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Food Properties Handbook Data and Models of Water Activity. I: Solutions This article was downloaded by: 10.3.98.104 On: 29 Sep 2021 Access details: subscription number Publisher: CRC Press Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: 5 Howick Place, London SW1P 1WG, UK Food Properties Handbook M. Shafiur Rahman Data and Models of Water Activity. I: Solutions and Liquid Foods Publication details https://www.routledgehandbooks.com/doi/10.1201/9781420003093.ch3 Piotr P. Lewicki Published online on: 28 May 2009 How to cite :- Piotr P. Lewicki. 28 May 2009, Data and Models of Water Activity. I: Solutions and Liquid Foods from: Food Properties Handbook CRC Press Accessed on: 29 Sep 2021 https://www.routledgehandbooks.com/doi/10.1201/9781420003093.ch3 PLEASE SCROLL DOWN FOR DOCUMENT Full terms and conditions of use: https://www.routledgehandbooks.com/legal-notices/terms This Document PDF may be used for research, teaching and private study purposes. Any substantial or systematic reproductions, re-distribution, re-selling, loan or sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The publisher shall not be liable for an loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material. CHAPTER 3 Data and Models of Water Activity. I: Solutions and Liquid Foods Piotr P. Lewicki CONTENTS 3.1 Introduction............................................................................................................................ 33 3.2 Water Activity of Solutions and Liquid Foods ..................................................................... 37 3.3 Semiempirical Equations .......................................................................................................48 3.4 Empirical Equations............................................................................................................... 54 References....................................................................................................................................... 62 3.1 INTRODUCTION Food is a multicomponent and multiphase system that is usually not in a thermodynamic equilibrium. This lack of equilibrium causes many chemical and physical changes, which are passed within the material during storage. Processing creates domains within the food with higher and lower concentration of constituents. Concentration gradients result in diffusion, which in turn enable contact between substrates and can facilitate chemical reactions. Redistribution of constituents, especially water, affects rheological properties of the material, hence its texture, structure, ability to creep and relax all change during storage. Interactions between polymers strongly influence properties of the material and depend on rotational and translational diffusion of polymer chains. In materials with interphase boundaries, mass and surface forces cause changes of structure and constituents, spatial concentration. Destabilization of foams and coalescence of emulsions is a macroscopic result of those changes. All the above-mentioned examples show that food is a dynamic system, far from the equilibrium state, which undergoes many changes during storage. Research conducted over the years prove that the course and the dynamics of all those changes are related to the thermodynamic state of water in the material (Lewicki, 2004). The thermodynamic state of water in food arises firstly from unusual properties of water and its ability to form strong hydrogen bonds. Interactions with hydrophilic solute lead to the formation of structure water and hydration water. On the other hand, an interaction with hydrophobic solute affects the structure of the solvent water. A clathrate-like structure is formed. Water molecule mobility in both structure and hydration state as well as in clathrate-like structure is reduced. In the presence of electrolytes, ionic interactions also occur and induce some structuring of water Downloaded By: 10.3.98.104 At: 10:12 29 Sep 2021; For: 9781420003093, chapter3, 10.1201/9781420003093.ch3 ß 2008 by Taylor & Francis Group, LLC. molecules. Finally, porosity of the material, which is quite common for foods, also affects the thermodynamic state of water. Curvature of the solvent surface in capillaries, in drops or interstices, reduces the ability of water molecules to do the work. The thermodynamic state of water is expressed by its Gibbs free energy, which is a criterion of feasibility of chemical or physical transformation. The Gibbs free energy is quantitatively expressed by the equation: G ¼ H À TS (3:1) where H is the enthalpy (J) T is the temperature (K) S is the entropy (J=K) and can be understood as total energy (H) diminished by unavailable energy (TS) Gibbs free energy in differential