Enthalpy of Solution and Hydration

5 Key excerpts on "Enthalpy of Solution and Hydration"

• 

  eBook - ePub

  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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  BIOS Instant Notes in Physical Chemistry

  • Gavin Whittaker, Andy Mount, Matthew Heal(Authors)
  • 2000(Publication Date)
  • Taylor & Francis

    (Publisher)

  endothermic .

  The entropy change due to breaking up the salt into its constituent gaseous ions is also positive, but in addition there is an entropy term due to ion solvation. Once the ion is solvated, the water molecules in the solvation shell are arranged around each ion with a center of symmetry in the system (Fig. 1 ). They are relatively tightly packed with respect to liquid water and hence have lower entropy and occupy a lower volume. In contrast, in the bulk solution, the water molecules are extensively hydrogen bonded (see Topic H6 ) in a relatively open tetrahedral arrangement (Fig. 2 ).

  Fig.2. The conflict in symmetry between bulk water and water in a hydration shell.

  This produces a zone of water between these two regions in which the conflict in symmetry disrupts the water structure and leads to an increase in entropy (see Topic ) and in the volume that the molecules occupy in this zone. Small, highly charged ions such as Li+ , Al3+ and F− have large solvation shells compared with the size of this zone and the effects of the solvation shell dominate. They are termed structure-making ions as solvation of these ions leads to an overall decrease in the entropy of the system on solvation. The overall volume of the system also decreases compared to the total combined volume of the salt and water before addition. For very small or highly charged ions this volume change can be sufficiently great that the volume of the solution is smaller than the original volume of water, even though salt has been added. In contrast, for relatively large ions (e.g. organic anions and cations, ClO4 − , Rb+ ) the effects of the intermediate zone outweigh those of the solvation shell, there is an overall increase in entropy and in the total volume of the system and as a result these are termed structure-breaking

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  Physical Chemistry of Foods

  • Pieter Walstra(Author)
  • 2002(Publication Date)
  • CRC Press

    (Publisher)

  The free energy is thus the property determining what will happen. If we add some sugar to water, it will dissolve and the sugar molecules will distribute themselves evenly throughout the liquid, because that gives the lowest free energy. In this case the increase in entropy has a greater effect than the increase in enthalpy (in crystalline sugar, the molecules attract each other and the enthalpy is thus lower than in solution). If we have pure oil droplets in water, they will rise to the surface (lower potential energy) and then coalesce into one layer (lower interfacial area and thus lower surface free energy). If we bring water to a temperature of-20°C, it will crystallize (lower enthalpy, which in this case more than compensates for the decrease in entropy). If we have a solution of ethanol in water with air above it, the ethanol will divide itself in such a way over the phases that its partial free energy (or chemical potential: Section 2.2.1) is the same in both; the same applies for the water. All these processes occur spontaneously, and they will never reverse if the external conditions (temperature, pressure, volume available) are left unaltered.

  All this applies, however, only to macroscopic amounts of matter. Thermodynamics is valid only for large numbers of molecules. If small numbers are considered, say less than a few times 100, exceptions to the rule stated above may occur; even at 10°C, a few water molecules may temporarily become oriented as in an ice crystal, just by chance, but macroscopically ice will never form at that temperature.

  Another remark to be made is that the absolute values of enthalpy and entropy are generally unknown. (Only a perfect crystal of one component at zero absolute temperature has zero entropy.) Quantitative results therefore mostly refer to some standard state (usually 0°C and 1 bar), where these parameters are taken to be zero. One always considers the change in thermodynamic properties, and that is quite sufficient. At constant pressure and temperature, the basic equation thus is

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  Hydrometallurgy

  Principles and Applications

  • T Havlik(Author)
  • 2014(Publication Date)
  • Woodhead Publishing

    (Publisher)

  0 is generally the most important factor controlling the stability of complex compounds. The standard entropies of the formation of cations in the aqueous solutions tend to more positive values at higher temperatures and for anions these values are more negative. Generally, it appears that as the temperature increases, the change of the entropy of the formation of complexes become more positive and the complex because more stable.

