Prediction of water activity of glucose and calcium chloride solutions

Size: px

Start display at page:

Download "Prediction of water activity of glucose and calcium chloride solutions"

Jeffery Newman
5 years ago
Views:

1 Journal of Food Engineering 57 (2003) Prediction of water activity of glucose and calcium chloride solutions A. Viet Bui a, H. Minh Nguyen a, *, Muller Joachim b a Center for Advanced Food Research, University of Western Sydney, Bld M8 Hawkesbury Campus, Lockbag 1797, Penrith South DC, NSW 1797, Australia b USFilter Memcor Research Pty, Ltd, South Windsor, NSW 2756, Australia Received 31 October 2001; accepted 15 June 2002 Abstract The water activity (a w ) of glucose and calcium chloride solutions in the intermediate concentration range and at temperatures between 20 and 35 C was determined. It was found that the a w measured at 25 C was in accordance with previous studies and fitted the NorrishÕs model well. However, temperature was found to have a more pronounced effect on a w of solutions at higher concentrations. A polynomial equation for h E =R was developed to correlate the effect of temperature on a w for various concentrations of the two solutions as follows: h E =R ¼ 446:52C 3 þ 349:34C 2 120:92C for glucose, and h E =R ¼ 9561:7C 3 þ 2853:8C 2 422:4C for calcium chloride solution. Ó 2002 Elsevier Science Ltd. All rights reserved. Keywords: Water activity; Temperature effect; Glucose; Calcium chloride 1. Introduction The development of osmotic distillation has been of increasing interest to many researchers and food processors. The process has been reported as applicable to the fruit juice and pharmaceutical industry in regard to the concentration of aqueous solutions (Hogan, Canning, Peterson, Johnson, & Michaels, 1998; Johnson, Valks, & Lefebvre, 1989). The process involves the use of electrolyte solutions which have low a w such as NaCl, CaCl 2, MgCl 2, etc. (hence low water vapour pressure) as the stripping solutions to concentrate an aqueous solution with higher a w such as fruit juice (higher water vapour pressure). Therefore, the prediction of the water activity of the solutions involved in the process is important for modelling and controlling the osmotic distillation process. While fructose is the main sugar in many fruit juices, glucose was chosen in our study because glucoseõs a w lowering behaviour is very similar to that of fructose and other sugars such as mannose and galactose (Chirife, Favetto, & Fontan, 1982; Leiras, Alzamora, & * Corresponding author. Fax: address: m.nguyen@uws.edu.au (H.M. Nguyen). Chirife, 1990). Moreover, glucose is more industrially important with wider applications. Data of water activity at 25 C of glucose in relation to its solute content has been well documented in literature (Chirife et al., 1982). This is also true in the case of CaCl 2 (Robison & Stokes, 1959). However, the effect of temperature on water activity of these two solutions has not yet been fully studied. Therefore, a study of the a w of glucose and CaCl 2 solutions in relation to temperature and solute content would be useful and beneficial for controlling and modelling the osmotic distillation process as well as other osmotic processes. 2. Theory As pointed out by Prausnitz, Lichtenthaber, and Azevedo (1986), water activity can be defined as a w ðt ; P; xþ ¼c w ðt ; P; xþx w ¼ f wðt ; P; xþ fw 0ðT ð1þ 0 ; P 0 ; x 0 Þ where x w is the mole fraction of water; c w activity coefficient of water; f w fugacity of water in the system at the current condition; T, P, x temperature, pressure and mole fraction of solute of the system; and the superscript ( 0 ) refers to the reference condition /02/$ - see front matter Ó 2002 Elsevier Science Ltd. All rights reserved. PII: S (02)

