Dehydration Kinetics of Tincal and Borax by Thermal Analysis

Ahmet Ekmekyapar, Ahmet Baysar,* and Asım Ku1nku1 l

Department of Chemical Engineering, Faculty of Engineering, Inonu University, 44100 Malatya, Turkey

The dehydration reaction kinetics of tincal and borax decahydrate was investigated bythermogravimetry (TG) and differential thermal analysis (DTA). Various methods were usedto analyze the TG and DTA data for determination of reaction kinetics. The activation energy,frequency factor, and order of reaction were calculated for both materials. The results obtainedfrom different methods were generally in good agreement. The results of tincal and borax werealso compatible.

Introduction

Approximately 60% of the known world boron re-serves are found in the western part of Turkey. Boronreserves include various minerals. Of these minerals,tincal, colemanite, and ulexite have very important com-mercial value. Boron and its compounds have a widefield of application in the industry. Particularly, boraxhas found wide areas of use such as borosilicate glasses,glass wool, ceramics, detergents, cement, and fire proofmaterials, etc. (Emir, 1979; Kocakusak et al., 1994).Many investigators have concluded from X-ray data

that borax decahydrate (Na2B4O7‚10H2O), which will becalled borax from this point on in this text, or tincalhas the structural formula of Na2(B4O5(OH)4)‚8H2O(Kocakusak et al., 1994; Waclawska, 1995; Kaynarca,1972). Anhydrous borax is produced by dehydration ofborax hydrates at approximately 600 °C.The dehydration process for borax is an important one

since by dehydration about 45% of the total weight isgiven off as water. Thus, dehydration becomes advan-tageous from the materials relocation point of view. Asa result of dehydration, the transportation costs of thisimportant industrial bulky material may then be re-duced. Moreover, anhydrous borax is a starting rawmaterial for many chemical processes. Lately, anhy-drous borax has been produced directly from tincalinstead of refined borax decahydrate. This material ispreferred over anhydrous borax produced from refinedmaterial with respect to various areas of usage (Sanıgok,1987). Hence, the dehydration reaction of tincal toanhydrous borax has become an important process. Thedesigner of dehydration equipment should have infor-mation about the kinetics of the reaction to effectivelydesign the reaction equipment.The kinetics of decomposition of solid materials using

thermal analysis devices (thermogravimetry (TG), dif-ferential thermal analysis (DTA), differential scanningcalorimetry (DSC)) has been commonly investigatedutilizing various theoretical methods. In such a work,Ozawa (1970) used thermal analysis derivative curvesto calculate kinetic parameters of various polymer ma-terials. Kissinger (1957) developed a method to deter-mine kinetic parameters from DTA data. Using DTAdata, he investigated the decomposition kinetics of mag-nesite, calcite, brucite, kaolinite, and halloysite to deter-mine the kinetic parameters for these materials.Salvador and Calvo (1992) established the differences

between isothermal and nonisothermal regimes for thedecomposition of solids. Considering these differences,they utilized the method of Coats and Redfern (1964)

to determine kinetic parameters of dehydration of zincacetate dihydrate.Using data obtained from thermal decomposition in

DSC, Duswalt (1974) studied thermal decomposition ofabout 10 different materials using the approaches ofMcCarty and Doyle (1962). In a detailed study, Mu andPerlmutter (1981a) investigated thermal decompositionof a large number of carbonates, carboxylates, oxalates,acetates, formates, and hydroxides. The order of reac-tion, activation energy, and frequency factor results formore than 40 materials were tabulated. Mericboyu etal. (1993) studied thermal decomposition of variousTurkish limestones by TG using the Coats and Redfernmethod.Although many studies on the decomposition of tincal

and borax have been reported (Kaynarca, 1972; Ko-cakusak et al., 1995, 1996; Waclawska, 1995), we havenot noticed any work on the kinetics of these materialsby nonisothermal analysis. Thus, the objective of thiswork was to determine the kinetic parameters of thedehydration of tincal and borax using various methodsutilizing TG and DTA data.

