Practical
4: Determination of Diffusion
Coefficient
Introduction
Diffusion is defined as a process of mass
transfer of individual molecules of a substance brought about by random
molecular motion and associated with a driving force such as concentration
gradient. Fick’s law states that the flux of material (amount dm in time dt)
across a given plate ( area A) is proportional to the concentration gradient
(dc/dx) , D is the diffusion coefficient or diffusivity for the solute.
Equation ( i ) is known as Fick’s first law.
dm =
-DA(dc/dx)dt Equation
(i)
Although the
diffusion coefficient, D, or diffusivity, as it is often called ,appears to be
proportionality constant, it does not ordinarily remain constant. D is affected
by concentration, temperature, pressure, solvent properties, and the chemical
nature of the diffusant. Therefore, D is referred to more correctly as a
diffusion coefficient rather as a constant. Fick’s second law is an equation
for mass transport that emphasizes the change in concentration with time at a
definite location rather than the mass diffusing across a unit area of barrier
in unit time.
An important
condition in diffusion is that of the steady state. Fick’s first law gives the
flux ( or rate of diffusion through unit area ) in the steady state of flow.
The second law refers in general to a change in concentration of diffusant with
time at any distance, x, in example; a non-steady state of flow).
If a solution which have neutral molecules with
concentration, Mo, put in a slim tube next to a water tube, diffusion can be
stated as
M = M0 eksp (-x²/
4 Dt) Equation (ii)
where M is the concentration at x distance from the
level between water and solution that measured at time t.
By changing equation (II) to
logarithm form, we can obtain
ln M = (ln M0 )(-x²/4Dt)
or 2.303 x 4D (log 10 M0 –log
10 M) t = x²) Equation
(iii)
Thus, one x² versus t graph can
produce a straight line which cross the origin with its gradient 2.303 x 4D
(log 10 M0–log 10 M). From here, D can be
counted.
If the molecules in the solution are
assumed to be a sphere shape, then the size and mass of the molecules can be
counted from Stokes-Einstein equation.
D = kT/6пŋa
Where k
= Boltzmann constant 1.38 x 1023 Jk-1
T = absolute temperature (K)
ŋ
= viscosity of the solvent (Nm-2s)
a = the
radius of the solute
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For the diffusion that involved charged particles, eq 3 needs to be modified by including the potential gradient effects that exist between the solution and solvent. However, the formation of the potential gradient can be overcome by adding in some sodium chloride into the solvent.
Agar gel contains a
semi-solid molecular net that can be interfering by water molecules. The water
molecules will form a continuous phase in the agar gel. By this, the solute
molecules can be diffused freely in the water, if not there will be no chemical
interaction and diffusion occur. Thus, these agar gels provide a suitable
supportive system that can be used in the experiment for diffusion of certain
molecules in a aqueous medium.
Procedures :
1. 7g of agar powder was
weighed and mixed with 420ml of Ringer solution in the 500mL beaker..
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2. The mixture in the
beaker was stirred and boiled on a hot plate until a transparent yellowish
solution was obtained.
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4. An agar test tube which
contained 5ml of 1:500,000 crystal violet was being prepared and it was used as
a standard system to measure the distance of the colour as a result of the
diffusion of crystal violet.
5. After the agar
solutions in the test tubes solidifying, 5ml of each 1:200, 1:400, 1:600
crystal violet solution were pour into each test tubes.
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6. The test tubes were
closed immediately to prevent the vapourization of the solutions.
7. Three test tubes were
put in room temperature,28 ºC while another three were put in 37ºC water bath.
8. The distance between
the agar surface and the end of cystal violet where that area has the same
color as in the indicator was measured accurately.
9. Average of the readings
were obtained, this value is x in meter.
10. The x values were recorded
after 2 hours and at appropriate intervals for 2 weeks.
11. Procedures 3 to 10 were
repeated for Bromothymol Blue solutions.
12. Graph of x² values (in
m²) versus time (in hours) was potted.
13. The diffusion
coefficient , D was determined from the graph gradient for both 28 ºC and 37 ºC
; the molecular mass of crystal violet and bromothymol blue were also determined by using N and V
equation.
Results:
After two weeks :
After two weeks :
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Crystal Violet System
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Bromothymol
Blue System
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Calculations:
From
equation: 2.303 x 4D (log 10 Mo – log 10 M) t = X²
Hence the gradient of
the graph = 2.303 x 4D (log 10 Mo - log 10 M)
1.