  At different temperatures from 25 °C, the change of the standard enthalpy of the reaction, ΔH T 0 , can be written in the following form:

  Δ

  H T 0

  = Δ

  H 298 0

  +

  ∫ 298 T

  δ Δ

  H 0

  δ T

  p

  dT

  .

    (4.62)

  Similarly, the change of the standard entropy may be expressed by the equation

  Δ

  S T 0

  = Δ

  S 298 0

  +

  ∫ 298 T

  δ Δ

  S 0

  δ T

  p

  dT

  .

    (4.63)

  Calculation of ΔG 0 at higher temperatures requires information on the temperature dependence of the changes of standard enthalpy and entropy. In this case it is considered that the pressure does not change, but at pressures other than normal pressure the effect of pressure on the values of ΔH 0 T and ΔS 0 T must taken into account.

  The change of the reaction enthalpy depends on the enthalpies of all reactants taking part. The thermal content, i.e., enthalpy is defined by the equation:

  H = U + pV

  were U is the total internal energy, p is pressure and V is the volume of the system.

  In other words, the thermal content must depend on the amount of heat required to increase the temperature of the system by one degree which is the heat capacity

  cv

  at constant volume and

  cp

  is constant pressure. To increase temperature dT at a constant volume the required amount of heat

  dqv

  is

  dqv  =

   d

  U = cv

  dT and consequently:

  c v

  =

  δ U

  δ T

  At constant pressure

  dqv

   = 

  dH–cp dT

  and consequently

  c P

  =

  δ H

  δ T

  p

  .

  These definitions of the heat capacities can be used to determine the relationship between the change of the total heat capacity of the reaction and the calorific effect of the reaction in relation to temperature. If the initial state is I and the final state II, then

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  Water-Insoluble Drug Formulation

  • Ron Liu, Ron Liu(Authors)
  • 2018(Publication Date)
  • CRC Press

    (Publisher)

  Equation 2.16 . The slope, therefore, can be derived mathematically from the expression:

  d   ln   X 2 i d ( 1 T )     =       −   Δ H ¯ f R

  (2.17)

  Thus, it can be seen that the greater the molar enthalpy of fusion, the greater the increase in solubility as the solution temperature is increased, and a steeper slope would be evident in a plot such as Figure 2.1 . Note that for a real solution, the enthalpy of solution, designated

  Δ

  H ¯

  sol'n

  ​

  , substitutes for the enthalpy of fusion in Equation 2.17 . The enthalpy of solution includes the enthalpy of fusion and the enthalpy associated with mixing of the hypothetical supercooled liquid form of the solute mass with the solvent.

  MOLAR HEAT CAPACITY

  The molar enthalpy for the transition from a solid to a supercooled liquid is not a constant with respect to temperature. The heat capacity of the solid and of the supercooled liquid forms of the solute at constant pressure influence the magnitude of the molar enthalpy for this transition at temperatures below the melting point. The heat capacity at constant pressure,

  C p

  , is the amount of energy in the form of heat,

  Δ q , ​

  required to raise the temperature of a particular material by a particular amount,

  Δ T ​

  (Dave et al., 2014):

  C p   =     ∂ q ∂ T   ~     Δ q Δ T

  (2.18)

  FIGURE 2.1 van’t Hoff plot of ideal mole fraction solubility as a function of the inverse solution temperature.

  The molar heat capacity at constant pressure,

  C ¯

  p

  , would be the heat capacity divided by the amount of that material in moles, n, expressed as follows to show the relevance of the molar enthalpy of fusion:

  C ¯ p   =     [ ( ∂ H ¯ f ∂ T ) p ] / ​ n

  (2.19)

  It is frequently assumed that the heat capacity of the solid at constant pressure,

  C ¯

  p , s

  , and the molar heat capacity of its liquid form at constant pressure,

  C ¯

  p , l

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