Theoretical Basis

Various theoretical methods for kinetic analysis havebeen reported in the literature. The methods used inthe present work are described briefly below. Reactionsof the type solid f solid + gas may be described bythe following equation:

In thermal analysis equipment, the temperature risesat a constant rate according to the T ) To + ât equationduring the reaction. This equation may be substitutedinto eq 1 and integrated. After integration for n * 1the following equation is obtained:

Since 2RT/E , 1, this term may be ignored. Then, eq2 may be rearranged by setting (1/(n - 1))((1 - x)1-n -1) ) f(x) and taking the natural logarithm of both sidesto get

* Author to whom correspondence should be addressed.

dxdt

) ko(1 - x)n exp(-E/RT) (1)

1n - 1( 1

(1 - x)n-1 - 1) )

koRT2

âEexp(-E/RT)(1 - 2RT

E ) (2)

ln(f(x)T 2 ) ) ln(koRâE ) - ERT

(3)

3487Ind. Eng. Chem. Res. 1997, 36, 3487-3490

S0888-5885(97)00018-3 CCC: $14.00 © 1997 American Chemical Society

From the graph of ln[f(x)/T2] vs 1/T using TG datakinetic parameters can be determined. This method ofcalculation is known as the Coats and Redfern method(1964).To utilize DTA data, Kissinger (1957) pointed out that

the reaction rate, dx/dt, gradually increases to a maxi-mum value and then decreases to zero as the reactantis depleted. The maximum reaction rate is reachedwhen d/dt(dx/dt) is zero. Differentiating eq 1 and settingit to zero after rearrangement, the following equationis obtained:

wherem denotes values at the maximum reaction rate.Equation 4 and eq 2 may be combined and rearrangedto obtain the log form of the equation

This equation is derived by Kissinger (1957), and fromthe slope of the plot of ln(â/Tm

2 ) vs 1/Tm the activationenergy of the dehydration reaction can be calculated.The approximation of Doyle (1962) using DTA datarequires a plot of log â vs 1/Tm. The slope of the lineobtained with this procedure gives the activation energyaccording to equation

The frequency factor, ko, may be determined by

The method described by McCarty (Duswalt, 1974)is similar to the approximation of Doyle, but it isexpected to give more accurate results. The activationenergy is given by

where Z ) E/RTm. In this equation, Z contains both Eand T as variables. Thus, the expression must be solvedby a trial and error procedure. The expression is solvedeasily for E by a simple computer program.

Experimental Section

The Borax used for experimental studies was highpurity material (Riedel brand, 99.94%). Tincal concen-trate samples were obtained from Etibank, Kırka Plant,Eskisehir, Turkey. The tincal concentrate was 95.3%pure Na2B4O7‚10H2O. The X-ray diffraction analysispowder patterns of the samples were taken, and theprimary peaks of the tincal concentrate correspondedto those of borax. Hence, the concentrate was mainlyformed from borax crystals.Shimadzu model TG and DTA machines were used

for thermal analysis of tincal and borax samples.Approximately 8-10 mg of samples were loaded for eachanalysis. Thermal gravimetric tests were performed at0.833 mL/s of nitrogen flow and 0.333 K/s constant

heating rate. DTA tests were also performed at 0.833mL/s of nitrogen flow and at 0.083, 0.167, 0.333, and0.500 K/s heating rates.TG curves for tincal and borax are given in Figure 1.

DTA curves for tincal and borax at various heating ratesare also presented in Figures 2 and 3, respectively.Conversions (x) of materials for different temperatureswere determined from the TG curves in Figure 1.Kinetic parameters were calculated from conversion andtemperature data with the help of the method of Coatsand Redfern. DTA curves indicate peak temperaturesfor different heating rates as in Figures 2 and 3. Themethods of Kissinger, McCarty, and Doyle use variousforms of heating rates and peak temperatures.

Figure 1. TG curves for tincal concentrate and borax samples.

Figure 2. DTA curves of a tincal concentrate sample at differentheating rates.

Figure 3. DTA curves of a borax sample at different heatingrates.

âERTm

2) kon(1 - x)m

n-1 exp(-E/RTm) (4)

ln( âTm2 ) ) ln(koRE ) - E

RTm(5)

∆log â∆(1/Tm)

= -0.457ER

(6)

ko ) âERTm

2exp(E/RTm) (7)

E )R(∆ln â/∆(1/Tm))

( 1Z + 3

- 1Z

- 1Z + 1

- 1Z + 4

- 1)(8)

3488 Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997

Results and Discussion

The dehydration of tincal or borax takes place ac-cording to the overall reaction

