Differential enthalpy of solution

Solution In this example, it is assumed that we add a solute to a large enough volume of solution so that the composition of the mixture does not change. The enthalpy change for this process is referred to as a differential enthalpy of solution. We can represent this process by... 

From thermodynamics, it is known that the mean differential enthalpy of solution, and the solubiiities of a gas, (in mol 1" ), as a function of absolute temperature are related by Equation (6.12) [765aa] ... 

DIFFERENTIAL ENTHALPIES OF SOLUTION FOR PHOSGENE IN VARIOUS ORGANIC SOLVENTS AT STANDARD PRESSURE... 

This equation has the same form as that obtained for ideal solubility but AHfvs has been replaced by the enthalpy of solution AHmjx. In non-ideal solutions of solids in liquids which do not follow either Henry s or Raoult s Laws, AHmix is the differential enthalpy of solution of the solute in the saturated solution. Both AGmix and AHmix are for non-ideal solutions similar to the reaction free energy we introduced when studying equilibrium in chemical reactions. They are all differential quantities AHmix is the enthalpy change when one mole of solute is added to an infinite volume of nearly... 

First let us consider a solution process in which solute is transferred from a pure solute phase to a solution. The molar differential enthalpy of solution, A o H, is the rate of change of H with the advancement soi at constant T and p, where soi is the amount of... 

The relations between A//(sol) and the molar integral and differential enthalpies of solution are illustrated in Fig. 11.9 on the next page with data for the solution of crystalline sodium acetate in water. The curve shows A//(sol) as a function of fsou with fsoi defined as the amount of solute dissolved in one kilogram of water. Thus at any point along the curve, the molality is /Mb = soi/(l kg) and the ratio A//(sol)/ soi is the molar integral enthalpy of solution A//m(sol, /mb) for the solution process that produces solution of this molality. The slope of the curve is the molar differential enthalpy of solution ... 

Thus La depends on the difference between the molar integral and differential enthalpies of solution. 

The third method assumes we measure the integral enthalpy of solution A//(sol) for varying amounts soi of solute transferred at constant T and p from a pure solute phase to a fixed amount of solvent. From Eq. 11.4.5, the molar differential enthalpy of solution is given by Asoi/f = dA//(sol)/ d soi when a is held constant. We make the substitution... 

For convenience of notation, this book will use Asoi.aT/ to denote the molar enthalpy difference i/A(sln) - H (s). Aso, aH is the molar differential enthalpy of solution of solid A in the solution at constant T and p. The first integral on the right side of Eq. 12.2.3 requires knowledge of Aso1,a7/ over a temperature range, but the only temperature at which it is practical to measure this quantity calorimetrically is at the equilibrium transition temperature Tf. It is usually sufficient to assume Asoi.aT/ is a linear function of T ... 

Here Aso1,a is the molar differential enthalpy of solution of solid or gaseous A in the liquid mixture, and Asoi,a1 is the molar differential volume of solution. Equation 12.3.5 is a relation between changes in the variables T, p, and Xa, only two of which are independent in the equilibrium system. 

If the solubility xb increases with increasing temperature, Asoi,b ° must be positive and the solution process is endothermic. A decrease of solubility with increasing temperature implies an exothermic solution process. These statements refer to a solid of low solubility see page 357 for a discussion of the general relation between the temperature dependence of solubility and the sign of the molar differential enthalpy of solution at saturation. 

The ideal solubility of a solid at a given temperature and pressure is the solubility calculated on the assumptions that (1) the liquid is an ideal liquid mixture, and (2) the molar differential enthalpy of solution equals the molar enthalpy of fusion of the solid (Asoi,B7/=Afus,B )-These were the assumptions used to derive Eq. 12.5.4 for the freezing-point curve of an ideal liquid mixture. In Eq. 12.5.4, we exchange the constituent labels A and B so that the solid phase is now component B ... 

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