1、Chapter 9SolutionsSolution CompositionSolutions(9.1)*A solution is a homogeneous mixture; that is, a solution is a one-phase system with more than one component.The mole fraction xi of species i is defined by (1.6)The (molar) concentration (or volume concentration) ci of species i is defined by The

2、mass concentration i of species i in a solution of volume V is defined by (9.2)*Physical ChemistrySolution CompositionSolutionsThe molarity is the molar concentration of a species for liquid solutions in moles per liter (dm3).The molarity mi of species i in a solution is defined by The solute molari

3、ty mB is (9.3)*SolutionSolvent (A)Solute (B)(1.4)Physical ChemistryPartial Molar QuantitiesSolutionsThe star indicates a property of a pure substance or a collection of pure substances.(9.4)Partial Molar Volumes0 25 50 75 100V (ethanol)/cm310099989796 75 50 25 0V (H2O)/cm3V /cm3Addition of 50.0 cm3

4、of water to 50.0 cm3 of ethanol at 20 oC and 1 atm gives a solution of 96.5 cm3 (Fig. 9.1, left).Physical ChemistryPartial Molar QuantitiesSolutions0 25 50 75 100V (ethanol)/cm310099989796 75 50 25 0V (H2O)/cm3V /cm3(1) different intermolecular forces(2) different packing of molecules(different size

5、s and shapes of the molecules being mixed)(9.5)The total differential of V (9.6)Physical ChemistryPartial Molar QuantitiesSolutions(9.6)The partial molar volume (9.7)*Physical Chemistrynj: the amount of a substance jnij: the amount of all other substances present are constantPartial Molar Quantities

6、SolutionsThe partial molar volume (9.7)*(9.8)Equation (9.6) esPhysical ChemistryV(a)V(b)xVThe partial molar volume is the slope of the graph of the total volume as the amount of j is changed, P, T, amount of other components being constantPartial Molar QuantitiesSolutionsThe partial molar volume (9.

7、7)*The partial molar volume of a pure substance is equal to its molar volume.(9.9)However, the partial molar volume of component j of a solution is not necessarily equal to the molar volume of pure j.(9.10)*Physical ChemistrySolution volume and partial molar volumesSolutionsDifferentiation of (9.12)

8、 at constant T, P, x1, x2, , xr gives(9.12)(9.15)(9.13)Equation (9.8) at constant T and P esAt fixed xi,Physical ChemistrySolution volume and partial molar volumesSolutionsComparison of the expressions (9.13) and (9.15) for dV gives(9.13)Equation (9.12) es(9.15)(9.16)*(9.12)sincePhysical ChemistrySo

9、lution volume and partial molar volumesSolutionsThe change in volume on mixing the solution from its pure components at constant T and P is given by the difference of (9.16) and (9.4)(9.16)*(9.4)(9.17)(9.16)*Mean molar volumePhysical ChemistryMeasurement of partial molar volumesSolutionsPartial mola

10、r volumes can be measured in several ways.With particular values of the parameters a, b, c, and withOne method is to measure the dependence of the volume on the composition and to fit the observed volume to a function of the mole fraction xA by using a computer curve-fitting problem (i.e., by findin

11、g the parameters that give a best fit of a particular function to the experimental data). Once the function has been found, its slope can be determined at any composition of interest by differentiation.Physical ChemistryUsing partial molar volumesSolutionsExample.Calculate the partial molar volumes

12、of ethanol and water in a solution prepared by mixing 1.000 kg of water and 500.0 g of ethanol.The total volume of an ethanol solution at 25 oC containing 1.000 kg of water is found to be given by the expressionwhere m is the molarity and m0 = 1 mol kg-1.Physical ChemistryUsing partial molar volumes

13、SolutionsMethod.Note that First calculate the molarity of ethanol (its molar mass is 46.069) and hence the total volume of the solution. Then determine the partial molar volume of ethanol by differentiation of V with respect to nE, where nE is the amount of C2H5OH in the solution.When the mass of so

14、lvent is 1.000 kg. The partial molar volume of water VW can then be obtained by usingsincePhysical ChemistryUsing partial molar volumesSolutionsAnswer.It follows that the molarity of ethanol in the solution is 10.85 mol kg-1 and hence that m/m0 = 10.85. The total volume of the solution is therefore

15、The amount of C2H5OH in the solution isHence, the volume is 1589 mL. The partial molar volume of ethanol is obtained fromPhysical ChemistryUsing partial molar volumesSolutionsAnswer.At the molarity of the solution , this expression evaluates to 56.75 mL mol-1.Physical ChemistryOther Partial Molar Qu

16、antitiesSolutionsThe partial molar volume (9.7)*The partial molar internal energy (9.18)(9.16)*(9.19)Physical ChemistryOther Partial Molar QuantitiesSolutionsThe partial molar enthalpy / entropy (9.20)The partial molar Gibbs energy / heat capacity(9.21)The partial molar Helmholtz energyPhysical Chem

17、istryOther Partial Molar QuantitiesSolutionsThe partial molar Gibbs energy is especially important since it is identical to the chemical potential (9.22)*If Y is any extensive property of a solution, the corresponding partial molar property of component i of the solution is defined by(9.23)(9.24)*Ph

18、ysical ChemistryOther Partial Molar QuantitiesSolutionsPartial molar quantities are the ratio of two infinitesimal extensive quantities and so are intensive properties. Analogous to (9.8), dY is(9.25)(9.26)* is a function of T, P, and the solution mole fractions. Because of intermolecular interactio

19、ns, is a property of the solution as a whole, and not a property of component i alone.Physical ChemistryRelations between Partial Molar QuantitiesSolutionsFor most of the thermodynamic relations, there are corresponding relations with the extensive variables replace by partial molar quantities. For

20、example, G, H, and S of a solution satisfy(9.28)(9.27)Another example is the first equation of (4.70)(9.29)Physical ChemistryRelations between Partial Molar QuantitiesSolutionsAnother example is the first equation of (4.70)(9.29)Partial differentiation of (9.29) with respect to ni gives(9.20)(9.22)*

21、(9.30)Physical ChemistryRelations between Partial Molar QuantitiesSolutionsSimilarly, partial differentiation with respect to ni of (9.7)(9.22)*(9.31)leads toPhysical ChemistryImportance of the Chemical PotentialsSolutionsThe chemical potentials are the key properties in chemical thermodynamics. The

22、 is determine reaction equilibrium and phase equilibrium. (9.31)(4.88)*(4.98)*(9.30)All other partial molar properties and all thermodynamic properties of the solution can be found from the is if we know the chemical potentials as functions of T, P, and composition.Physical ChemistryMixing Quantitie

23、sSolutionsSimilar to defining(9.31)(9.30)(9.17)(9.32)(9.33)Just asGibbs energy of mixingPhysical ChemistryMixing QuantitiesSolutions(9.31)Taking of (9.32)(9.32)Physical ChemistryMixing QuantitiesSolutions(9.34)(9.35)Similarly, taking of (9.32)Physical ChemistryMixing QuantitiesSolutions(9.35)(9.28)(9.33) (9.27)(9.30)(4.51)Physical ChemistryMixing QuantitiesSolutions(4.51)(9.31)(9.34)(9.35)Taking of (9.32)Physical ChemistryDetermination of Mixing QuantitiesSolutionsLet the amounts of two perfect gases in the two containers by nA and nB, both are