Peter Atkins • Julio de Paula Atkins’ Physical Chemistry Eighth Edition Chapter 5 – Lecture 2 Simple Mixtures Copyright © 2006 by Peter Atkins and Julio de Paula

The Chemical Potential of Liquids Need to know how Gibbs energy varies with composition Recall that at equilibrium: μA (liq) = μA (vapor) Ideal solutions Use * to designate pure substances

Fig 5.10 Eqilibrium between liquid and condensed phases For pure substance A: When B is added: A and B both volatile Combining : Raoult’s law:

Fig 5.11 Ideal binary mixture Definition of ideal solution

Fig 5.12 Near-ideal mixture of benzene and toluene Note: and are straight lines, indicating a nearly ideal solution: which becomes:

Fig 5.13 Molecular basis of Raoult’s law for a volatile solvent and volatile solute solvent molecules

Fig 5.14 Strong deviations from Raoult’s law Notice that Raoult’s law is obeyed increasingly closely as the component in excess (solvent) approaches purity Nonpolar Polar

Ideal-dilute solutions In ideal solutions, both solvent and solute obey Raoult’s law. In real solutions at low concentrations: Solute = PB ∝ Solute Called an ideal-dilute solution Raoult’s law: PA = XAPA* Henry’s Law: PB = XBKB where KB is an empirical constant in units of P

Fig 5.14 Very dilute solution behavior Henry’s law PB = XBKB PA = XAPA*

Fig 5.16 Henry’s law description of solute molecules in a very dilute solution Solvent molecules environment differs only slightly from that of pure solvent However, solute molecules are in an entirely different environment from that of the pure solute solvent

Fig 5.17 Experimental vapor pressures of a mixture of acetone and chloroform

The Properties of Solutions Liquid mixtures of ideal solutions ΔHmix = 0

The Properties of Solutions Liquid mixtures of real solutions Recall that ΔG = ΔH - TΔS Therefore: ΔGmix < 0 or ΔGmix > 0 Depends on relative magnitudes of ΔHmix and ΔSmix and T

Three types of interactions in the mixing process: solute-solute interaction solvent-solvent interaction solvent-solute interaction ΔH1 ΔH2 DHmix = DH1 + DH2 + DH3 ΔH3

Enthalpy changes accompanying solution processes: The enthalpy change of the overall process depends on H for each of these steps Enthalpy changes accompanying solution processes:

Enthalpy is only part of the picture Increasing the disorder or randomness of a system tends to lower the energy of the system Solutions favored by increase in entropy that accompanies mixing

Factors Affecting Gibbs Energy of Mixing can hydrogen bond with water Acetone is miscible in water Figure 13-10-01UN Title: Polar liquids tend to dissolve readily in polar solvents. Caption: Water is both polar and able to form hydrogen bonds (Section 11.2). Thus, polar molecules, especially those that can form hydrogen bonds with water molecules, tend to be soluble in water. Acetone is a polar molecule with the structural formula shown in the figure and mixes in all proportions with water. Acetone has a strongly polar C=O bond and pairs of nonbonding electrons on the O atom that can form hydrogen bonds with water. Notes: Keywords: ΔGmix < 0 Hexane is immiscible in water C6H14 ΔGmix > 0 H2O