Chapter 9 The Behavior of Solutions 1 9.2 Raoult’s Law and Henry’s Law (1) Initially evacuated vessel at T liq. A (2) spontaneously evaporate until P in the vessel ° reaches the saturated vapor pressure of liq. A, p A, at T (3) a dynamic equilibrium established between the rate of evaporation of liq. A & the rate of condensation of vapor A. 2 9.2 Raoult’s Law and Henry’s Law • re(A) α the # of A atoms in the vapor phase, ° thus, rc(A) = kp A , and at equilibrium (9.1) • Similarly, pure liquid B (9.2) re(A) rc(A) liq. A 3 9.2 Raoult’s Law and Henry’s Law (A) the effect of the small addition of liquid B to liquid A Assume (1) the composition of the surface of the liquid = that of the bulk liquid, XA, (2) the sizes of A & B atoms comparable (9.3) (9.4) 4 9.2 Raoult’s Law and Henry’s Law • From (9.1) and (9.3) gives (9.5) and from (9.2) and (9.4) gives (9.6) • Raoult’s law: the vapor pressure exerted by a component i in a solution = (the mole fraction of i in the solution) X (the saturated vapor pressure of pure liquid i ) at T of the solution. 5 9.2 Raoult’s Law and Henry’s Law • Requirements: the intrinsic rates of evaporation of A and B ≠ f(comp. of the solution) i.e., the magnitudes of the A-A, B-B, and A-B bond energies in the solution are identical 6 9.2 Raoult’s Law and Henry’s Law (B) If A-B >> A-A and B-B and a solution of A in B is sufficiently dilute: A atom at the surface surrounded only by B, A in a deeper potential E well than are the A atoms at the surface of pure liq… difficult to be lifted to vapor, evaporation rate is decreased to re(A) to re’(A) 7 9.2 Raoult’s Law and Henry’s Law (9.7) re(A) > re’(A) (9.8) ’ (9.9) • A similar consideration of dilute solutions of B in A gives ’ (9.10) • (9.9),(9.10) : Henry’ law 8 9.2 Raoult’s Law and Henry’s Law Beyond a critical value of XA, re’(A) becomes composition- dependent. Henry’s law works only over initial conc. range in reality. A-A, B-B attraction greater A-B attraction greater 9 9.3 The Thermodynamic Activity of a Component in Sol’n (9.11) If the vapor above the solution is ideal (9.12) • If the component i exhibits Raoultian behavior, then (9.13) (9.14) 10 9.3 The Thermodynamic Activity of a Component in Sol’n 11 9.4 The Gibbs-Duhem Equation • In many cases, the extensive properties of a component in a multicomponent solution are amenable to exp. measurement ! • The other component’s prop. can be obtained by a general relationship i.e., Gibbs-Duhem Eq. • Q is an extensive molar property 12 9.4 The Gibbs-Duhem Equation at const. T and P The partial molar value 13 9.4 The Gibbs-Duhem Equation If differentiate, From the comparison of (9.16) & (9.18) Gibbs – Duhem Eq. 14 9.5 The Gibbs Free Energy of Formation of a Solution * Molar free E of a solution & partial molar f.e. of solution of composnents w/ free energy as an extensive prop. (9.21) For 1 mole of solution (9.22) (9.23) =0 by G-D (9.24) (9.25) (9.26) (9.27a) 15 9.5 The Gibbs Free Energy of Formation of a Solution (9.27b) 16 9.5 The Gibbs Free Energy of Formation of a Solution * The free E change due to the formation of a solution P o equil. @ T o i Pi > Pi o Vapor, Pi (b) decrease to Pi pure i pure i (a) (c) evaporation condensation 1 mole (d) ∆G(d) = ∆G(a) + ∆G(b) + ∆G(c) = 17 9.5 The Gibbs Free Energy of Formation of a Solution o Pi equil. @ T (9.28) pure i o Pi > Pi pure i 18 9.5 The Gibbs Free Energy of Formation of a Solution The Change in Gibbs Free Energy Due to the Formation of a Solution (9.29) or (9.30) for 1 mole of solution (9.31) (9.32) 19 9.5 The Gibbs Free Energy of Formation of a Solution (9.33a) (9.33b) 20 9.6 The Properties of Raoultian Ideal Solutions • Raoultian : • For an ideal binary A-B solution (9.34) 21 9.6 The Properties of Raoultian Ideal Solutions • For the species i occurring in a solution (9.35) • For pure i (9.36) 22 9.6 The Properties of Raoultian Ideal Solutions (i) The Change in Volume Accompanying the Formation of an Ideal Solution (9.37) (9.38) 23 9.6 The Properties of Raoultian Ideal Solutions 24 9.6 The Properties of Raoultian Ideal Solutions (ii) The Heat of Formation of an Ideal Solution • Gibbs-Helmholtz equation (9.39) • For the pure component (9.40) (9.41) 25 9.6 The Properties of Raoultian Ideal Solutions (iii) The Heat of Formation of an Ideal Solution (9.42) (9.43) 26 9.6 The Properties of Raoultian Ideal Solutions (iv) The Entropy of Formation of an Ideal Solution Eq. (9.44) shows that the entropy of formation of an ideal binary solution is independent of temperature (9.44) 27 9.6 The Properties of Raoultian Ideal Solutions (v) The Entropy of Formation of an Ideal Solution (4.17) 28 9.6 The Properties of Raoultian Ideal Solutions (vi) The Entropy of Formation of an Ideal Solution (9.45) 29 9.6 The Properties of Raoultian Ideal Solutions (vii) The Entropy of Formation of an Ideal Solution 30.