Free Energy of Dissolution

4 Key excerpts on "Free Energy of Dissolution"

• 

  eBook - ePub

  Physical Chemistry

  How Chemistry Works

  • Kurt W. Kolasinski(Author)
  • 2016(Publication Date)
  • Wiley

    (Publisher)

  Ionic compounds are held together by one of the strongest of all intermolecular interactions – the electrostatic interactions of full positive and negative charges. Nevertheless, ionic compounds display a full range of solubility from sparingly soluble to highly soluble. The factor that controls the extent of dissolution in cold thermodynamic terms is the Gibbs energy change. However, to understand dissolution on a molecular level we need to look at the enthalpy and entropy changes and how they relate to molecular processes.

  Consider the dissolution of KCl in water at 298 K. The values in Table 11.3 reveal that Δsol H°m = 17.22 kJ mol−1 and Δsol S°m = 76.4 J mol−1 K−1 . Therefore, Δsol G°m = −5.56 kJ mol−1 . The negative value of Δsol G°m indicates a spontaneous process, that is, KCl dissolves in water. The process, in this case, is driven by entropy, not enthalpy. The reaction

  Table 11.3

  Selected thermodynamic properties of a few ions and ionic compounds in aqueous solutions. m% represents the solubility in mass percent.

  Na+	K+	F−	Cl−	Ag+
  S°m (aq)/J K−1 mol−1	59.0	102.5	−13.8	56.5	72.7
  KF	KCl	NaF	NaCl	AgCl
  S°m (aq)/J K−1 mol−1	66.6	82.6	51.1	72.1	96.3
  m%	50.41	26.22	3.97	26.45	0.00019
  Δsol H°m /kJ mol−1	−17.73	17.22	0.91	3.88	65.4
  S°m (aq)/J K−1 mol−1	22.1	76.4	−5.9	43.4	32.9
  Δsol G°m /kJ mol−1	−24.3	−5.56	2.67	−9.06	55.6

  is endothermic because the sum of all the intermolecular forces acting on the reactants side is stronger than the sum of the intermolecular forces in the solution. These intermolecular forces include the electrostatic interactions of the ions with each other. These electrostatic interactions are screened in the solvated state by the water molecules that intercede in between the ions to keep them separated. Solvation and these interactions are discussed in greater detail in Chapter 14. Importantly, one other set of intermolecular interactions is being hidden by the way we have written the solvation reaction. We must also consider the effect of the solute on the structure of the solvent and the hydrogen bonding between water molecules. For very dilute solutions when the solution is acting ideally, the electrostatic interactions of ions will be the predominant factor in determining the energetics. At higher concentrations, as non-ideality sets in, changes in the solvent interactions also have to be taken into consideration. Usually, Δsol H°m is small for monovalent ions, with a magnitude of less than 40 kJ mol−1

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  Gibbs Energy and Helmholtz Energy

  Liquids, Solutions and Vapours

  • Emmerich Wilhelm, Trevor M Letcher, Emmerich Wilhelm, Trevor M Letcher(Authors)
  • 2021(Publication Date)
  • Royal Society of Chemistry

    (Publisher)

  5 These thermochemical quantities, when coupled with the corresponding solvation quantities through a straightforward application of the appropriate thermodynamic cycles or thermocycles, lead to the most important thermochemical quantities in solution, such as the free energy of formation of key metabolites in aqueous solutions. Accurate experimental measurement of these thermochemical quantities in solution is not an easy task, hence reliable calculation schemes and predictive methods will be very much needed at least for the foreseeable future. It is particularly in this context that a reliable estimation of solvation Gibbs energy over a broad range of external conditions is highly desirable in vital and practical applications. Of much interest is, of course, the development of a predictive tool for this solvation quantity.

  Various attempts have been reported for the prediction of solvation Gibbs energies. The molecular-based approaches (molecular simulations, COSMO-type calculations, etc. ) are often used as they provide fairly accurate results but they are often time consuming.

  6 ,7

  Simpler methods, such as the Linear Solvation Energy Relationship (LSER),

  8 ,10

  are faster but less accurate. With LSER, in particular, only solvation Gibbs energy values at 298.15 K and ambient pressure are calculated. Of interest is the work of Hsieh and Lin,

  11 ,13

  who showed that solvation Gibbs energy data from molecular simulation could be used as input parameters of cubic EOSs for estimating the attractive and co-volume parameters.

  Recently, an interesting strategy was proposed by Privat and co-workers14 to predict solvation Gibbs energies through the semi-predictive UMR–PRU cubic EOS.

  15 ,16

  This model is known for providing accurate predictions of fluid-phase equilibria and related thermodynamic quantities (enthalpy, heat capacity, density, etc. ) from ideal to complex mixtures. This EOS uses advanced mixing rules for EOS mixture parameters from combination with the UNIFAC activity coefficient model at a null reference pressure.20 These mixing rules enable this EOS to describe the behavior of mixtures containing polar or associating compounds with reasonable accuracy.