2 244 A.V. Bui et al. / Journal of Food Engineering 57 (2003) Assuming the ideality of the behaviour of gaseous water at ambient temperature and atmospheric pressure, one can take the ratio of the fugacities as equal to the ratio of partial pressures of water. Hence, the a w of a system can be defined as a w ¼ p w ¼ RH ð2þ pw where p w and pw 0 are the vapour pressures of water in the system and of pure water at the same temperature; RH is the equilibrium relative humidity of the air layer just above the system. Several theoretical and empirical models have been developed to predict a w of electrolyte and non-electrolyte solutions as reviewed by Sereno, Hubinger, Comesan~a, and Correa (2001). Details of the models are described by individual authors, but some of them are summarised by Bell and Labuza (2000). Most of the late models are complicated and requiring other data inputs. Among them, the Norrish model, while simple, is the most suitable for the determination of water activity of solutions in the intermediate moisture range (Bell & Labuza, 2000; Chirife et al., 1982; Leiras et al., 1990). In our study, the Norrish equation has been employed to describe the effect of solute content on a w of a solution. For a multi-component solution, the water activity can be determined by lnða w Þ¼lnðX w ÞþðK 0:5 i X i þ K 0:5 iþ1 X iþ1 þþ 2 ð3þ where K i are constants (i ¼ 2 n); X w is the mole fraction of water; and X i is the mole fraction of solute (i) in the solution. For a single solute solution as in the case of our study, Eq. (3) can be written as follows: lnða w Þ¼lnðX w ÞþK 2 X 2 2 or ln a w X w ¼ K 2 X 2 2 ð4þ ð5þ Hence, a plot of lnða w =X w Þ versus the square of (X 2 ) will be a straight line with the slope K 2. It is true for nonelectrolyte solutions over the whole range of concentrations (Chirife et al., 1982). However, it is worth noting that K 2 values for electrolyte solutions are constant over a specific range of concentrations, but it may vary when the solution concentration switches from one range to another (Bell & Labuza, 2000). An intercept, therefore, should be included in the equation when the solute content range starts from a point other than zero. Hence Eq. (5) can be modified as follows: a w ln ¼ K 2 X 2 2 þ A ð6þ X w where A is the intercept. Beside the solute content, temperature also affects the a w of a solution. From the well-known Gibbs Helmholtz equation described by Prausnitz et al. (1986) and Raab and M uhlbauer (1998): oðg E =RT Þ ¼ H E ð7þ ot RT 2 P;x (where G E, H E are excess Gibbs free energy and excess enthalpy, J, respectively; R is the ideal gas constant J/ mol K). The dependence of the activity coefficient (and water activity) on temperature can be derived by writing (7) on the partial property basis in noting that lnðc i Þ¼ ge i RT Replacing (8) into (7), we obtain: ½o lnðc w ÞŠ P;x ¼ he R ot T 2 ð8þ ð9þ where gi E, he are the molar Gibbs free energy and molar excess enthalpy or partial molar heat of mixing respectively (J/mol). Integrating the above equation with respect to constant pressure and solute content along the path of temperature T 1 to T 2, and with regard to Eq. (1), one can derive the dependence of water activity of a solution on temperature as follows: ln a w1 ¼ he 1 1 ð10þ a w2 R T 1 T 2 where a wi is the water activity at temperature T i (K) (i ¼ 1; 2). Eq. (10) is the well-known Clausius-Clapeyron equation. From Eq. (10) it can be seen that a plot of lnða w Þ versus 1/T will be a straight line and the slope is the value of (h E =R). Therefore, if the water activity of a solution of a specified concentration is measured at two different temperatures, at least, then it can be determined at any given temperature by interpolation or extrapolation in a range of 10 K. In our study, four temperatures were employed to determine the best-fit slope (h E =R) for different concentrations of glucose and calcium chloride solutions. 3. Experimental 3.1. Solution preparation Glucose powder with purity 100% (Glucodin Energy Powder, Australia) and analytical grade CaCl 2 2H 2 O crystals 99 þ % (Aldrich Chemical Company Inc., USA) were used in the experiment, the solvent being distilled water.

