Verification of the Schulze-Hardy Rule A Colloid Chemistry Experiment Waldemar Nowicki and Graiyna Nowicka
A.Mickiewicz University, Faculty of Chemistry, Department of Physical Chemistry, Poznan, Poland In our previous article ( I ) we describe,I a laboratory experiment on the kinetics of colloidal suspension coagulation induced by an indifferent electrolyte. The determination procedure of the critical coagulation concentration cCst of the electrolyte was given, and an extension of the experiment to the verification of the Schulze-Hardy rule was also proposed. However, the time required to complete the extended version of the experiment exceeds the standard laboratory period (4-5 h). In the present paper we describe a simple and inexpensive experiment for verifying the Schnlze-Hardy rule in one laboratory period. The Destabilizing Power of the Electrolyte
According to the Schulze-Hardy rule, known since about 1880, the destabilizing power of the electrolyte is principally due t o the valence of its ion that has charge opposite to the colloidal particle surface (counter ion), whereas the nature and valence of its ionic species with the same sign (co-ions) have relatively little effect. For this reason trivalent salts of aluminum and iron are the most widely used inorwnic coaeulants in water clarification and wastewater katment; The efficiencies of various electrolvtes in destabilizine a given hydrophobic sol are expressed"in terms of c&, whFch is the minimum concentration of a particular electrolyte required to produce rapid coagulation. The dependence between the counter ion valence and c&, can be derived from the DLVO theory. The text by Hiemenz (2)is recommended to students as an introduction to DLVO theory, by which we write the following relation. c,,
where Kis a constant characteristic of the colloidal system examined and denendent on the incident light waveleneth: v, is the original number of particles in thLsystem; t is'ihi time of coagulation; and 1 is the sample thickness that the light traverses. Equation 4 can be approximately applied to colored colloidal systems. Equation 4 also permits the determination of the stability ratio from the apparent absorbance data. Assume that Am,,A, andAmi,are the apparent absorbances, measured aRertime t, of rapidly coagulating, slowly coagulating, and stable sol. Using eq 4, one can write A, = K(1+k,v,t)l (5)
A,,
= K1
(6) because for rapid coagulationprocesses, W = 1,whereas for the stable sol, W + =-. If the initial concentration of primary particles in all three samplesis the same, the stability ratio canbe related to the measured absorbances by
constant
=-
2
where z is the valence of the counter ion. For z = 1, 2, and 3, the centvalues fulfill the following ratio.
indicating an extremely strong effect of counter ion valence on the destabilizing action of the electrolyte. In general, cCmis experimentally evaluated from the dependence of the coagulation rate on the concentration of a given electrolytecE. The ratio between the rate constant of rapid coagulation k, and the slow coagulation rate constant k, is defmed as the stability ratio W. k
w =-
k,
(3)
As follows from the DLVO theory, log W is linearly dependent on log CE in the slow coagulation domain, that is, for c~ < c-,. Extrapolation of experimental data to log W = 0 allows one to determine the cent value. Absorption Measurements for Observing the Coagulation One of the most suitable methods for observing the coagulation process is the light scattering technique because 624
the experimental turbidities can be interpreted in terms of the number and size of scattering centers. For low varticle concentrations, absorption meas&ments can be applied. Bv combining the Smoluchowski's and Ravleiph's theorieione can reiate the apparent absorbance oi'thecolloldal system ( A , to the stah~l~ty ratlo {IVI (see also rrf 1 , as follows.
Journal of Chemical Education
Experimental
A gold hydrosol stabilized by citrate ions (3)is proposed as the colloidal system to be studied. (The color of the gold hydrosol changes with the extent of coagulation. Thoroughly coagulated hydrosol is dark blue.) Hence electrolytes with cations varying in valence but with the same anion are used as coagulators. After time t from the initiation of coagulation with the electrolyte, the process is stopped by the introduction of a protective colloid (e.g., gelatin). Next, the apparent absorbance~are measured, and stability ratios are calculated. The cdt value for a given electrolyte is found from the plot of log W versus log c ~(The . application of gold hydrosol does not make the experiment expensive because the sol concentration is very low.) Preparation of Gold Hydrosol To a 400-mL Erlenmeyer flask containing 200 mL of boiling, distilled water, add 3.0 mL of 0.60%wlv trivalent gold chloride solution. When the solution boils again, add 10 mL of a 1%wlv sodium citrate solution with s t i n g . The solution changes color initially (after about 1 min) to blue and finally (afier about 5 min) to a deep wine red. (Abluish
fmal sol suggests an insufficient purity of the glass or the chemicals used.) The above procedure is applied twice, and the two sol samples obtained are combined and cooled to room temperature (From experience, we recommend small sol portions). Finally, 20 mL of 0.10 M nitric acid are added slowly, under continuous stirring, to the obtained 400 mL of gold hydrosol in order to reduce the stabilizing effect of the citrate ions. Preparation of Gelatin Solution
Add 0.10 g ofgelatin powder with stirringto about 50 mL of distilled water in a beaker. Then leave it to swell for about half an hour. ARenvards. the beaker and its contents are carefully heated in a water bath (about 40 "C) and stirred until the eelatin comoletelv dissolves. ARer cooline. the solution is cansferred to a ~OO-mI. volumetric fla& and water is added to the mark. Determination of ccrit for Electrolyte with Monovalent Cation A series of about 20 electrolyte solutions (e.g., potassium nitrate) is ~reoared.Each has a 5-mL volume. and the concentrations v&y linearly between 0.000 and'0.100 M. We recommend using an automatic pipet in preparing the solution series. At regular intervals (e.g., 15 s) 5 mL of gold hydrosol are introduced to each electrolyte solution, and the contents are thoroughly mixed. About 5 min after the sol is brought into contact with the electrolyte solution, s t o the ~ coaeulation bv introducine 1mL of eelatin solution. The contact time of sol and eledrolyte berore addition of gelatin ( t )must be exactly the same in all samples. Acomparative sample of a noncoagulating system is preoared as follows. Mix 5 mL of water with 5 mL of eold hv&sol, and then introduce 1mL of gelatin solutioi.
