Measuring Gas Diffusion Coefficient of Acetone with Winkelmanns Method

OBJECTIVES:

Determine the gas diffusion coefficient of acetone using the established Winkelmann’s method

OVERVIEW

The knowledge of physical and chemical properties of certain materials is important because very often process engineering deal with the transformation and distribution of these materials in bulk. One such property is diffusivity. Mass transfer by diffusion takes place when there is a concentration gradient of the diffusing component. Naturally, the diffusion in gas phase is much faster than the diffusion in liquid phase due to the small spaces between the molecules that hinder other molecule movement.

Other factors that will effect the diffusion are temperature, density, concentration and other external factors.

INTRODUCTION

This experiment has been designed for students experiment on the technique of determining diffusivity of the vapor of a volatile liquid based on the established Winkelmann’s method. In this method the volatile liquid is allowed to evaporate in a vertical glass tube over the top of which a stream of vapor-free gas is passed.

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A water bath is provided for maintaining a steady temperature so that there is no eddy current in the vertical tube and mass transfer takes place from the surface by molecular diffusion alone. The rate of evaporation can be followed by the rate of fall of the liquid surface. A traveling microscope is provided for determining, the liquid fall. With the knowledge of the concentration gradient, the diffusivity of the vapor of the volatile liquid can then be calculated.

THEORY

When a concentration gradient exists within a fluid consisting of two or more components, there is a tendency for each constituent to flow in such a direction as to reduce the concentration gradient.

This is called mass transfer. Mass transfer takes place in either a gas phase or a liquid phase or in both simultaneously.

When a liquid is allowed to evaporate in a narrow vertical tube and a steady temperature is maintained, mass transfer takes place from the surface by molecular diffusion alone. This is the technique developed by Winkelmann to determine the diffusivity of the vapor of a volatile liquid. By monitoring the evaporation rate, which is the rate of fall of liquid surface, and with the knowledge of concentration gradient, one may then calculate the diffusivity.

The rate of mass transfer is given by:

where,
D=diffusivity [m2/s]
CA=saturation concentration at interface [kmol/m3]
L=effective distance of mass transfer [m]
CT=total molar concentration [kmol/m3]
CBm=logarithmic mean value of CB [kmol/m3]

Considering the evaporation of the liquid:

where,
L=density of liquid [kg/m3]
M=molecular weight [kg/kmol]

Combining equations 1 and 2 we get,

Integrating and putting L = L0 at t = 0:

Values of L0 or L will not be measured accurately but accurate values of (L – L0) are available.

Thus, rearranging equation 4:

or,

A plot of t/ against will give a slope s:

Diffusivity D can then be calculated from equation 6:

START UP AND SHUT- DOWN PROCEDURES

Start-up Procedure

1. Prior to running an experiment, students are advised to perform the following start-up procedure:
2. Fill the water bath with clean (preferably filtered) water to approximately 30 mm from the top.
3. Plug the mains cable to the electrical supply. Be sure that the voltage of the supply is correct to suit the equipment.
4. Switch on the main power on the control panel.
5. Adjust the set-point value on the temperature controller to 50 °C.

Warning!!Do not set the temperature controller beyond 70 °C.

1. Switch on the heater. Observe the water temperature heats up to 50 °C and remains constant.
2. Switch on the air pump. Adjust the needle valve so that a steady low velocity of air stream is detected at the end of the flexible tubing.
3. The equipment is now ready for student experiment.

Priming Procedure for the Capillary Tube

Before using the capillary tube in an experiment using acetone, students are advised to clean the inside of the tube.

1. Prepare a weak solution of detergent.
2. Use a Hirschmann pipette to fill the tube with the solution. Tapping the outside of the tube may be necessary if the solution is trapped and does not flow down.
3. Turn the tube upside-down and shake. Empty the tube.
4. Repeat steps 2 to 3 with acetone.
5. The tube is now ready for student experiment.

Shut-down Procedure

1. After the completion of an experiment, students are advised to shut down the equipment as follows:
2. Switch off the heater and air pump.
3. Adjust the set-point value of the temperature controller to approximately 5 degree below the room temperature.
4. Allow the water to cool down until it is safe to touch. Open the drain valve and empty the water tank.
5. Detach the flexible tubing and clean the capillary tube for next use. (Refer to priming procedure)
6. Switch off the main power. Unplug the main cable if the equipment will not be used for a long period.

EXPERIMENTAL PROCEDURES

1. Perform the start-up procedure as outlined in section 3.
2. Initially switch off the air pump.
3. Partially fill the capillary tube with acetone to a depth of about 35 mm.
4. Carefully insert the capillary tube through the fitting on top of the water bath cover. Do not over-tighten the fitting.
5. Observe the initial level of acetone through the microscope. Record the level in the table.
6. Connects the flexible tubing from the air pump line to one end of the capillary tube. Switch on the air pump.
7. fter 10 minutes, switch off the air pump. Disconnect the flexible tubing and detach the capillary tube from the fitting. Observe and record the level of the acetone.
8. Repeat steps 5 to 6 at 10 minutes intervals.
9. Record the time, acetone level and liquid fall in the table below.

RESULT

Time,
t
(ks)
Level of
Acetone, L
(mm)
Liquid Fall
(L - L0)
(mm)

t/(L - L0)
(ks/mm)

TUTORIALS

Plot t/ against. Determine gas diffusivity, D from the obtained slope, s. Attached all of your calculation at the appendix in the experiment report. Compare the experimental value with the theoretical value that can be predicted from empirical equations (e.g. modified Maxwell’s equation by Gilliland). Discuss the factors that effect the diffusion of acetone from the graph that have been plotted. Base on objective of the experiment and the theory in gas diffusion makes a conclusion from your finding.

SAFETY AND MAINTENANCE

General Safety Procedure

Always read and understand the manual properly before attempting to operate the equipment. Always wear proper attire during laboratory session. It is highly recommended that eye protection and gloves are used. Be careful when handling hazardous material. Always refer to the material safety data sheet. Avoid inhaling in great amount any hazardous material. Avoid any spillage onto electrical components to prevent electrical shock. Avoid touching hot surfaces (e.g. heater) to prevent skin burn. Always conduct experiment in a properly ventilated room.

General Maintenance Procedure

Do not operate the equipment if any of the components is found to be faulty. Consult the instructor for assistance. Disconnect the equipment from electrical supply when not in use. Drain the water from the water bath.

Clean the water bath thoroughly after use.

Values for Calculation:

1. ρ L = 760.0 kg/m3
2. M = 58.08 kg/kmol
3. Partial pressure P* = 0.8062 atm

where for acetone,
CB1=0.0377 kmol/m3
CB2=0.00731 kmol/m3
CA=0.0304 kmol/m3
CT=0.0377kmol/m3