form: dG ¼ dH À TdS À SdT (3:2) Substituting dH ¼ dE þ PdV þ VdP and dE ¼ TdS – PdV yield the differential change in the Gibbs free energy: dG ¼ VdP À SdT (3:3) where E is the internal energy (J) P is the pressure (Pa) V is the volume (m3) The above equation applies to a homogeneous system of constant composition in which only work of expansion takes place. In an open multicomponent system, the Gibbs free energy will depend not only on the temperature and pressure, but also on the amount of each component present in the system. Hence G ¼ f (T, P, n1, n2, ..., nn)(3:4) where n1, n2,...,nn is the number of moles of component 1, 2, . , n. Under this situation, change of Gibbs free energy is described by the equation: @G @G Xnj @G dG ¼ dP þ dT þ dn (3:5) @P @T @n i T,nj P,nj ni T,P,nj in which i denotes that component where concentration changes and j denotes all those components where concentration remains constant. The partial molar Gibbs free energy @G (3:6) @n i T,P,nj expressed by Equation 3.6 is called chemical potential of component i and is denoted as mi.It represents the change in Gibbs free energy of the system caused by addition of one mole of Downloaded By: 10.3.98.104 At: 10:12 29 Sep 2021; For: 9781420003093, chapter3, 10.1201/9781420003093.ch3 ß 2008 by Taylor & Francis Group, LLC. component i keeping temperature, total pressure, and number of moles of all other components constant. Then Equation 3.3 can be written as follows: X ¼ À þ : dG VdP SdT midni (3 7) Gibbs has shown that for any system the necessary and sufficient condition for equilibrium is the equality of chemical potential of component i in all phases. That is I ¼ II ¼ III : mi mi mi (3 8) where the superscripts refer to different phases. Dividing Equation 3.3 by the number of moles of component i, the following can be written: dG V S ¼ dP À dT (3:9) dni dni dni Denoting V=dni ¼ vi and S=dni ¼ si, Equation 3.9 becomes ¼ À : dmi vidP sidT (3 10) where 3 vi is the molar volume (m =mol) si is the molar entropy J=(mol K) At constant temperature ¼ : dmi vidP (3 11) Taking the substance as an ideal gas, Lewis obtained chemical potential in terms of easily measurable properties. RT RT v ¼ and dm ¼ dP (3:12) i P i P where R is the gas constant (J=mol K). Integrating Equation 3.12 the following formula is obtained: À ¼ p : mi mi RT ln (3 13) p where mi is the chemical potential of component i at standard conditions p is the initial pressure in the system In a real system properties of gases deviate from the ideal one and to account for the deviation Lewis proposed a new function called fugacity, f. Hence, Equation 3.13 for a real gas takes the following form: À ¼ fi : mi mi RT ln (3 14) fi In a pure ideal gas fi ¼ pi, the partial pressure of the gas. The no ideality of the gas follows from the existence of intermolecular forces (Prausnitz, 1969). The ratio between fugacities is called activity, a. Hence, Equation 3.14 becomes À ¼ : mi mi RT ln ai (3 15) Downloaded By: 10.3.98.104 At: 10:12 29 Sep 2021; For: 9781420003093, chapter3, 10.1201/9781420003093.ch3 ß 2008 by Taylor & Francis Group, LLC. Table 3.1 Fugacity and Activity of Water Vapor in Equilibrium with the Liquid at Saturation and at Pressure 0.01 MPa Temperature (8C) Pressure (kPa) Fugacity (kPa) Activity 0.01 0.611 0.611 0.9995 10 1.227 1.226 0.9992 20 2.337 2.334 0.9988 40 7.376 7.357 0.9974 60 19.920 19.821 0.9950 80 47.362 46.945 0.9912 100 101.325 99.856 0.9855 120 198.53 194.07 0.9775 140 361.35 349.43 0.9670 160 618.04 589.40 0.9537 180 1002.7 939.93 0.9374 Source: Adapted from Hass, J.L., Geochim. Cosmochim. Acta, 34, 929, 1970. Analysis of data presented in Table 3.1 shows that in the range of temperatures important for food processing, the water vapor deviates from the ideal gas by not more than by 6%, and at ambient temperature and pressure, the deviation is less than 0.2%. Thus, under the conditions experienced in food processing and storage activity, water vapor at saturation can be assumed to be equal to 1 and it can be written as fw ¼ pw : (3 16) fw pw where pw and pw are the vapor pressure of water in the system and of pure water at the same temperature and total pressure, respectively. Equation 3.16 is used to calculate water activity in food when partial pressure of water vapor over that food is known. Assuming that food is in equilibrium with the gas phase, the activity of gas phase calculated from Equation 3.16 is taken as the activity of water in solid or liquid food according to Equation 3.8. Taking a system consisting of an ideal solution and an ideal gas, the equilibrium state can be described as follows: solution ¼ vapor : mi mi (3 17) An ideal solution behaves analogously to an ideal gas and follows Raoult’s law.
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