Absorbances of eold hvdrosol samoles coamlated to a different extent are measured using'any sigple spectroohotometer (e.e.. S~ekol-CarlZeiss) at 660 nm in a l-cm ilmgth, cuvet~.'(6hoiceof the analytical wavelength follows from Fieure 1 . ) Thp absorbance of the comoarative sample, containing stable, noncoagulating sol is also measured, and it is assumed to be A,. Next, absorbances of approximately the same value (determined at the highest salt concentrations) are separated from among all other values. Their mean value is then calabove c,"~the coaguculated. It is accepted asA,,because lation rate does not depend on the electrolyte concentration. Consequently, the remaining absorbances, that is, A < Amin,are assumed to be measured as for systems in which only slow coagulation took place. For each A value the stability ratio W is calculated from eq 7. Then the obtained results are represented in the log W versus log CE coordinate system. The precision of log W determination depends strongly on the A - Amh result (eq 7); it is lowest for the lowest electrolyte concentration. Therefore, the experimental points in this region that considerably deviate from the straight line in the log W versus log CE plot should be eliminated. The c,"~ is then found from the dependence of log W versus log CE. A point at which the line intersects the x axis correspondsto log ( c ~ JThus, . cCdtis found from
where a and b denote the slope and the intercept of the straight line. For the determination of linear function parameters we recommend using the least-squares method. Determination of ccr,t Values for Electrolytes Contaming Polyvalent Counter Ions
Magnesium or calcium nitrate and aluminum or lanthanum nitrate are recommended as electrolytes with divalent and trivalent counter ions. The c,"~values for Mg(N03)~or Ca(N03)~and A1(NO3I3or La(NO3I3 are roughly estimated from eq 2 using the cCmpreviously determined for KNOB.Next the concentration ranges in which the solutions series must be prepared are established for each electrolyte. The highest electrolyte concentration of the series should be twice that of the rouehly estimated c,, and the series should comprise 15-20 sol;tions of progressively lower concentrations. Further, the rest of the procedure is the same as that described above for the determination of cmt for KN03. The proportion of the cCdtvalues obtained for electrolytes with mono-, di-, and trivalent counter ions is calculated and cornoared to that eiven bv ea 2. Fieure 2 shows de~~pendenciks between log W a n i log CE dGermined for the eold hvdrosol coarmlated with the electrolvtes tabulated gelow kith their &responding cCd valueLobtained by a student in our laboratory. ~
-
0
420
470
520
570
620
670
720
Wavelength [nm] Figure 1. Absorbance-wavelength dependence for noncoagulated (solid line) and coagulated (dashed line) citrate gold hydrosol.
~
Thus, their ratio is 100:1.3:0.07
which well satisfies eq 2. The experiment described above can be, of course, restricted to the determination of cCdtfor a given electrolyte. Then the addition of HN03 to gold hydrosol is not needed, Volume 71 Number 7 July 1994
625
Figure 2. The dependencies between log Wand log q oMained for electrolytes with mono-, di-, and trivalent counter ions and for acidified gold hydrosoi.
Figure 3. Log Wversus log q dependencies obtained forelectrolytes with mono- and divalent counter ions and forgold hydrosol (nonacidified)stabilized by citrate ions.
and this makes the experiment even easier to carry out. Unfortunately, c&t determined for electrolytes with trivalent counter ions and HNOs-kee gold hydrosol strongly deviates from the value calculated kom eq 1on the basis of c&t obtained for electrolytes with mono- and divalent counter ions. Experimentally found values of c&t for A1(NO3I3and La(NO& are only about twice as small as the ones determined for nitrates with divalent counter ions.
The dependence of log Won log CE obtained with nonacidified citrate gold hydrosol for KN03, Mg(NO&, and Ca(N03h is shown in Figure 3. The corresponding cet values are 46,0236, and 0.85 mM.
626
Journal of Chemical Education
Literature Cited 1. Naari&, W.;Noaricka,G.J. C k m . Edue. 1891,68,523625.
2. Hiwenz. P.C. P6ncipks of Cdldd and Surfan Clremrstry;Manel Dekker: ~ Ymkand B a d , 1986. 3. Turkwich, J.: Stevenmn,P.C.:HiUer, J.DiscussFomdoySae. lW1,11,55-75.
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