  15 ,17 ,19

  Since the UNIFAC model is fully predictive, the only input parameters required by the UMR–PRU EOS are the critical temperature, T

  ci

  , critical pressure, P

  ci

  , and the acentric factor, ω i , of each component i , in addition to the UNIFAC group interaction parameters.

  This chapter focuses on the EOS approach to solvation Gibbs energy since this is the most appropriate approach for efficient thermodynamic studies over a broad range of external pressure and temperature. As mentioned already, of much interest are, of course, predictive tools for the above quantity, which ultimately may lead to the reliable prediction of formation free energies in solution. Therefore, in the first part of the chapter, the UMR–PRU EOS, being a very simple to implement and representative cubic EOS model, is used for the prediction of solvation Gibbs energies. In an effort, however, to gain better insight into solvation phenomena, a fairly recently developed solvation model,3 based on a versatile molecular EOS approach known as LFHB (Lattice Fluid with Hydrogen Bonding) model,

  21 ,22

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  General Chemistry for Engineers

  • Jeffrey Gaffney, Nancy Marley(Authors)
  • 2017(Publication Date)
  • Elsevier

    (Publisher)

  Section 12.5 .

  The change in enthalpy when a solution is formed from the pure substances is called the enthalpy of solution (ΔH soln ), which is the enthalpy change associated with the dissolution of a solute in a solvent at constant pressure. The net enthalpy change when a solution forms involves three processes as shown in Fig. 12.1 .

  Fig. 12.1 Enthalpy changes during solution formation. If ΔH soln  < 0, the dissolution will be exothermic (left) and if ΔH soln  > 0, the dissolution will be endothermic.

  (1)  

  Separation of the solvent molecules (ΔH 1 ).

  (2)  

  Separation of the solute molecules (ΔH 2 ).

  (3)  

  Joining the separated solvent molecules and the separated solute molecules together to form a solution (ΔH 3 ).

  The enthalpy of solution is the sum of these three processes:

  Δ

  H soln

  = Δ

  H 1

  + Δ

  H 2

  + Δ

  H 3

    (5)

  Both process (1) and process (2) involve the disruption of attractive forces within the molecules or ions and require energy added to the system. So, both ΔH 1 and ΔH 2 are positive values. Process (3) involves the formation of attractive forces between the solute and solvent molecules, which releases energy. So, ΔH 3

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  Developing Solid Oral Dosage Forms

  Pharmaceutical Theory and Practice

  • Yihong Qiu, Yisheng Chen, Geoff G.Z. Zhang, Lawrence Yu, Rao V. Mantri(Authors)
  • 2016(Publication Date)
  • Academic Press

    (Publisher)

  Whether a solid is crystalline or amorphous, neighboring molecules are closely associated with each other through intermolecular forces. Dissolution involves the breaking of these existing intermolecular interactions and the formation of new interactions with the solvent (usually water). The solid dissolution process generally involves two sequential steps. The first step is the interaction between solid and solvent molecules to form solvated molecules (solvation), which takes place at the solid–liquid interface. The second step is the mass transport of solvated molecules from the solid–liquid interface to the bulk solution. These two steps govern the rate and extent of solid dissolution. Solubility, a basic property for solids, controls the first step. Transport, on the other hand, usually controls the second step, which is generally slower than the first step. Overall, dissolution is governed by solubility and transport processes.

  The first step of dissolution can be viewed as a pseudochemical reaction that is governed by the same principles as regular chemical reactions. The solvation process is reversible, and solubility is reached when the reaction reaches equilibrium. This process can be described by its Gibbs free energy (ΔG ):

  Drug + Solvent ↔ Solvated Drug

  (9.53)

  (9.53)

  Δ G = Δ H − T Δ S

  (9.54)

  (9.54)

  This reaction involves both the breakage of existing intermolecular interactions (drug-drug, solvent-solvent) and the formation of new intermolecular interactions (drug-solvent). The net entropy (ΔS ) change for this reaction is generally positive (dissolution causes an increase in disorder), which is favorable for dissolution. Therefore, the extent of dissolution is often determined by the net enthalpy change (ΔH ). If the net enthalpy change is negative or close to zero, the reaction will continue until all the available solids are dissolved. The empirical rule, “like dissolves like,” therefore, has a thermodynamic basis. On the other hand, if the net enthalpy change (ΔH ) is positive, the reaction will progress until equilibrium is reached (ΔG =0). A saturated solution is obtained.

  The reaction rate V is described kinetically by

  V =

  k 1

  [ Drug ] [ Solvent ]

  k 1

  = A

  e

  –

  E a

  / R T

  (9.55)

  (9.55)

  The overall rate of dissolution is controlled by the slower step of the two-step dissolution process. Thermodynamically, the activation energy E a for the formation of a solvated drug should be less than the energy to break water-water or drug-drug intermolecular interactions. Since hydrogen bonding is among the strongest intermolecular interactions, the activation energy for reaction (Eq. 9.53

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