Both tincal and borax start losing water at approxi-mately 330 K, and weight loss is completed at about875 K.According to the Coats and Redfern method, the left

side of eq 3 must be plotted vs 1/T. Various plots ofln[f(x)/T2] vs 1/T for different values of reaction orders(n) were constructed, but the best fit was observed fora reaction order of 2 by regression analysis. The plotsfor tincal and borax are given in Figure 4. Clearly, thedehydration reaction occurs in two separate steps. Thereaction order for both steps is 2 for both materials.Bearing in mind that the structural formula of borax

and tincal is Na2(B4O5(OH)4)‚8H2O, 2 mol of waterexists as hydroxyl groups associated with four boronatoms and the other 8 mol exists as bound H2Omolecules. As seen in Figure 4, the second step dehy-dration reaction starts at about 415 K. At this temper-ature, the weight loss corresponds to 8 mol of water.The rest of water in the form of hydroxyl groups is lostat higher temperatures. Since hydroxyl groups areincluded in the borate matrix, the removal of this wateris expected to take place with a higher thermal drivingforce. In the literature, the decomposition of many solidmaterials has been reported to take place in steps (Muand Perlmutter, 1981a,b). Khadikar et al. (1993) alsofound that the decomposition of thallium(III) citrateoccurs in three steps. In a structural study, Waclawska(1995) has determined that the decomposition of boraxtoo occurs in steps. For the method of Coats andRedfern, the frequency factors and activation energieswere calculated for each step separately since thereaction takes place in two steps. Using the slopes oflines in Figure 4, the activation energies for tincal andborax were calculated. Similarly, the frequency factorsfor both materials were obtained from the intercept oflines in Figure 4.The method proposed by Kissinger utilizes DTA data.

As indicated by eq 5, the ln(â/Tm2 ) vs 1/Tm graph gives a

straight line. The graphs for tincal and borax are givenin Figure 5. The activation energies were calculatedfrom the slope of the lines, and the frequency factorswere obtained from the intercept of the lines.

The approximation of Doyle uses eq 6 with DTA data.If the logarithm of heating rates is plotted against 1/Tm,the slope will be equal to -0.457E/R. From the slope,activation energy, and eq 7 the frequency factor iscalculated. The approximation of McCarty which issimilar to that of Doyle utilizes eq 8 for the determina-tion of activation energy. The frequency factor iscalculated from eq 7 as in the method of Doyle. Theresults for the dehydration of tincal and borax aresummarized for four different methods in Table 1.The results in Table 1 show a good agreement in

general. Activation energies between 72 and 76 kJ/molfor tincal and 67 and 73 kJ/mol for borax were calcu-lated. It is clear that the results of tincal and boraxare also in good agreement between themselves. Theresults reported in Table 1 (except for the Coats andRedfern method) correspond to the overall dehydrationreaction.The decomposition reactions of solids are generally

reported to be first order in the literature, but manydecomposition reactions are found to be second order(Mu and Perlmutter, 1981a). In the present work, wehave determined that the dehydration of tincal andborax takes place in two steps, with both steps beingsecond order. The sums of activation energies for bothsteps in the Coats and Redfern method approximatelygive values close to the results of the other methodsreported in Table 1.Although the method of Coats and Redfern requires

detailed calculations, the calculations can be carried outonly with the use of a single TG curve. The netadvantage of this method is the determination of thereaction order and steps, simultaneously. The rest ofthe methods (Kissinger, Doyle, and McCarty) used inthis work utilize DTA peak temperatures obtained atvarious heating rates. In deriving the theory of thesemethods, the reaction order does not appear in theequations. Thus, the reaction order cannot be deter-mined by these methods. Kissinger (1957) showed that

Figure 4. Plot for determination of reaction order and activationenergy of tincal concentrate and borax samples by the Coats andRedfern method.

Na2B4O7‚10H2O98heat

Na2B4O7 + 10H2O (9)

Figure 5. Kissinger plot for tincal concentrate and borax samples.

Table 1. Kinetic Parameters for Dehydration of TincalConcentrate and Borax Samples

tincal borax

method E, kJ/mol ko, s-1 E, kJ/mol ko, s-1

Coats andRedfernstep 1 61.10 0.21 × 107 65.86 0.19 × 108step 2 11.55 0.22 6.75 0.04

Kissinger 73.79 0.54 × 109 67.86 0.10 × 109Doyle 75.89 0.11 × 1010 70.16 0.23 × 109McCarty 74.00 0.59 × 109 68.08 0.11 × 109

Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997 3489

the reaction order may be determined from the DTApeaks by calculating a shape index. But the orderdetermined by such an index is rough and approximate.Van Dooren and Muller (1983) also noted that the orderdetermined by the shape index approximately repre-sents the actual reaction order. The methods of DoyleandMcCarty are fundamentally similar. But, Doyle hasmathematically simplified the equation, and its use iseasy. The Kissinger method does not have practicaladvantages over the McCarty method.Based on the results of this work, the dehydration

reaction is proposed to take place according to thefollowing mechanism:

Glossary

E: activation energy, kJ mol-1

x: conversion

ko: frequency factor, s-1

T: absolute temperature, K

â: heating rate, K s-1

n: reaction order

R: universal gas constant, J mol-1 K-1

t: time, s

Literature Cited

Coats, A. W.; Redfern, J. P. Kinetic Parameters from Thermo-gravimetric Data. Nature 1964, 20, 68.

