University of Nizwa

College of Engineering

Department of Chemical and Petrochemical Engineering

Unit Operations Laboratory

Experiment 1: Diffusion

Student Name:

Student ID:

Date of Experiment:

Date of Report Submission:

Student Signature:

Theory

Diffusion is the transport matter from one point to another point by kinetic energy of random molecularmotion. It occurs in gases, liquids and solids. The most common driving force of diffusion is a concentration gradient of diffusing fluid. A concentration gradient tends to move the fluid in such a direction as to equalize concentrations and destroy the gradient. Diffusion also can force by an activity gradient, pressure gradient, temperature gradient or external force field. Diffusion is not restricted to molecular transfer through stagnant layers of solid or fluid. It also takes place when fluids of different composition are mixed.

Fick’s Law of Diffusion

The general equation for one-dimensional and steady-state diffusion, where the concentrations at any point do not change with time is being expressed as follow:

Where,

JA is the average diffusion or molar flux of A across unit area perpendicular to x-direction (mol/cm2.sec)

DAB is volumetric diffusivity or diffusion constant of A with respect to B (cm2/sec)

is concentration gradient of species A in x-direction (mol/cm4)

Generally, diffusivity was found to be dependant on:

• Species characteristics

• Effect of surrounding environment (temperature, pressure and concentration)

• State of the species involved (solid, liquid or gas)

• Other species in the system.

  1. Gas Diffusion Coefficient

Objectives

  • Measurement of mass transfer rates without convective effects
  • Fick’s Law measurement of diffusion coefficients

The rate of mass transfer is expressed as below

Where,

D is the diffusivity for the system, m2/s

CA is the saturation concentration at interface, kmol/m3

L is the effective distance of mass transfer, m

CT is the total molar concentration, kmol/m3

CBM is the logarithmic mean value of CB, kmol/m3

given the evaporation rate is

Where,

ρL is the density of liquid, kg/m3

M is the molecular weight of liquid, kg/kmol

Solve the equation above,

By plotting a graph versus -

The slope, S, of graph is

From Equation above, D can be calculated as: D=

Where,

D is the diffusivity for the system, m2/s

CA is the saturation concentration at interface, mol/m3

L is the effective distance of mass transfer, m

CT is the total molar concentration, mol/m3

CBM is the logarithmic mean value of CB, mol/m3

ρL is density of the test fluid (g/m3)

M is the molecular weight (g/mol)

S is the slope of the graph (t/L+Lo) vs. (L-Lo) (s/m2)

To find CT:

Where

ns = 1 mol

Vs = 0.022415m3

Ts = 273K

T = water bath temperature in Kelvin

P & Ps = 1 atm

To find CA:

Antoine’s equation of methanol is given:

Antoine’s equation of acetone is given:

Where T = Water Bath Temperature (oC)

Given:

Where

p = P (atm) obtained from the Antoine equation

P = atmospheric pressure (atm)

CT = total molar concentration, kmol/m3

To find CBM:

P = P (atm) obtained from the Antoine equation

Substitute all the values into equation below to obtain the diffusivity:

D=

For a binary mixture of low density or ideal gases, the diffusivity is composition dependent. It increases with the temperature and varies inversely with pressure. For this, the kinetic theory shows that:

On the other hand, diffusivity of non-ideal gases is composition dependent.

Equipment and Accessories

  • LS-32136–A Gas Diffusion Coefficient Apparatus
  • Methanol or acetone as test fluid.
  • Small syringe

Setup

LEGEND

A – Control panel

B – Air blower

C – Thermostatic water bath tank

D – Drain Valve

E – T-tube

F – Heater

G – Table Top

H – Vernier Scale

I – Telescope

J – Digital readings

Procedure

1. Pour tap water into the acrylic water bath tank. Fill the water till the water level is 25mm below the top of the tank.

2. Fill the test liquid (Methanol or Acetone) into the glass T-tube using syringe. The level of the test liquid should not exceed the water level.

3. Then measure the initial effective distance of mass transfer and state it as Lo.

4. Switch on the main switch on the panel.

5. Turn on the heater, and let the water to heat up to 60°C.

6. Connect the air tube which connected with the blower to T-tube.

7. Switch on the blower to high air flow.

8. Adjust the telescope until it focusing the test liquid level at the T-tube.

9. Wait till the water reached the set temperature. Tare zero the reading of the digital vernier scale reading.

10. Start the stopwatch, at the same time keep an eye on the liquid level.

11. For every 15 minutes elapsed, read the new test liquid level in the T-tube. Record the value. The reading would be in negative reading, kindly ignore the negative sign.

12. Repeat steps 11 in order to get 5 sets of data.

13. Compute the given table.

14. Plot the graph of t/(L+L0) in x-axis versus L-Lo.

15. By using the equation and correct information, calculate the binary diffusion coefficient for the test liquid.

Gas Diffusion Apparatus T-tube

2. Liquid Diffusion Coefficient

Objectives

Determine the diffusion coefficient of NaCl solution in de-ionized water

Introduction

The Diffusion apparatus uses vertical capillaries 5.0 mm long with a diameter of 1.2 mm, which restricts the diffusion to one dimension. The concentration at the lower ends is assumed constant and the concentration at the top ends is effectively zero during the experiment.


