OBJECTIVE :
To
determine the value of diffusion coefficient, D.
THEORY :
Diffusion,
which is the spontaneous movement of solutes from an area of high concentration
to an area of low concentration can be explained by Fick’s law which states
that the flux of material (amount dm in time dt) across a given plane (area A)
is proportional to the concentration gradient dc/dx.
dc
dm = -
DA dt ----------- (i)
dx
D is the diffusion coefficient or
diffusivity for the solute, in unit m²sֿ¹.
If a solution containing neutral particles with the
concentration Mₒ, is placed within a cylindrical tube next to a water column,
diffusion can be stated as
M = Mo eksp (-x2/
4Dt) ---------- (ii)
where M is the concentration at
distance x from the intersection between water and solution that is measured at
time t.
By changing equation (ii) to its
logarithm form, we get
ln M = ln M0
– x2/ 4Dt
or 2.303 x 4 D ( log10 M0
– log10 M) t = x2 ---------- (iii)
Thus aplot of x² against t can produce a
straight line that passes through the origin with the slope 2.303 x 4D (log 10
M0–log 10
M ). From here, D can be counted.
If the particles in the solution are
assumed to be spherical, their size and molecular weight can be calculated by
the Stokes-Einstein equation.
D = kT/ 6πηa
It is known that molecular weight
M=mN (N is Avogadro’s number 6.02 x 1023 mol-1 ).
∴M = 4/3πa3N ρ ---------- (v)
Diffusion for charged particles,
equation (iii) needs to be modified to include potential gradient effect that
exists between the solution and solvent. However, this can be prevented by
adding a little sodium chloride into the solvent to avoid the formation of this
potential gradient.
Agar gels contain a partially strong
network of molecules that is penetrated by water. The water molecules form a
continuous phase around the gel. Thus, the molecules of solutes can diffuse
freely in the water if chemical interactions and adsorption effects do not
exist entirely. Therefore, the gel forms an appropriate support system to be
used in diffusion studies for molecules in a medium of water.
MATERIALS: APPARATUS:
Agar powder 500
mL beaker
Ringer’s solution 5
mL pipette
1 : 500000 crystal violet solution Glass
rod
1 : 200 crystal violet solution 14
test tubes with covers
1 : 400 crystal violet solution Hot plate
1 : 600 crystal violet solution
1 : 500000 bromothymol blue solution
1
: 200 bromothymol blue solution
1
: 400 bromothymol blue solution
1
: 600 bromothymol blue solution
EXPERIMENTAL PROCEDURES :
1) 7g of agar powder was
weighed and mixed with 420ml of Ringer solution in the 500mL beaker..
2) The mixture in the beaker
was stirred and boiled on a hot plate until a transparent yellowish solution
was obtained.
3) About 20ml of the agar
solution was pour into each 6 test tubes. The test tubes were then put in the
fridge to let them cool.
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.
6) The test tubes were closed
immediately to prevent the vaporization 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 crystal 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 1 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.
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
Crystal
violets at room temperature (28°C)
Crystal
violets in water bath (37°C)
Bromothymol
blue at room temperature (28°C)
Bromothymol
blue in water bath (37°C)
At concentration 1:200
Gradient = 2.303x4D(log10Ma-log10
M)
(14-6)x10-4 =2.437x10-9 = 2.303x4D(log10Ma-log10
M)
(6.2-2.4)(86400)
2.437x10-9 = 2.303x4D[log10(1/200)-log10(1/500
000)]
D = 7.785 x10-11 m2s-1
At concentration 1:400
Gradient = 2.303x4D(log10Ma-log10
M)
(12-6)x10-4 =1.929x10-9 = 2.303x4D(log10Ma-log10
M)
(6.6-3)(86400)
1.929x10-9 = 2.303x4D[log10(1/400)-log10(1/500
000)]
D = 6.762x10-11 m2s-1
At
concentration 1:600
Gradient = 2.303x4D(log10Ma-log10
M)
(5.2-1.2)x10-4 =1.157x10-9 = 2.303x4D(log10Ma-log10
M)
(6-2)(86400)
1.157x10-9 = 2.303x4D[log10(1/600)-log10(1/500
000)]
D = 4.3x10-11 m2s-1
Average
diffusion coefficient: 6.282x10-11 m2s-1
At concentration 1:200
Gradient = 2.303x4D(log10Ma-log10
M)
(25-10)x10-4 =4.34x10-9 = 2.303x4D(log10Ma-log10
M)
(5.8-1.8)(86400)
4.34x10-9 = 2.303x4D[log10(1/200)-log10(1/500
000)]
D = 13.865x10-11 m2s-1
At concentration 1:400
Gradient = 2.303x4D(log10Ma-log10
M)
(12-5)x10-4 =2.7x10-9 = 2.303x4D(log10Ma-log10
M)
(5-2)(86400)
2.7x10-9 = 2.303x4D[log10(1/400)-log10(1/500
000)]
D =9.464 x10-11 m2s-1
At
concentration 1:600
Gradient = 2.303x4D(log10Ma-log10
M)
(10-1)x10-4 =2.604x10-9 = 2.303x4D(log10Ma-log10
M)
(5-1)(86400)
2.604x10-9 = 2.303x4D[log10(1/600)-log10(1/500
000)]
D = 9.678x10-11 m2s-1
Average
diffusion coefficient: 11.002x10-11 m2s-1
At concentration 1:200
Gradient = 2.303x4D(log10Ma-log10
M)
(12-4)x10-4 =2.205x10-9 = 2.303x4D(log10Ma-log10
M)
(5.8-1.6)(86400)
2.205x10-9 = 2.303x4D[log10(1/200)-log10(1/500
000)]
D = 7.044x10-11 m2s-1
At concentration 1:400