Doyle, C. D. Estimating Isothermal Life from ThermogravimetricData. J. Appl. Polym. Sci. 1962, 6 (24), 639.

Duswalt, A. The Practice of Obtaining Kinetic Data by DifferentialScanning Calorimetry. Thermochim. Acta 1974, 8, 57.

Emir, B. D. Tinkal konsantresinden Borik Asit ve Sodyum SulfatUretimi. Ph.D. Dissertation, Istanbul Technical University,Istanbul, 1979.

Kaynarca, N. Dehydration of Tincal and Borax in Fluidized Bed.M.S. Thesis, METU, Ankara, 1972.

Khadikar, P.; Joshi, A.; Parnerkar, S.; Karmarkar, S.; Karmarkar,S. Thermogravimetric (TG, DTG and DTA) Studies on Thallium-(III) Citrate. Chim. Acta Tur. 1993, 21, 117.

Kissinger, H. E. Reaction Kinetics in Differential Thermal Analy-sis. Anal. Chem. 1957, 29 (11), 1702.

Kocakusak, S.; Ayok, T.; Akcay, K.; Koroglu, H. J.; Ekinci, E.;Tolun, R. Akıskan Yatakta Granul-Susuz Borax Uretimi, I.Ulusal Kimya Muhendisligi Kongresi, METU, Ankara, Septem-ber 1994; Vol. 2, Paper 8.5.

Kocakusak, S.; Koroglu, H. J.; Ekinci, E.; Tolun, R. Production ofAnhydrous Borax Using Microwave Heating. Ind. Eng. Chem.Res. 1995, 34 (3), 881.

Kocakusak, S.; Akcay, K.; Ayok, T.; Koroglu, H. J.; Savascı, O. T.;Tolun, R. Production of Anhydrous Crystalline Borax in Fluid-ized Bed. Ind. Eng. Chem. Res. 1996, 35 (4), 1424.

Mericboyu, A.; Kucukbayrak, S.; Durus, B. Evaluation of theKinetic Parameters for the Thermal Decomposition of NaturalTurkish Limestones from Their Thermogravimetric CurvesUsing A Computer Program. J. Therm. Anal. 1993, 39, 707.

Mu, J.; Perlmutter, D. D. Thermal Decomposition of Carbonates,Carboxylates Oxalates, Acetates, Formates and Hydroxides.Thermochim. Acta 1981a, 49, 207.

Mu, J.; Perlmutter, D. D. Thermal Decomposition of InorganicSulfates and Their Hydrates. Ind. Eng. Chem. Process Des. Dev.1981b, 20, 640.

Ozawa, T. Kinetic Analysis of Derivative Curves in ThermalAnalysis. J. Therm. Anal. 1970, 2, 301.

Salvador, A. R.; Calvo, A. G. Kinetic Analysis of NonisothermalDecomposition of Solids. Dehydration of Zinc Acetate Dihydrate.Int. Chem. Eng. 1992, 32 (4), 726.

Sanıgok, U. Anorganik Endustriyel Kimya, Istanbul UniversitesiYayınları, Sıra No. 3451, Istanbul, 1987.

Van Dooren, A. A.; Muller, B. W. Effects of Experimental Variableson the Determination of Kinetic Parameters with DifferentialScanning Calorimetry. I. Calculation Procedures of Ozawa andKissinger. Thermochim. Acta 1983, 65, 257.

Waclawska, I. Thermal Decomposition of Borax. J. Therm. Anal.1995, 43, 261.

Received for review January 6, 1997Revised manuscript received May 12, 1997

Accepted May 19, 1997X

IE970018R

X Abstract published in Advance ACS Abstracts, July 15,1997.

Na2(B4O5‚(OH)4)‚8H2O98330-415 K

Na2B4O5‚(OH)4 + 8H2O

Na2B4O5‚(OH)498415-875 K

Na2B4O7 + 2H2O (10)

3490 Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997