ú l o h a J . S o p o u š e k
/54/
9.a-b
1. Matter transport phenomena
1.a. Determination of diffusion coefficient of ammonia inside
membrane
The mass transport through the membrane occurs when it is permeable to the
substance. An example of selectively permeable membrane may be the cell wall
for the metabolites but also the hydrophobic foil of the ion-selective electrode for
ammonia.
The membrane separates the outer and inner ammonia solution (see FIGURE 1).
Ammonia can be generated in the inner solution by release from NH4Cl solution by the
addition of NaOH. Ammonia diffuses into an outer solution where it can be neutralized
to the 𝑁𝑁𝑁𝑁4
+
salt by acid. If the acid is weak (e.g. boric acid), the pH changes, which can
be observed, for example, by changing the
colour of the acid-base indicator.
The amount of ammonia 𝑑𝑑𝑑𝑑 that passes
through the membrane for time 𝑑𝑑𝑑𝑑 (ie diffusion
flux) is proportional to membrane area 𝑆𝑆 and
concentration gradient 𝑑𝑑𝑐𝑐/𝑑𝑑𝑑𝑑. This is known as
1ST
FICK'S LAW OF DIFFUSION:
( )dxdcSD
dt
dn /⋅⋅−= (1.1.)
where 𝑥𝑥 is the distance coordinate and 𝐷𝐷 is the
diffusion coefficient of the migrating substance.
Diffusion coefficient depends on the material of
the membrane and on the temperature (to a
lesser extent depends on the migrating
substance concentration and pressure). The
negative sign indicate that the substance flow
goes in the direction of decreasing
concentration.
The diffusion of the substance can be nonstationary
or stationary. In the event of the stationary diffusion, the concentration
gradient across the membrane is a constant value that can be obtained as
𝑑𝑑𝑑𝑑
𝑑𝑑𝑑𝑑
=
(𝑐𝑐𝑜𝑜 − 𝑐𝑐𝑖𝑖) 𝑙𝑙⁄ where 𝑐𝑐𝑜𝑜 and 𝑐𝑐𝑖𝑖 are, respectively, the substance concentrations in the outer
and the inner solution at time 𝑡𝑡, 𝑙𝑙 is the thickness of the membrane. The diffusion
boundary conditions are in TABLE I.

FIGURE 1: Experimental scheme: Si, So ...
inner and outer solution. M...membrane,
T...tube. M1, M2...rotary stirring elements.
The meanings of the other symbols are in
the text.
TABLE I: Concentration conditions of stationary diffusion over membrane. β = 𝑉𝑉𝑜𝑜 𝑉𝑉𝑖𝑖⁄ is the ratio
between the volumes of the outer and inner solution. The stationary diffusion occurs immediately.
Time Inner concentration Outer concentration
𝑡𝑡 = 0
𝑡𝑡 > 0
𝑐𝑐𝑖𝑖
𝑡𝑡=0
𝑐𝑐𝑖𝑖
𝑡𝑡=0
− β𝐶𝐶
𝑐𝑐𝑜𝑜
𝑡𝑡=0
= 0
𝑐𝑐𝑜𝑜
𝑡𝑡
= 𝐶𝐶
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/55/
9.a-b
Law of Conservation of Matter applied for the stationary diffusion of the substance from
inner to outer solution yields the difference in concentrations on both sides of the
membrane that is given by an expression 𝐶𝐶 − (𝑐𝑐𝑖𝑖
𝑡𝑡=0
− β 𝐶𝐶) = −𝑐𝑐𝑖𝑖
𝑡𝑡=0
+ 𝐶𝐶(1 + β) which is
valid at any experimental time 𝑡𝑡. The concentration of the substance in the outer
solution 𝐶𝐶 is given by expression 𝐶𝐶 = 𝑛𝑛/𝑉𝑉𝑖𝑖 where 𝑛𝑛 is the amount of substance that has
passed through the membrane. The adjustement provides differential change: 𝑑𝑑𝑑𝑑 =
𝑉𝑉𝑖𝑖 𝑑𝑑𝑑𝑑 . After inserting these relationships into the 1st
Fick’s Law (9.1.) we get:
𝑉𝑉𝑖𝑖 �
𝑑𝑑𝑑𝑑
𝑑𝑑𝑑𝑑
� = −𝐷𝐷𝐷𝐷
−�𝑐𝑐𝑖𝑖
𝑡𝑡=0
−𝐶𝐶(1+β)�
𝑙𝑙
(1.2.)
We separate the variables 𝐶𝐶, 𝑡𝑡 and we choose the upper and lower bounds of the
integrals according to the experimental conditions:
∫
1
�𝑐𝑐𝑖𝑖
𝑡𝑡=0
−𝐶𝐶(1+β)�
𝑑𝑑𝑑𝑑
𝐶𝐶
0
=
𝐷𝐷𝐷𝐷
𝑙𝑙⋅ 𝑉𝑉𝑖𝑖
∫ 𝑑𝑑𝑑𝑑
𝑡𝑡
0
(1.3.)