Crystal Violet system
with dilution 1:200 (28ºC)
Gradient = 2.868×10-5 cm2/sec
M = 1:500000 Ma = 1:200
= 1 / 500000 =
1 / 200
= 2 x 10-6 =
5 x 10-3
2.303 x 4D (log 10 Mo – log 10 M) = 2.868×10-5 cm2/sec
2.303x4D
[log 10 (5x10-3 )-log 10 (2x10-6 )]
= 2.868×10-5 cm2/sec
D =
9.162×10-7 cm2/sec
2. Crystal
Violet system with dilution 1:400 (28ºC)
Gradient
= 2.409×10-5 cm2/sec
M = 1:500000 Ma = 1:400
= 1 / 500000 = 1 / 400
= 2 x 10-6 = 2.5 x 10-3
2.303 x 4D (log 10 Mo –
log 10 M) = 2.409×10-5 cm2/sec
2.303x4D
[log 10 (2.5x10-3 )-log 10 (2x10-6
)] = 2.409×10-5 cm2/sec
D= 8.444×10-7 cm2/sec
3. Crystal Violet system with dilution 1:600
(28ºC)
Gradient =5.373×10-6
cm2/sec
M = 1:500000 Ma = 1:600
= 1 / 500000 = 1 / 600
= 2 x 10-6 = 1.67 x 10-3
2.303 x 4D (log 10 Mo –
log 10 M) = 5.373×10-6 cm2/sec
2.303x4D
[log 10 (1.67x10-3 )-log 10 (2x10-6
)] = 5.373×10-6 cm2/sec
D =
1.996×10-7 cm2/sec
Average
of Diffusion Coefficient, m²/hour for Crystal Violet system at 28ºC
= (9.162×10-7 cm2/sec
+ 8.444×10-7 cm2/sec +1.996×10-7 cm2/sec)
/ 3
= 6.534×10-7 cm2/sec
4. Crystal
Violet system with dilution 1:200 (37ºC)
Gradient = 3.689×10-5 cm2/sec
M = 1:500000 Ma = 1:200
= 1 / 500000 = 1 / 200
= 2 x 10-6
= 5 x 10-3
2.303 x 4D (log 10 Mo – log 10 M) = 3.689×10-5 cm2/sec
2.303x4D
[log 10 (5x10-3 )-log 10 (2x10-6 )]
= 3.689×10-5 cm2/sec
D =
1.179×10-6 cm2/sec
5. Crystal
Violet system with dilution 1:400 (37ºC)
Gradient =2.582×10-5 cm2/sec
M = 1:500000 Ma = 1:400
= 1 / 500000 = 1 / 400
= 2 x 10-6 = 2.5 x 10-3
2.303 x 4D (log 10 Mo –
log 10 M) = 2.582×10-5 cm2/sec
2.303x4D
[log 10 (2.5x10-3)-log 10 (2x10-6)]
= 2.582×10-5 cm2/sec
D =
9.051×10-7 cm2/sec
6. Crystal Violet system with dilution 1:600 (37ºC)
Gradient =8.264×10-6 cm2/sec
M = 1:500000 Ma = 1:600
= 1 / 500000 = 1 / 600
= 2 x 10-6 = 1.67 x 10-3
2.303 x 4D (log 10 Mo –
log 10 M) = 8.264×10-6 cm2/sec
2.303x4D
[log 10 (1.67x10-3 )-log 10 (2x10-6
)] = 8.264×10-6 cm2/sec
D = 3.070×10-7 cm2/sec
Average
of Diffusion Coefficient, m²/hour for Crystal Violet system at 37ºC
= (1.179×10-6 cm2/sec
+9.051×10-7 cm2/sec +3.070×10-7 cm2/sec)
/ 3
= 7.970×10-7 cm2/sec
7. Bromothymol Blue system with dilution 1:200
(28ºC)
Gradient =3.750×10-5 cm2/sec
M = 1:500000 Ma = 1:200
= 1 / 500000 = 1 / 200
= 2 x 10-6
= 5 x 10-3
2.303 x 4D (log 10 Mo – log 10 M) = 3.750×10-5 cm2/sec
2.303x4D
[log 10 (5x10-3 )-log 10 (2x10-6
)] = 3.750×10-5 cm2/sec
D=1.198×10-6
cm2/sec
8. Bromothymol Blue
system with dilution 1:400 (28ºC)
Gradient =2.642×10-5 cm2/sec
M = 1:500000 Ma = 1:400
= 1 / 500000 = 1 / 400
= 2 x 10-6 = 2.5 x 10-3
2.303 x 4D (log 10 Mo –
log 10 M) = 2.642×10-5 cm2/sec
2.303x4D
[log 10 (2.5x10-3)-log 10 (2x10-6)]
= 2.642×10-5 cm2/sec
D =
9.261×10-7 cm2/sec
9. Bromothymol Blue system with dilution 1:600 (28ºC)