Equipment and Accessories

  • LS-32136-B liquid diffusion apparatus
  • Conductivity probe and meter
  • Magnetic stirrer and magnetic bar
  • Beaker 1000mL, 200mL, 20mL
  • NaCl solution
  • Digital weighing scale

Setup

LEGEND

A = J-Tube holder

B = J-Tube with honeycomb

C = Conductivity probe

D = Conductivity meter

E = Magnetic stirrer

F = Liquid vessel

G = Communication port

Procedure to determine the CM value

1. Prepare the solution for 0.002, 0.003, 0.004, 0.005, 0.006 and 0.007 M of NaCl.

2. By using the conductivity probe and meter, determine the conductivity value for all the different M of NaCl.

3. Record these readings to the table 1 provided.

  1. Plot the graph of conductivity versus concentration of NaCl. The slope of this line is the (CM).

CM is the electrical conductivity change per unit molarity change (dilute solutions) Ω-1 M-1 or Siemens M-1. You need this value in later experiment

5. After you finished the experiment, clean and wash the probe with de-ionised water to remove all traces of salt.

Procedure

  1. Prepare the solution of 0.5M NaCl.
  2. Clamp the higher end of the J-tube to the J-tube holder (A). Be careful when clamping the J tube.Do not over tighten the screw as this may damage the glassware.
  3. Pour NaCl solution to the J-tube until the liquid just reaches the top of the capillaries. Kindly wipe away the excess solution with a soft tissue.
  4. Insert the conductivity probe (C) to the liquid vessel (F). Ensure the cable is connected to the digital conductivity meter (D).
  5. Connect the digital meter to laboratory 240VAC power supply. SwitchON the power supply.
  6. Place the liquid vessel on the magnetic stirrer (E). Place the white magnetic bar into the liquid vessel.
  7. Pour 1000mL of de-ionised water into the liquid vessel (F).
  8. Switch ON the magnetic stirrer. Set the speed to about 200rpm.
  9. Switch ON the conductivity meter. Ensure there is reading shown in the meter.
  10. Place the J-tube holder together with J-tube into the test vessel. Care must be taken in this procedure.No solution should be dropped to the de-ionised water.
  11. Fill the test vessel with small amount of de-ionised water until the capillary tops are submerged approximately 5mm below the surface of the water. (Reminder: Please record the amount of wateradded to the test vessel).
  12. At the same time when the capillary tops are submerged, start the stop watch.For every 2 minutes elapsed, kindly take the conductivity value for a time period of 14 minutes. Record the data in Table 2
  13. Once the experiment done, kindly remove all the glassware and rinse with de-ionised water.
  14. The test liquid can be disposed of in the laboratory sink.
  15. You may run repeat the experiment using different stirring speed, NaCl concentration or another salt such as KCl.
  16. Tabulate the table 2 and plot the graph. Find the slope of dk/dt (from 2 mins to 14 mins)
  17. Calculate the diffusion coefficient for the test solution.

University of Nizwa

College of Engineering

Department of Chemical and Petrochemical Engineering

Unit Operations Laboratory

Experiment 1: Diffusion

Lab Report

Student Name:

Student ID:

Date of Experiment:

Date of Report Submission:

Student Signature:

  1. Gas Diffusion

Data

Initial Effective distance of mass transfer,

Lo = ______mm

Test fluid = ______

Table 1

Time (s) / ∆H (mm)
0
900
1800
2700
3600

Table 2

Time (s) / New Effective Distance of mass Transfer , L(mm) / L+Lo, (mm) / t/(L+Lo), (s/mm) / L-Lo, (mm)
0
900
1800
2700
3600

Useful Information:

Lo = Initial effective distance of mass transfer when t = 0

L, new effective distance of mass transfer = Lo + ΔL

Calculations

Solve for the Diffusivity,

  1. Get the slope s from the graph. Show the graph
  1. Solve for the
  1. Solve for
  1. Solve for Diffusivity

s =

  1. Show the complete calculations

Discussions

  1. Comment on the results of diffusivity of methanol obtained

.

  1. What are the factors affecting gas diffusion

2.Liquid Diffusion

Data

Table 1. Determination of CM value

Concentration (M) / Conductivity Value (μs)

Table 2. Determination of Coefficient of Diffusion of NaCl

Time (s) / Conductivity Value (μs)
0
120
240
360
480
600
720
840

Calculations

  1. Get the slope from the graph. Show the graph
  1. Solve for the diffusion coefficient

Additional Data

x = 0.5 cm

D = 0.12 cm

N = 108

Reminder : change the micro Siemens value to siemens value

Discussions

1)Comment on the results of the coefficient of diffusion of NaCl obtained

2)What are the factors affecting liquid diffusion

3)Compare the rate of diffusion of gas and liquid, why do you expect a faster gas diffusion ?

4)Is a larger value of coefficient of diffusion Dmeans that the molecules or atoms are spread out at a higher or lower rate, why ?

1