Idea Transcript
METU Chem. Eng. Dept. Ch.E. 320 Chem. Eng. Lab I EXPERIMENT 39 MEASUREMENT OF LIQUID DIFFUSION COEFFICIENT OBJECTIVE To determine the diffusion coefficient of solutions of NaCl, CaCl2, or KCl. PRELIMINARY WORK
Review the theoretical aspects of diffusion in liquids.
Review ionic conductivity under electrical fields in solutions, and methods of measuring electrical conductivity.
Appropriate references are cited at the end of this manual. Experiment place: A Blok Room A-113 OUTLINE OF THE EXPERIMENTAL METHOD When two solutions of different concentrations, originally at equilibrium with their surroundings, are contacted, a concentration gradient is created and mass transfer starts until a new equilibrium. In case of no motion or convection, species move through the interphase by diffusion from high to low concentration regions until new and homogeneous solutions result. The experimental setup has a hook-shaped diffusion cell, the top of which is covered by a honeycomb of numerous small glass capillary pipes. A small volume of a concentrated salt solution is placed in the diffusion cell and the cell is placed in a large volume of pure water in a container. Mass transfer thus initiated causes the salt ions to diffuse in effectively one dimension through the capillaries to the other side (pure water), while naturally water molecules should move in the opposite direction (though negligibly slowly in comparison to salt molecules).
The bulk liquid is agitated without disturbing diffusion at the honeycomb surface and a homogeneous binary mixture is ensured. Increase in concentration of bulk liquid is a result of diffusion, and can be determined as a function of time by an indirect measurement of ionic conductivity. Fick’s law, together with a proper relation between concentration and conductivity can be used to determine D AB, the diffusion coefficient of salt in water.
1/4
METU Chem. Eng. Dept. Ch.E. 320 Chem. Eng. Lab I
Experiment 39 Liquid Diffusion Coefficient
QUESTIONS FOR PREPARATION Answer the following questions to your lab notebook 1. What is the Fick’s first law of diffusion? 2. Why is there a negative sign in Fick’s law? 3. What happens to diffusivity if the concentration of solution decreases? 4. What are ionic conductance and resistance? What is the unit of conductivity? 5. Derive the equation 1 given below starting with the Fick’s law. DAB =
4Vx dk . .10 3 d NMC m dt 2
(Eqn.1)
where (with nominal dimensions), V = Volume of water in outer vessel, L
1.0
x = Length of capillaries, cm
0.45
d = Diameter of capillaries, cm
0.1
N = Number of capillaries
121
M = Molarity of salt solution in diffusion cell, g-mole/L Cm = Change in conductivity per change in molarity (dilute solutions) dk = Rate of change of conductivity with time (slope of the graph) dt
Ω-1.L.mol-1 Ω-1sec-1
Note that, a) The Fick’s law is
J=-DAB.C/x
(Eqn.2)
where, J: Diffusion flux in x direction, mole/cm2.sec C: Concentration, mole/cm3 X: Distance through which diffusion occurs, cm
2/3
METU Chem. Eng. Dept. Ch.E. 320 Chem. Eng. Lab I
Experiment 39 Liquid Diffusion Coefficient
b) The concentration gradient, C/x, can safely be considered as ΔC/Δx and the concentration at lower end of capillaries may be taken constant as the salt concentration, while at the top it may be taken as zero during the experiment due to the large amount bulk liquid in the container, c) Mass transfer rate into the bulk liquid by time is the result of diffusion flux (J=(1/A).dm/dt, where A is the cross sectional area perpendicular to direction of diffusion, and dm/dt is the mass transfer rate into bulk liquid), d) The mass that is transferred can be written in terms of concentration in the bulk liquid, which can in turn be related to change in electrical conductivity in this liquid by time, and e) The electrical conductivity is generally a linear function of concentration for sufficiently dilute solutions.
EXPERIMENTAL SETUP
Diffusion cell
distilled water Vessel
conductivity leads
stirrer bar magnetic stirrer conductivity meter
EXPERIMENTAL PROCEDURE 1. Check that the conductivity electrode is located centrally in the vessel with the holes in the shield aligned vertically. 2. Prepare (if it is not ready) a 1 M solution of a specified salt in water.
3/3
METU Chem. Eng. Dept. Ch.E. 320 Chem. Eng. Lab I
Experiment 39 Liquid Diffusion Coefficient
3. Fill the acrylic vessel with 1 L of distilled or deionized water using the measuring jug supplied. 4. Fill the glass diffusion cell with salt solution using the syringe supplied. Ensure that the glass hook and plastic honeycomb are filled with the solution and no air bubbles trapped. This can be achieved by immersing the hook into a beaker full of salt solution while forcing liquid through the capillaries using the syringe filled with the same solution. 5. Locate the lid (with the glass diffusion cell fitted) on top of the vessel. 6. Steady the lid on top of the vessel and check that the top of the honeycomb of capillaries is flush with the surface of the water. 7. Place the stirrer bar on the bottom of acrylic vessel and locate the vessel on top of the battery-operated stirrer. 8. Connect the conductivity electrode to the socket at the top of the conductivity meter. Set the range switch to 199.9 µS on the meter and switch on by pressing the POWER button. The REC button, if pressed, keeps the meter permanently powered (if REC is not indicated on the display the meter will automatically switch off 10 minutes to save the battery). 9. Switch on the magnetic stirrer and adjust the speed control until the contents of the diffusion vessel is gently agitated without any vortex formation or excessive motion at the surface. 10. Start to record the conductivity immediately after placing the glass diffusion cell into the vessel. Readings should be taken typically at 60 second intervals. The experiment should continue for at least 2000 seconds. CALCULATIONS 1. Prepare a data sheet to record conductivity (S) as a function of time (seconds). 2. You should have graph paper and ruler when coming to the experiment. Now during the experiment, plot a graph of readings of conductivity (S) as a function of time (seconds), and determine the slope of the best-fit straight line (ignore any non-linearity immediately after immersing the cell).
4/3
METU Chem. Eng. Dept. Ch.E. 320 Chem. Eng. Lab I
Experiment 39 Liquid Diffusion Coefficient
3. Determine (if not known) the Cm value, by a separate series of measurements, as the slope of a graph of conductivity versus concentration for very dilute solutions such as 0.001M, 0.002 M, etc. 4. Determine the diffusion coefficient using the equation 1. 5. Compare the experimental result with literature values.
SUGGESTED REFERENCES 1. Incropera, P.F., Dewitt P.D., “Fundamentals of Heat and Mass Transfer”, 5
th
Ed., John Wiley and Sons, USA. 2. Bird, R.B., Stewart, W.E., Lightfoot N.E., “Transport Phenomena”, 2
nd
Ed.,
John Wiley and Sons, New York 3. McCabe, W. L., Smith J. C., and Harriott, P., Unit Operations of Chemical Engineering, 6th ed., McGraw Hill Co., New York 4. Treybal, R. E., Mass Transfer Operations, McGraw Hill Co., New York 5. Barrow, G.M., “Physical Chemistry”, 2nd Ed., McGraw-Hill, New York 6. Skoog, D.A., West, D.M., “Principles of Instrumental Analysis”, Holt, Rinehart and Winston, Inc., New York 7. Skoog, D.A., West, D.M., “Fundamentals of Analytical Chemistry”, 2nd Ed., Holt, Rinehart and Winston, Inc., New York
5/3