Integrating this equation provides:
−
1
(1+β)
𝑙𝑙𝑙𝑙 �
�𝑐𝑐𝑖𝑖
𝑡𝑡=0
−𝐶𝐶(1+β)�
𝑐𝑐𝑖𝑖
𝑡𝑡=0 � =
𝐷𝐷𝐷𝐷
𝑙𝑙⋅ 𝑉𝑉𝑖𝑖
⋅𝑡𝑡 (1.4.)
𝐷𝐷 =
𝑙𝑙⋅ 𝑉𝑉𝑖𝑖
𝑆𝑆𝑆𝑆⋅(1+β)
𝑙𝑙𝑙𝑙 �
𝑐𝑐𝑖𝑖
𝑡𝑡=0
𝑐𝑐𝑖𝑖
𝑡𝑡=0
−𝐶𝐶(1+β)
� = 𝐴𝐴⋅𝑙𝑙𝑙𝑙 �
𝑐𝑐𝑖𝑖
𝑡𝑡=0
𝑐𝑐𝑖𝑖
𝑡𝑡=0
−𝐶𝐶(1+β)
� (1.5.)
The equation (1.5.) can be used to calculate the diffusion coefficient 𝐷𝐷 of ammonia by
data analysis from experiment in FIGURE 1.
TASK: Determine the diffusion coefficient of ammonia through the ion selective
membrane (producer: ORION co., dimensions: 𝑆𝑆 = 0.6 𝑐𝑐𝑐𝑐2
, 𝑙𝑙 = 0.032 𝑐𝑐𝑐𝑐).
LABORATORY AIDS AND CHEMICALS: pH-meter with accuracy ±0,001pH,
electromagnetic and mechanical stirrer, tube with ammonium permeable
membrane, stopwatch, 2 beakers (100-150 cm3
), 1 beaker (50 cm3
), 2 volumetric glass
pipettes (25 cm3
, 10 cm3
), burette (10 cm3
), indicator (0.1% bromocresol green (CAS
No: 76-60-8) in ethanol), stock solutions: 2% H3BO3, 0,01M NH4OH, 0,1M NH4Cl and
0.1M NaOH.
INSTRUCTIONS: Get acquainted with the use of the pH-meter with the combined
glass ion selective electrode.
1. CALIBRATION MEASUREMENT. Prepare the base solution of boric acid by mixing
100 cm3
of 2% boric acid stock solution with 1 cm3
stock solution of indicator. Prepare
the base solution of ammonia by mixing 50 cm3
of 0.01mol dm-3
NH4OH with 0.5 cm3
stock solution of indicator. Pour the 50 cm3
of the base solution of boric acid with
indicator into beaker and measure the initial pH. Add the volume 0.5 cm3
of the basic
ammonium hydroxide solution to the measured solution and measure the pH. Repeat
both the addition of the 0.5 cm3
of the basic ammonium hydroxide solution to the
solution and the pH measuring. Make the ten additions in total and perform ten pH
measurements.
2. DIFFUSION COEFFICIENT MEASUREMENT. Use the remaining basic boric acid solution
with the indicator after removing 1ml (ie volume will be exactly 50ml). Put the
magnetic stirrer element into solution. Pipette the volume 7 cm3
of 0.1 M NH4Cl and
1 cm3
of 0.1M NaOH into the tube with membrane. Close the tube using the special
stopper with mechanical stirrer Si (see FIGURE 1). Switch the mechanical stirrer Si on.
Temporarily remove the unit of the electromagnetic stirrer and coat the beaker with
?

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ú l o h a J . S o p o u š e k
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9.a-b
the basic boric acid solution on the tube from the bottom side. Switch the
stopwatches on at this moment. Support the beaker with the basic boric acid solution
by electromagnetic stirrer unit. Switch the stirrings on and choice the low rates. Adapt
the rotary parts if need. Insert the pH sensor carefully into the outer solution and
fasten it to the stand so that the sensor does not come into contact with stirring
element. Measure the pH for 20-30 minutes at 30 sec intervals.
REPORT: The calculated starting ammonia concentration ci
t=0
in the tube.
CALIBRATION TABLE 1: for all additions of ammonia base solution into base solution
of boric acid: total volume of ammonia solution added, total volume, calculated
ammonia concentration 𝐶𝐶 in the solution, measured pH. REVERSE CALIBRATION GRAPH 1:
dependence of ammonia concentration on pH. Make the nonlinear regression using the
polynomial of grade 3 if need. TABLE 2: for all measuring times: pH, ammonia
concentration 𝐶𝐶 according to the calibration curve, values: factor A and argument of
natural logarithm in relation (1.5.), diffusion coefficient. NEXT: statistical analysis of the
experiment for diffusion coefficient D (ie remove the outlying values, consider the trend
of D, calculate the 95% Student`s or Normal confidence interval for D).