Gradient = 1.872×10-5 cm2/sec
M = 1:500000 Ma = 1:600
= 1 / 500000 = 1 / 600
= 2 x 10-6 = 1.67 x 10-3
2.303 x 4D (log 10 Mo –
log 10 M) = 1.872×10-5 cm2/sec
2.303x4D
[log 10 (1.67x10-3 )-log 10 (2x10-6
)] = 1.872×10-5 cm2/sec
D = 6.955×10-7 cm2/sec
Average of Diffusion Coefficient, m²/hour for
Bromothymol Blue system at 28ºC
=
(1.198×10-6 cm2/sec + 9.261×10-7 cm2/sec
+6.955×10-7 cm2/sec) / 3
=
9.399×10-7 cm2/sec
10. Bromothymol Blue system with dilution 1:200
(37ºC)
Gradient = 3.211×10-5 cm2/sec
M = 1:500000 Ma = 1:200
= 1 / 500000 = 1 / 200
= 2 x 10-6
= 5 x 10-3
2.303 x 4D (log 10 Mo – log 10 M) = 3.211×10-5 cm2/sec
2.303x4D
[log 10 (5x10-3 )-log 10 (2x10-6 )]
= 3.211×10-5 cm2/sec
D =
1.026×10-6 cm2/sec
11. Bromothymol Blue system with dilution 1:400
(37ºC)
Gradient =2.441×10-5 cm2/sec
M = 1:500000 Ma = 1:400
= 1 / 500000 = 1 / 400
= 2 x 10-6 = 2.5 x 10-3
2.303 x 4D (log 10 Mo –
log 10 M) = 2.441×10-5 cm2/sec
2.303x4D
[log 10 (2.5x10-3)-log 10 (2x10-6)]
= 2.441×10-5 cm2/sec
D =
8.556×10-7 cm2/sec
12. Bromothymol Blue system with dilution 1:600
(37ºC)
Gradient =1.560×10-5 cm2/sec
M = 1:500000 Ma = 1:600
= 1 / 500000 = 1 / 600
= 2 x 10-6 = 1.67 x 10-3
2.303 x 4D (log 10 Mo –
log 10 M) = 1.560×10-5 cm2/sec
2.303x4D
[log 10 (1.67x10-3 )-log 10 (2x10-6
)] = 1.560×10-5 cm2/sec
D =
5.796×10-7 cm2/sec
Average of Diffusion Coefficient, m²/hour for
Bromothymol Blue system at 37ºC
=
(1.026×10-6 cm2/sec+8.556×10-7 cm2/sec+5.796×10-7
cm2/sec) / 3
=
8.204×10-7 cm2/sec
Questions:
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3.
Between the crystal violet
and bromothymol blue, which diffuse quicker? Explain if there are any
differences in the diffusion coefficient values.
The
crystal violet will diffuse faster as its molecular size is smaller than
bromothymol blue. From the diffusion coefficient calculated, the D for crystal
violet is bigger than D of bromothymol blue. The higher the diffusion
coefficient, the faster the diffusion rate. Thus, the statement that crystal
violet diffuse faster is proven correct.
Discussion:
Diffusion is a passive process by
which a concentration difference is reduced by a spontaneous flow of matter.
The solute will spontaneously diffuse from a region of high chemical potential
to a region of low chemical potential. This means that it is from a region of
high concentration to a region of low concentration; in which the solvent
molecules move in the reverse direction. This experiment is carried out to determine
the diffusion coefficient of the crystal violet and bromothymol blue. The
controlled variables in this experiment are the size of the particles and also
the temperature. Factors such as viscosity and concentration of agar gel may
affect the rate of diffusion too.
