J . S o p o u š e k ú l o h a
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9.a-b
1. Matter transport phenomena
Matter transport occurs most commonly by mechanical and convection
movements over long distances or diffusion and migration to smaller distances.
The driving forces of diffusion of molecules, atoms and ions are the gradients of the
chemical potentials that can be approximated at ideal conditions by the concentration
gradients of the transporting components for uncharged particles. The driving force
depends also on external electric field that is important if the migrating component has
electric charge.
Diffusion of uncharged component is described by 1st
and 2nd
Fick's law if behaviour of
component is close to ideal. Important are bound conditions of diffusion. The diffusion
problem can be treated numerical or analytical way from mathematical point of view.
In open systems (e.g., living cells), a stationary diffusion and migration occur frequently.
The constant concentration gradients are stabilised within matter transport thought the
system at stationary state.
1.a. Determination of transference number from rate of interface
motion
In the same electric field, different ions move with different speeds. That results in
special migrating effect. The mixture of two electrolytes, having a common anion
(eg Cl)
and different cations, create an interface with a change in cation concentration.
The interface moves to the cathode. The solution involving a faster cation (eg H+
) is
called the leading electrolyte, the solution with slower cation (eg Cd+2
) is called the
indicator electrolyte. Monitoring of this phenomenon is the basis of today's
electromigration analytical methods,
such as isotachophoresis or capillary
electrophoresis.
The monitoring of the interface
between electrolytes can be done with
a simple experiment (see Figure 1).
The leading electrolyte is a solution of
hydrochloric acid (coloured by crystal
violet). The indicator electrolyte is a
solution of CdCl2 which is formed in
the anode space by electrochemical
oxidation of the cadmium electrode
after application of external voltage.
Crystal violet dissociates weakly,
migrates therefore at a negligible rate,
and its colour is pH-dependent (purple
at neutral pH, blue at acidic pH). The
colour change of the solution
visualizes the interface between the
leading and the indicator electrolyte.
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Figure 1: Scheme of transmission number
measurement in HCl. S…switch.
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9.a-b
The displacement ∆𝑙𝑙 of the interface means that the hydrogen ions have given, within
time interval (𝑡𝑡2 − 𝑡𝑡1) , to the cathode the charge:
+⋅∆=⋅∆⋅=+
H
cVclSq (1.1.)
where 𝑆𝑆 is the interface area and 𝑐𝑐 is the concentration of hydrogen ions.
Contemporary, the chloride ions transferred the charge 𝑞𝑞−
in the opposite direction to
anode. In total, the charge |𝑞𝑞| = |𝑞𝑞+| + |𝑞𝑞−| was transferred. The absolute values of the
charges |𝑞𝑞+|, |𝑞𝑞−| are not equal because in the same electric field the ions H+
and Clmove
by different absolute velocities and in the opposite directions.
The part that the ion contributes to the absolute value of the total transmitted charge is
the so-called transference number. For hydrogen cation in Figure 1:
q
FVc
q
q
t H
⋅∆⋅
==
+
+
+ (1.2.)
where F is Faraday's constant (96 484 C.mol-1
).
The total passed electric charge |𝑞𝑞| can be determined by the integration of the electric
current 𝐼𝐼 flowing over time:
∫ ⋅=
2
1
t
t
dtIq (1.3.)
The upper and lower bounds of the integral are selected according to experiment
conditions (usually two passes through two significant positions on volume-calibrated
tubes). The transference number of hydrogen ions in HCl at 25 °C is t+=0,8209. The
sum of the transference numbers of all moving ions is equal to 1.
TASK: Determine the transference number of hydrogen cation and chloride anion
by the interface motion method in 0.01M HCl. Use the digital ammeter to transfer
data to PC for automatic recording of electric current over time.
LABORATORY AIDS AND CHEMICALS: Glass volume scale tube with water jacket
ending with cadmium electrode, argent chloride electrode, 0.1M KCl for electrode
preservation, syringe (5 cm3
) with polyethylene hose, thermostat (if higher
measurement accuracy is required), DC power supply (300 V), switch and connection
wires, digital ammeter connected to a PC, beaker (50 cm3
), 0.01M HCl coloured with
1.10-4
M crystal violet (CAS No 548-62-9).
The voltage used on the electrodes will be up to 300 V, therefore caution should
be exercised when working with the apparatus under electrical voltage.
INSTRUCTIONS: Suck the solution of 0.01M HCl coloured with crystal violet in the
syringe with a thin hose and push it into volume scale tube (see Figure 1). There
must be no bubble at the bottom near Cd electrode (anode). Insert the argent chloride
electrode (cathode) into the top of the tube. Remove the excess solution with cotton
tampon. Switch the thermostat on and wait for the temperature stabilisation if you want
to achieve higher measurement accuracy.
Check the electrical circuit, familiarize yourself with the operation manual of the
ammeter, turn the computer on, set up the data collection to one times per (3-5)
seconds. Ask the supervisor for supervision and turn on the power supply. After
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9.a-b
stabilizing the instrument, set the power source to =300 V. Turn the switch S on and
start the data collection.
Observe the colour interface and record the time and the current when the interface
passes through the first mark (0 cm3
) on the scale tube (when the interface crosses the
mark, you can turn off and immediately turn on the circuit by switch S). Record the
passes through next marks (0.3, 0.6, 0.9 and 1.2 cm3
) in the same way.
After the measurement, replace the solution in the scale tube with a new HCl solution
and repeat the entire measurement 2 times. Leave the distilled water inside the scale
tube after you finish the work.
Use the trapezoidal method to numerically calculate the integral value in eqn
(1.3.) (for example, apply MS EXCEL). Substitute the limits a, b of the integral by
the times when interface passes through selected volume marks. You can get four
charges |𝑞𝑞| from each experiment (ie 8-12 in total). Perform a statistical evaluation of
the acquired transmission number values.
REPORT: GRAPH 1: One selected record of electric current dependence on time
with volume values near time marks. TABLE 1-3: for each electric current
dependence: marked times 𝑡𝑡𝑖𝑖 and 𝑡𝑡𝑖𝑖+1, currents 𝐼𝐼𝑡𝑡𝑖𝑖
and 𝐼𝐼𝑡𝑡𝑖𝑖+1
, volumes: 𝑉𝑉𝑡𝑡𝑖𝑖
, 𝑉𝑉𝑡𝑡𝑖𝑖+1
and
∆𝑉𝑉 = 𝑉𝑉𝑡𝑡𝑖𝑖+1
− 𝑉𝑉𝑡𝑡𝑖𝑖
, passed electric charge |𝑞𝑞|, transference number of hydrogen cation t+
and chloride anion t-. NEXT: Average of t+ and t- , confidence interval of t+ and t- ,
comparison with tabulated transference numbers.
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