIONS Diffusion is a spontaneous movement of particles from an area of high concentration to an area of low concentration until it reaches its equilibrium [2] as shown in Diagram 2. Diffusion mainly occurs in gaseous state or within gas molecules and liquid molecules. The molecules of gases are in constant motion and collide with other molecules. The movement of particles goes from a high concentration gradient to a low concentration gradient as time passed by. As in this experiment, the diffusion process happened between sodium chloride (NaCl) particles and distilled water particles.

Time

Diagram 3

Firstly, the trend of the graph of conductivity as a function of time for 1 M and 4 M of NaCl solutions were increasing. The trend of the graph showed that the longer the time, the higher the conductivity. The equation for 1 M of NaCl solution was y = 0.6379x + 29.182 and for 4 M of NaCl was y = 1.9514x + 17.371. The diffusivity for 1 M of NaCl solution was 1.218×10-7 m2/min and for 4 M of NaCl was 3.045×10-8 m2/min. From the result of the experiment, based on the equation of conductivity, it was showed that 1 M of NaCl solution has higher diffusivity values which was 1.218×10-7 m2/min compared to 4 M of NaCl solution which was 3.045×10-8 m2/min. But from the theory of Fick’s Law, it is stated that the higher the concentration of solution, the higher the diffusivity. This is because the number of collision increases as the number of molecules increases. When the number of collision increases, the concentration gradient also increases. As the concentration gradient increases, the driving force increases. Thus, the value of diffusivity will increase. That is why when the higher the concentration of NaCl, the higher the diffusivity. When the concentration of NaCl increases, the values of conductivity will increases, thus increasing the values of diffusivity. In addition, conductivity is the ability of a solution to

conduct electricity [3]. It is dependent on the presence of ions in the solution. Ions are derived from ionic compounds that dissolve in water, such as NaCl. That is why when the concentration increases, the number of molecules will increases. As the number of molecules increases, the number of ion presence in the solution will increase, thus the values of conductivity and diffusivity increases. Any errors could be happened during the experiment. Firstly, small bubbles were trapped in the conductivity probe. These bubbles can cause error in getting the conductivity values. If the bubbles are not removed before starting the experiment, then the values of the conductivity will not be accurate. Secondly, the NaCl and the distilled water are not mixed thoroughly or unevenly. This fact is due to the stirrer bar was not spinning fast enough so that the NaCl and distilled water can be mixed well. Next, the NaCl was already being mixed with distilled water before the experiment started. This happened when the capillaries are not properly fitted into the diffusion cell.

7.0 SAMPLE CALCULATIONS

y = 0.6379x + 29.182;

Diffusivity for 1 M Sodium Chloride Solution D=

D = diffusivity (cm2 / s) V = volume of water in diffusion vessel (cm3)

x = length of capillaries (cm) d = diameter of capillaries (cm) N = number of capillaries M = molar concentration of the salt solution (M) CM = conductivity change per unit molar concentration change (dilute solution) (µS / M) dk/dt = rate of change of conductivity with time * CM = 4.1 x 105 µS / M

(

)

8.0 CONCLUSIONS Based on this experiment, the results showed that the conductivity for both concentrations increased by time. The conductivity value for 4 M NaCl was started with 37.3 μS then ended with 95.7 μS at 40 minute while the conductivity for 1 M NaCl was started with value 34.9 μS and ended with value 54.3 μS. So the hypothesis; the longer the time, the higher the conductivity was accepted. Besides, the diffusivity was higher for 4 M which has a value of 3.045 x 10⁻⁸ m²/min while for 1 M has a value of 1.218 x 10⁻⁷ m²/min, so it could be concluded that the higher the concentration of the salt solution, the higher the diffusivity of the solution.

10.0RECOMMEDATIONS 1. Replace the NaCl solution with calcium chloride (CaCl) solution. It is because calcium chloride is more effective than sodium chloride since each molecule produces three ions in solution compared to two for NaCl. So it may speed up the rate of diffusion. 2. Repeat the experiment three times to get the average reading of conductivity for each concentration of sodium chloride. 3. Provide the reading level of water at diffusion vessel to get accurate reading when the distilled water is filled. It helps to speed up the time during set up the liquid diffusion coefficient apparatus. 4. Make sure no bubbles appear at conductivity probe. It is because the bubbles can affect the conductivity reading. 5. Make sure the capillaries are not floating when NaCl is filled in diffusion cell. This method to ensure no air accumulated in it. 6. Perform the experiment in a windy area. It is because the windy condition can speed up the rate of diffusion.

11.0 REFERENCES [1] Bennett, C. O. & Myers, J. E. (1982), Chemical Engineering Series (3rd ed.). New York: McGraw-Hill, Inc., Page 491 [2] diffen (2012). Retrieved July 6, 2013, from http://www.diffen.com/difference/Diffusion_vs_Osmosis [3] eHow (2013). Retrieved July 6, 2013, from

http://www.ehow.com/facts_5942108_effect-solution-concentrationconductivity.html [4] Calcium Chloride (2008). Retrieved July 6, 2013, from http://hyperphysics.phy-astr.gsu.edu/hbase/chemical/saltcom.html

12.0 APPENDICES