Analysis Of Thermodynamic Polioquality

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In thermodynamic equilibrium, solubility of a solid solute in a liquid solvent can be calculated by the following equation [8]: x^ideal=x_s γ_s =exp[〖-∆H〗_fus/RT_m (T_m/T-1)-〖∆C〗_p/R (ln⁡〖T_m/T〗-T_m/T+1)] (1 where ΔHfus is the enthalpy of fusion at the melting point temperature Tm, R is the universal gas constant, γs is the activity coefficient of the solid in the solution, xs is the equilibrium concentration in the solution, and xideal is the ideal solubility independent of the solvent. ΔCp is the difference in heat capacity of the subcooled liquid and crystalline solute commonly assumed as zero.
For nonideal solution, γ2 must be estimated from either experimental data or a …show more content…

The calculation of Φ_i^*, θ_i^ʹ and θ_i requires the UNIQUAC parameters ri and qi for the pure components. These can be found in reference tables or calculated based on the volume and area parameters by group contribution methods [27-29]. r=∑_(i=1)^m▒〖n_i×R_i 〗 (20 q=∑_(i=1)^m▒〖n_i×Q_i 〗 (21
Where m is the number of functional groups in the molecule, n is the number of times each functional group is repeated in the molecule and Ri and Qi are the group volume and area …show more content…

Using this Table and equations 20 and 21, the r, q and qʹ parameters for medetomidine salts and solvents are listed in Table 2. In this development, z is the coordination number and is usually taken equal to 10.0 [8]. τ_ij and τ_ji are the binary interaction parameters and can be related theoretically to the interaction energy between components i and j. In the frame of the UNIQUAC model, the binary interaction parameters are considered as adjustable parameters. For a binary system involving a solute (component 1) and a solvent (component 2): ln⁡〖γ_1=ln⁡〖(Φ_1^*)/x_1 +z/2 q_1 ln⁡〖θ_1/(Φ_1^* )+Φ_2^* (l_1-r_1/r_2 l_2 )-q_1^ʹ ln⁡(θ_1^ʹ+θ_2^ʹ τ_21 )+θ_2^ʹ q_1^ʹ (τ_21/(θ_1^ʹ+θ_2^ʹ τ_21 )-τ_12/(θ_2^ʹ+θ_1^ʹ τ_12 ))〗 〗 〗 (22 ln⁡〖γ_2=ln⁡〖(Φ_2^*)/x_2 +z/2 q_2 ln⁡〖θ_2/(Φ_2^* )+Φ_1^* (l_2-r_2/r_1 l_1 )-q_2^ʹ ln⁡(θ_2^ʹ+θ_1^ʹ τ_12 )+θ_1^ʹ q_2^ʹ (τ_12/(θ_2^ʹ+θ_1^ʹ τ_12 )-τ_21/(θ_1^ʹ+θ_2^ʹ τ_21 ))〗 〗 〗 (23
E. Optimization of the adjustable

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