Gradient = 2.303x4D(log10Ma-log10
M)
(8-4)x10-4 =1.781x10-9 = 2.303x4D(log10Ma-log10
M)
(4.4-1.8)(86400)
1.781x10-9 = 2.303x4D[log10(1/400)-log10(1/500
000)]
D =6.243 x10-11 m2s-1
At
concentration 1:600
Gradient = 2.303x4D(log10Ma-log10
M)
(7.6-2)x10-4 =1.62x10-9 = 2.303x4D(log10Ma-log10
M)
(6.4-2.4)(86400)
1.62x10-9 = 2.303x4D[log10(1/600)-log10(1/500
000)]
D = 6.021x10-11 m2s-1
Average
diffusion coefficient: 6.436x10-11 m2s-1
At concentration 1:200
Gradient = 2.303x4D(log10Ma-log10
M)
(16-6)x10-4 =2.894x10-9 = 2.303x4D(log10Ma-log10
M)
(5.4-1.4)(86400)
2.894x10-9 = 2.303x4D[log10(1/200)-log10(1/500
000)]
D =9.245 x10-11 m2s-1
At concentration 1:400
Gradient = 2.303x4D(log10Ma-log10
M)
(15-5)x10-4 =2.63x10-9 = 2.303x4D(log10Ma-log10
M)
(6-1.6)(86400)
2.63x10-9 = 2.303x4D[log10(1/400)-log10(1/500
000)]
D =9.219x10-11 m2s-1
At
concentration 1:600
Gradient = 2.303x4D(log10Ma-log10
M)
(11-3)x10-4 =2.205x10-9 = 2.303x4D(log10Ma-log10
M)
(6-1.8)(86400)
2.205x10-9 = 2.303x4D[log10(1/600)-log10(1/500
000)]
D = 8.195x10-11 m2s-1
Average
diffusion coefficient: 8.886x10-11 m2s-1
Discussion
Agar diffusion
refers to the movement of molecules through the matrix that is formed by the
gelling of agar. When performed under controlled conditions, the degree of the
molecule's movement can be related to the concentration of the molecule. Agar
will be the inert medium that we are using to investigate diffusion through.
Agar is extracted from seaweed and after dissolving it in hot water it cools to
form a 'solid' jelly. The agar that will be used will be made alkaline by
adding small amounts of sodium hydroxide
In the experiment, crystal violet
diffuse faster than bromothymol blue solution.
Crystal violet with molecular formula C25N3H30Cl
has molecular weight of 407.979 g mol-1 while bromothymol blue
solution with molecular formula C27H28Br2O5S
has molecular weight of 624.38 g mol−1. Molecular weight is how much mass each
particle has or how heavy it is. The heavier the particle, the slower it is
going to move ii solidified agar solution, assuming energy of the system
remains constant.
For a given concentration gradient, a
molecule's rate of diffusion is inversely proportional to its frictional
coefficient, which depends on both size and shape. Assuming that the particle
has a constant shape, a sphere, then
rate of diffusion is inversely proportional to the radius or diameter of the
diffusing molecule. Assuming particle density doesn’t change, particle mass is
proportional to the cube of particle radius. Graham's law states that the rate
of effusion of a gas is inversely proportional to the square root of its
molecular weight
Rate1
/ Rate2 = square root of (Mass2 / Mass 1)
As the experiment is done in two
different temperature of 28oC water bath and 37oC room
temperature, the higher the temperature gives higher rate of diffusion. As the
temperature increases, the amount of energy available for diffusion is
increased. There would be increase in
molecules' speed (kinetic energy). So the molecules move faster and there will be
more spontaneous spreading of the material which means that diffusion occurs
quicker. Thus the rate of diffusion will be faster as the temperature
increases. From Stokes-Einstein equation:
D
= kT/6пŋa
(D = kT/9 and 9 =6пŋa)
The concentration also varies for
each crystal violet and bromothymol blue solution. For higher concentration of
solution gives higher rate of diffusion. When a substance is diffusing between
two compartments, the greater the concentration difference between the two
compartments, the faster the substance will diffuse (faster rate of diffusion).
diffusion will occur from areas of high concentration to low concentration. Fick's
First Law states that the flux, J, of a component of concentration, C,
across a membrane of unit area, in a predefined plane, is proportional to the
concentration differential across that plane), and is expressed by:
Where J – Flux, D –
diffusion coefficient, δC/δx – concentration gradient
(C is concentration and x is distance of
movement perpendicular to the membrane surface )
Crystal violet diffuse faster than
bromothymol blue solution. The diffusion coefficient value calculated from the
experiment for crystal violet has higher value compared to the value of diffusion coefficient for
bromothymol blue solution.
CONCLUSION
The diffusion coefficient of crystal violet at 28oC
is 6.282x10-11 m2s-1
while at 37oC is 11.002x10-11
m2s-1. diffusion coefficient of bromothymol blue at
28oC is 6.436x10-11
m2s-1 while at
37oC is 8.886x10-11
m2s-1 the factor that influence the ratof diffusion
is concentration, temperature and molecular weight since the surface area, Permeability
is kept constant. diffusion rate is faster in the concentration of diffusing
molecules 1:200> 1:400> 1:600.
REFERENCE
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