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CuSO4, Cu(ClO4)2 and Cu2P2O7 <strong>of</strong> the same Cu 2+ concentration (0.1 mol.dm –3 ) as a stock<br />
solution for diffusion experiments <strong>of</strong> the same time duration (24 hours). F<strong>in</strong>ally, the solution<br />
pH – dependency and solution ionic strength dependency <strong>of</strong> the diffusion process was<br />
checked by dilut<strong>in</strong>g CuCl2 salt us<strong>in</strong>g the differently concentrated hydrochloric acid and<br />
sodium chloride, respectively. For all <strong>of</strong> these experiments the same Cu 2+ concentration<br />
(0.1 mol.dm –3 ) as well as the time duration (24 hours) was used and the same experimental<br />
technique (see above) was adopted.<br />
RESULTS AND DISCUSSION<br />
The value <strong>of</strong> calculated effective diffusion coefficient <strong>of</strong> copper(II) ions <strong>in</strong> humic gel was<br />
7.96×10 -10 m 2 .s –1 . This value is <strong>in</strong> good agreement with the one pre–determ<strong>in</strong>ed by another<br />
experimental method (see [3]) and was used for all follow<strong>in</strong>g calculations. As can be seen on<br />
Fig. 3 and Fig. 4, total diffusion flux <strong>of</strong> Cu 2+ through solution–gel phase <strong>in</strong>terface l<strong>in</strong>early<br />
<strong>in</strong>creases with the <strong>in</strong>itial concentration <strong>of</strong> copper(II) <strong>in</strong> solution and with the square root <strong>of</strong><br />
time duration <strong>of</strong> diffusion experiment. The later dependency is however much more<br />
complicated; the nonzero <strong>in</strong>tercept <strong>of</strong> the regression l<strong>in</strong>e <strong>in</strong>dicates that the l<strong>in</strong>earity is just<br />
illusory and <strong>in</strong> fact the dependency is curved. Klučáková et al. <strong>in</strong> [5] stated the equation for<br />
the total diffusion flux across the solution–gel <strong>in</strong>terface:<br />
ε c D τ<br />
0<br />
g<br />
m = (1)<br />
1+<br />
ε D / π<br />
g D<br />
<strong>in</strong> which m stands for the total diffusion flux, c0 is <strong>in</strong>itial concentration <strong>of</strong> the ion <strong>in</strong> solution,<br />
τ is the time duration <strong>of</strong> the diffusion, ε is ratio <strong>of</strong> ion concentration <strong>in</strong> the gel and <strong>in</strong> the<br />
solution <strong>in</strong> f<strong>in</strong>al equilibrium (at the “end <strong>of</strong> diffusion”), Dg and D is diffusion coefficient <strong>of</strong><br />
cupric ions <strong>in</strong> humic gel and <strong>in</strong> solution, respectively. Follow<strong>in</strong>g this equation the value <strong>of</strong> ε<br />
was calculated from total diffusion flux correspond<strong>in</strong>g to c0 and τ values. It was found that for<br />
the same duration <strong>of</strong> diffusion experiment this value is constant for different <strong>in</strong>itial<br />
concentrations <strong>of</strong> the solution but it varies for different duration <strong>of</strong> experiment (Fig. 5). This<br />
fact could be expla<strong>in</strong>ed by the apparatus construction (small solution volumes – gel weight<br />
ratio) or by the time–consum<strong>in</strong>g formation <strong>of</strong> some stable structural or chemical complexes<br />
between gel and ions. This affects the mobility <strong>of</strong> ions (retention <strong>of</strong> ions can lead up to their<br />
immobilization <strong>in</strong> gel) and their equilibrium <strong>in</strong> gel and solution. This fact could expla<strong>in</strong><br />
mentioned deformation <strong>of</strong> total flux time dependency as well.<br />
The knowledge <strong>of</strong> the ε value allows<br />
the calculation <strong>of</strong> theoretical<br />
y = 6.454E-03x<br />
concentration pr<strong>of</strong>iles <strong>of</strong> the copper (II)<br />
R<br />
ions <strong>in</strong> the humic gel (used<br />
mathematical apparatus is presented <strong>in</strong><br />
detail <strong>in</strong> reference [5]) for <strong>in</strong>dividual<br />
experiment conditions (<strong>in</strong>itial<br />
concentration, time duration). The<br />
example on Fig. 6 shows very good<br />
agreement between calculated and<br />
measured concentration pr<strong>of</strong>iles.<br />
2 50<br />
40<br />
= 1.000E+00<br />
30<br />
20<br />
10<br />
0<br />
0 2000 4000 6000 8000<br />
total flux [mol.m -2 ]<br />
c0 [mol.m -3 ]<br />
Fig. 3 The total diffusion flux dependency on<br />
the <strong>in</strong>itial concentration <strong>of</strong> Cu 2+ <strong>in</strong> the<br />
solution (diffusion duration 24 hours)<br />
Sborník soutěže Studentské tvůrčí č<strong>in</strong>nosti Student 2006 a doktorské soutěže O cenu děkana 2005 a 2006<br />
Sekce DSP 2006, strana 225