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hydroxonium and hydroxide concentrations, but still neutral conditions. Consequently, the pH shift alone cannot exactly describe the dissociation equilibrium shift and thus the pKa shift is used. By using the regression equation from Marshall and Frank (60), the negative logarithm of the ion product Kw ([mol kg 1]2) of water substance (Eq. 5.19) can be calculated with a deviation of 0.01 at <200 C, 0.02 at 374 C, 0.3 at >374 C, and 0.05 0.3 at high pressures. log 10 ( Kw ) = log 10 ([ H 3O+ ] [OH ]) (5.19)
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The modeled dissociation equilibrium shift in pure water showed large variations with pressure and temperature (Fig. 5.9). Especially the hightemperature area is a matter of particular interest for the application of supercritical water in food technology (Fig. 5.9a). After extrapolation up to 1400 MPa (Fig. 5.9b), an estimation about the Kw characteristics at the current technical limit for spore inactivation studies could be given. For any equilibrium reaction, the pressure and temperature dependence of the equilibrium constant is described by Planck s equation (69) (Eq. 5.20): V d ln ( K ) = dp T R T (5.20)
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where p is the pressure (MPa), T the absolute temperature (K), V the reaction volume at atmospheric pressure (cm3 mol 1), and R the gas constant 8.3145 cm3 MPa K 1 mol 1. The reaction volume V is equal to the difference of the partial volumes of products and reactants. It includes the volume change because of alteration
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Pressure [MPa]
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-lg Kw 2 1200 [mol kg 1]
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Figure 5.9 Dissociation equilibrium shift (negative logarithm of the ion product Kw [mol kg 1]2) in pure water under different p-T conditions up to 1000 MPa and 1000 C (a) and with adiabatic lines (--) up to 140 C extrapolated up to 1400 MPa (b) (60, 65).
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CHEMICAL AND MATRIX EFFECTS
in binding length and angle Vintrinsic as well as solvational properties Vsolvational (Eq. 5.21): V = Vintrinsic + Vsolvational (5.21)
For industrial applications, such property changes of food matrices are important. Figure 5.10 shows in situ pH shifts in food systems (milk, pea soup, baby mashed carrots with maize, herring with tomato sauce; for the detailed ingredients, see Annex) and N-(2-Acetamido)-2-aminoethanesulfonic acid ACES buffer in dependence of temperature. To remove all external effects, all data were divided by the pH-values of the temperature stable phosphate buffer. Hence, in Fig. 5.10, pH differences between food and phosphate buffer are shown. ACES buffer had the highest pH shift and all other food systems had lower temperature dependencies. To investigate the temperature and pressure dependence of the dissociation equilibrium shift, different buffer systems were modeled. The created p-T diagrams of the calculated pKa value have shown different changes (Fig. 5.11). Different initial temperatures and the adiabatic heating (dashed line) due to the pressure buildup process required the implementation of the speci c temperature dependences, respectively. These temperature dependences can be very high and could compensate the advantages of the low isothermal pressure dependence. The diversity of iso-pKa lines in buffer solutions resulted mainly from the different dissociation reactions and consequently different standard molar enthalpies ( rH0) or reaction volumes ( V).
1.10 1.05
ACES Milk Peas Carrot Herring
1.10 1.05 1.00 0.95 0.90 0.85 0.80 0.75 0.70 0 10 20 30 40 50 60 70 80 90
pHX /pHPBS [-]
1.00 0.95 0.90 0.85 0.80 0.75 0.70
Temperature [ C]
Figure 5.10 Real pH shift in food systems (milk, pea soup, baby mashed carrots with maize, herring with tomato sauce) and 0.01 M ACES buffer in dependence of temperature (65).