When a graph x² against time t is
plotted, a straight line is obtained with the gradient of 2.303 x 4D (log 10
Mo- log 10 M) . From here D can be calculated. We can know the both
28ºC and 37 ºC system, the rate of diffusion from the result that is 1:200 >
1:400 > 1:600.
M is the system with the dilution
1:500,000. It acts as a standard system during the experiment. When Mo is increased,
(log 10 Mo- log 10
M) will increased. This causes the concentration gradient become larger,
therefore the driving force for the occurrence of diffusion would be larger and
the diffusion process will become faster.
As we can see from the result of
this experiment, the rate of diffusion is faster when the temperature is
higher. This occurs when the test tube is put in the water bath at the
temperature of 37°C. The test tube located in the lab at room temperature 28°C
show a lower rate of diffusion. Such situation can be explained using the
kinetic energy theory. As the temperature increase, the kinetic energy of the
molecule will also increase. This will provide them energy to free from the
intermolecular attractive forces and thus making them easier to escape and
enter the agar. For the test tubes at room temperature, the kinetic energy is
not so strong and this causes the molecules hard to free themselves. Thus, the
rate of diffusion is influence by the temperature.
The second factor that we tested in
this experiment is the molecular size of particles. The molecular weight of crystal violet is
smaller than that of bromothymol blue. Thus, the diffusion rate of the crystal
violet is faster than the bromothymol blue. As the size is smaller, it will be
easier for the molecules to move into the restricted space between agar
molecules. For the bigger size of bromothymol blue molecules, they might get
trapped at the small space and unable to move forward and this gives a lower
diffusion rate.
From the result that we obtained, at
room temperature 28°C, the diffusion coefficient for crystal violet is 6.534 x10-7 cm2/sec and bromothymol blue is 9.399 x10-7cm2/sec
while for the experiment that carried out in the water bath with temperature
37°C, the D for crystal violet and bromothymol blue are 7.97 x10-7cm2/sec
and 8.204 x10-7cm2/sec respectively. The D for crystal
violet supposes to be higher than that of bromothymol blue. This may due to
some errors that occurs during the experiment. The measurement taken be
different people may be a little bit different and this will lead to the
inconsistency of the readings. Besides, the colour of the dyes are not very
obvious and this cause the measuring process become difficult and in accurate.
Other than that the agar gel also
can influence the rate of diffusion. When the concentration of gel substance is
increase, the size of the hole will decrease and the diffusion rate will
decrease too as the hole size same with the size of the diffuse molecule.
Moreover, the viscosity of the solution in the hole also can influence the
diffusion rate. When the crystallinity of the gel medium is increased, the
diffusion rate will decrease. The larger the volume fraction of crystalline
material, the slower the movement of diffusion molecules. This can be happened
because crystalline regions of the gel medium represent an impenetrable barrier
to the movement of solute particles where it have to circumnavigate through it.
Precaution:
1. The
test tubes which contain agar solution should be closed immediately after added
crystal violet solution to avoid vaporization.
2. The
test tubes should be put straight in the test tube rack so that the level of agar
is same in all test tubes to get a more accurate reading.
3. Few
readings of each test tube should be taken to calculate the average readings of
distance moved.
4. Observer
should be the same people when taking the reading for every test tube because
different people will measure different distances.
5. The
level of eyes of observer should be parallel to the ruler or measuring scale to
avoid parallax errors.
Conclusions:
Diffusion coefficient, D for
Crystal Violet system at 28ºC is is 6.534 x10-7 cm2/sec
while at
37ºC is 7.97 x10-7cm2/sec. The diffusion coefficient, D for
Bromothymol Blue system at 28ºC is 9.399 x10-7cm2/sec
while at
37ºC is 8.204 x10-7cm2/sec. The temperature and
concentration of diffusing molecules are the main factors for this experiment. The
rate of diffusion will be higher at higher temperature. The rate of diffusion
of crystal violet also is higher than that of bromothymol blue. In both 28ºC
and 37ºC system, diffusion rate is faster in the concentration of diffusing
molecules 1:200> 1:400> 1:600.
References:
1. A.T.Florence and D.Attwood.Physicochemical Principles of Pharmacy, 3rd
edition, 1998. Macmillan Press LTD.
2. Physical Pharmacy, by Alfred
Martin, 4th Edition.
3.http://chemwiki.ucdavis.edu/Physical_Chemistry/Kinetics/Complex_Reactions/Ionic_Mobility_and_Electrophoresis/Diffusion
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