Chapter 9

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Chapter 9

The Behavior of Solutions

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9.2 Raoult’s Law and Henry’s Law

(1) Initially evacuated vessel at T

(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.

liq. A

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9.2 Raoult’s Law and Henry’s Law

• r_e(A) α the # of A atoms in the vapor phase, thus, r_c(A) = kp^°_A , and at equilibrium

(9.1)

• Similarly, pure liquid B

(9.2)

liq. A r_e(A) r_c(A)

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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, X_A,(2) the sizes of A & B atoms comparable

(9.3) (9.4)

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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.

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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

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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 r_e(A) to r_e’(A)

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9.2 Raoult’s Law and Henry’s Law

(9.7) (9.8) (9.9)

• A similar consideration of dilute solutions of B in A gives

(9.10)

• (9.9),(9.10) : Henry’ law

r_e(A) > r_e’(A)

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9.2 Raoult’s Law and Henry’s Law

Beyond a critical value of X_A, r_e’(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

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9.3 The Thermodynamic Activity of a Component in Sol’n

• If the component i exhibits Raoultian behavior, then

(9.13)

(9.14) (9.11)

(9.12)

If the vapor above the solution is ideal

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9.3 The Thermodynamic Activity of a Component in Sol’n

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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

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at const. T and P

The partial molar value

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If differentiate,

From the comparison of (9.16) & (9.18)

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9.5 The Gibbs Free Energy of Formation of a Solution

(9.21)

(9.23)

(9.24)

(9.26)

(9.27a) (9.22)

(9.25)

* Molar free E of a solution & partial molar f.e. of solution of composnents w/ free energy as an extensive prop.

For 1 mole of solution

=0 by G-D

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(9.27b)

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* The free E change due to the formation of a solution

pure i

P_i ^oequil. @ T

pure i

P_i ^o> P_i

(a)

(b)

(c)

(d)

decrease to P_i Vapor, P_i ^o

1 mole

condensation evaporation

∆G_(d) = ∆G_(a) + ∆G_(b) + ∆G_(c)

=

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(9.28) pure i

P_i ^oequil. @ T

pure i

P_i ^o> P_i

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or

for 1 mole of solution

The Change in Gibbs Free Energy Due to the Formation of a Solution

(9.29)

(9.30)

(9.31)

(9.32)

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(9.33a) (9.33b)

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9.6 The Properties of Raoultian Ideal Solutions

• Raoultian :

• For an ideal binary A-B solution

(9.34)

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• For the species i occurring in a solution

• For pure i

(9.35)

(9.36)

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(i) The Change in Volume Accompanying the Formation of an Ideal Solution

(9.38) (9.37)

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(ii) The Heat of Formation of an Ideal Solution

• Gibbs-Helmholtz equation

• For the pure component

(9.39)

(9.40)

(9.41)

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(iii) The Heat of Formation of an Ideal Solution

(9.42)

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(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)

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(v) The Entropy of Formation of an Ideal Solution

(4.17)

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(vi) The Entropy of Formation of an Ideal Solution

(9.45)

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(vii) The Entropy of Formation of an Ideal Solution