3 A.V. Bui et al. / Journal of Food Engineering 57 (2003) Moisture content of the glucose powder was checked by conventional moisture content test in an oven at 105 C for 24 h prior to use. In the mean time, the glucose powder was held in a sealed container. The moisture content of the powder was recorded at 10 0:01%. Distilled water and the glucose powder were weighted by a scale with precision of 0.01 g to prepare solutions of concentrations 30.0%, 35.0%, 40.0%, 45.0%, 50.0%, 55.0%, 60.0% w/w. Pearson Square principle was employed in the calculations of the weights the reagents. The preparation by this way may lead to an error of 0.03%. Unlike glucose powder, calcium chloride crystals are very hygroscopic that absorbs moisture rapidly. So dilution should take place immediately after opening the sealed CaCl 2 2H 2 O container. In order to obtain the intended CaCl 2 -equivalent concentrations of 27.0%, 31.5%, 36.0%, 40.5%, 45.0% w/w, these concentrations were converted into the corresponding molarity m in which molecular weight of for CaCl 2 was used instead of for CaCl 2 2H 2 O. Then the molarity m was multiplied by to obtain the necessary weight of CaCl 2 2H 2 O for solution preparation. The amount of distilled water was then equal to 1000 g deducted by m ð2 18:015Þ g which accounts for the presence of two molecules of water on the dihydrate calcium chloride molecule. Weighting the calcium chloride encountered an error of 0.05 g which lead to solution concentration uncertainty of 0.15%. Adequate amount of the reagent and distilled water for any solution of about g was kept tightly closed in a plastic screw-capped container. The container was then shaken well and held in hot water (60 C) for an hour to ensure dissociation of all the crystals. It should be noted that calcium chloride solution of 45% at 20 C is at critical saturation point, hence any decrease of temperature or presence of any foreign CaCl 2 crystals will rapidly cause crystallisation. The concentrations were then double checked by comparing the refractive index with the one obtained from the CRC handbook (Lide, 2001). All the containers were then kept in a water bath at the temperatures of 20, 25, 30, 35 C for 3 h prior to any a w measurement Water activity measurement The instrument used in the study was an AQUA LAB water activity meter, model series 3TE by Decagon Devices, Inc. Pullman, Washington 99163, USA. This is a temperature-controlled water activity meter with a built-in infrared temperature sensor and a cooled-mirror dewpoint sensor. Water activity of the sample is determined on the basis of the dewpoint temperature of the air at equilibrium state in the sealed chamber and the sample surface temperature. These temperatures are measured by the sensors. The equipment operates within the temperature range of 5 43 C, and measures the a w values from to with a precision of After 30 min of warming up the water activity meter, standard salt solutions were used to confirm the proper functioning of the instrument. To minimise temperature drop of a sample when being placed in the holder, the spare holder was held in front of an air heater while the other one was in use. Samples were randomly taken and filled up to half of the holder for measurement. The measurements were in triplicate and here means were taken for analysis. The interval between measurement of the samples must be at least 15 min to allow the deposited moisture to escape from the instrument thus ensuring the accuracy of the readings. 4. Results and discussion The experimental measurements of the a w of the two solutions of different concentrations and temperatures are tabulated in Table 1. The obtained data indicate that solute content of a solution has the most significant effect, while temperature appears to have significant effect on water activity of low-water-activity solutions, such as in the case of calcium chloride solution of 27% up. For comparison purpose and for prediction of water activity of the two solutions at 25 C as a reference, the K 2 value in Eq. (5) for glucose solution was taken as equal to 2:11 0:11 obtained from Chirife et al. (1982) as recommended by Sereno et al. (2001), while K 2 for CaCl 2 was obtained from the best fit analysis of the data of Robison and Stokes (1959) as shown in Fig. 1. By using the K 2 values shown in Fig. 1 for CaCl 2 (where m is the molarity of solute, r 2 is the square of the Table 1 The experimentally measured a w of glucose and CaCl 2 solutions Concentration (%) Temperature ( C) Glucose solution CaCl 2 solution

4 246 A.V. Bui et al. / Journal of Food Engineering 57 (2003) Fig. 1. Linear regression between lnða w =X w Þ and square of solute content X 2 2 of CaCl 2 at 25 C: m solute molarity; K 2, A constants in Eq. (6); r 2 square of the correlation coefficient. Fig. 2. Effect of temperature on a w of glucose solution. correlation coefficient), and K 2 ¼ 2:11 for glucose (Chirife et al., 1982), the measured a w at 25 C and the predicted ones are in very good agreement as shown on Table 2. The effect of temperature on water activity of the two solutions is shown in Figs. 2 and 3, and the slopes (h E =R) derived from the best fit regression are listed in Table 3. It should be mentioned that temperature readings on the water activity meter differed from the preset one by 0.2 C even though the temperatures of the solutions had been carefully monitored during the experiment. The data illustrate a trend that absolute values of (h E =R) depend on the nature of the solute and increase as the concentration of the solution increases. Analysis of the data indicates a very good correlation between (h E =R) and concentration as shown in Figs. 4 and 5. Knowing that when solute concentration approaches 0% Table 2 Comparison between measured and predicted values of a w at 25 C C (%) a w measured b a w predicted a Da w Glucose solution a w measured b a w predicted b CaCl 2 solution a Chirife et al. (1982). b This work. Fig. 3. Effect of temperature on a w of CaCl 2 solution. Table 3 The best-fit constant h E =R along the path C C (%) h E =R (K) r 2 Glucose solution CaCl 2 solution r 2 is the square of the correlation coefficient. the value of (h E =R) approaches 0, too. In other words, the intercepts of the derived equations must be 0. The derived equations to describe the relationship between the (h E =R) values and the concentration C of the two solutions are as follows:

5 A.V. Bui et al. / Journal of Food Engineering 57 (2003) the final equations for water activity prediction for the two studied solutions at any given concentration and temperature as follows: For glucose solution: " a w ¼ 1 C # 2 1 0:9C exp C 2: C exp ð 446:52C 3 þ 349:34C 2 120:92CÞ 1 T 1 298:15 For CaCl 2 solution: ð13þ Fig. 4. Effect of glucose concentration C on (h E =R). if m ¼ " # 2 1 C a w ¼ 1 0:83766C exp C 86:68 6:16 5:16C exp ð 9561:7C 3 þ 2853:8C 2 422:4CÞ 1 1 ð14þ T 298:15 if m ¼ 7:5 10 " 2 1 C a w ¼ 1 0:83766C exp C 44:33 0:522# 6:16 5:16C exp ð 9561:7C 3 þ 2853:8C 2 422:4CÞ 1 1 ð15þ T 298:15 Fig. 5. Effect of CaCl 2 concentration C on (h E =R). For glucose: h E =R ¼ 446:52C 3 þ 349:34C 2 120:92C For CaCl 2 : h E =R ¼ 9561:7C 3 þ 2853:8C 2 422:4C ð11þ ð12þ where C is the solute content of the solutions in decimal figures. Eqs. (11) and (12) show consistency of the values of (h E =R) when extrapolating to low concentration of the two solutions. In addition, the r 2 values are more than 0.99 (see Figs. 4 and 5), the derived equations can be successfully used to predict the temperature effect on water activity of both solutions. If the water mole fraction X w and the solute mole fraction X i of the two solutions in Eqs. (5) and (6) are calculated by the solutionsõ concentration C (in decimal figures), then combining Eqs. (6), (10), and (11), (12) with T 1 ¼ 25 C as the reference temperature will earn The developed equations successfully predict the water activity of glucose and calcium chloride solutions with good agreement to the measured ones. For glucose solution, the average error is in just a small margin of 0.001, while for calcium chloride solution this figure is Though a bit higher, this accuracy is still considered acceptable. 5. Conclusion The results reported in this paper confirm that water activity of electrolyte and non-electrolyte solutions in the intermediate concentration range can be measured and predicted by applying the Norrish equation. The value of (h E =R) correlates very well with the solute content of the solutions, hence the derived polynomial equations can be used to describe the temperature effect on water activity. Temperature shows significant effect on water activity of a solution when its a w value is below 0.975, or at a concentration higher than 20% and 7% for glucose and calcium chloride solutions respectively.

6 248 A.V. Bui et al. / Journal of Food Engineering 57 (2003) Eqs. (13) (15) can be applied to successfully determine the water activity of glucose and calcium chloride solutions over the studied concentration and temperature ranges. The equations can also be used to predict water activity of these two solutions up to temperature of 45 C. Finally, it is important to note that instrument calibration, proper solution preparation, temperature control, and time between observations are essential features to ensure the accuracy of a w reading. References Bell, L. N., & Labuza, T. P. (2000). Moisture sorption practical aspects of isotherm measurement and use (2nd ed.). American Association of Cereal Chemists Inc. Chirife, J., Favetto, G., & Fontan, C. F. (1982). The water activity of fructose solution in the intermediate moisture range. Lebensmittel Wissenschaft Technologie, 15, Hogan, P. A., Canning, R. P., Peterson, P. A., Johnson, R. A., & Michaels, A. S. (1998). A new option: Osmotic distillation. Chemical Engineering Progress (July), Johnson, R. A., Valks, R. H., & Lefebvre, M. S. (1989). Osmotic distillation a low temperature concentration process. Australian Journal of Biotechnology, 3, , 217. Leiras, M. C., Alzamora, S. M., & Chirife, J. (1990). Water activity of galactose solutions. Journal of Food Science, 55(3), Lide, D. R. (2001). CRC handbook of chemistry and physics (2000) (81st ed.). USA: CRC Press. Prausnitz, J. M., Lichtenthaber, R., & Azevedo, E. (1986). Molecular thermodynamics of fluid-phase equilibria (2nd ed.). Prentice Hall, New York: Englewood Cliffs. Raab, J. D., & M uhlbauer, A. L. (1998). Phase equilibria measurement and computation. London: Taylor & Francis. Robison, R. A., & Stokes, R. H. (1959). Electrolyte solutions. London: Butterworths. Sereno, A. M., Hubinger, M. D., Comesan~a, J. F., & Correa, A. (2001). Prediction of water activity of osmotic solutions. Journal of Food Engineering, 49,

KEMS448 Physical Chemistry Advanced Laboratory Work. Freezing Point Depression

KEMS448 Physical Chemistry Advanced Laboratory Work Freezing Point Depression 1 Introduction Colligative properties are properties of liquids that depend only on the amount of dissolved matter (concentration),