Ideal and Dilute Solutions 2/21/2016

Master Thermodynamics Equations

Chemical Potential Diffusion from high to low potential. Chemical potential is a Partial Molar Quantity Sum of moles of components

Chemical Potential of a Binary (A & B) Mixture Chem. Potential applied to other variables:

Measures of Composition s = solute ; A = solvent; V = Tot. Vol. of solution. Weight %: Mole Fraction: Molarity: Molality: Different Composition Equations for different Laws

Other Partial Molar Quantities Partial Molar Volume: Partial Molar Enthalpy: Partial Molar Entropy:

Calculation for Partial Molar Volumes V = f(n A, n B constant P & T constant composition

Calculation for Partial Molar Volumes: 100 mL EtOH and 100 mL H 2 O EtOH (A): d = g/mLM = 46.1 g/mol Water (B): d = g/mLM = 18.0 g/mol Calculate moles of each component: Calculate mole fraction of A and use previous Partial Molar Volume curves to get partial molar volumes for both ethanol and water. Calculate Total Volume:

Raoult’s Law & Ideal Solutions Vapor Pressure (VP)  P i (escaping tendency   g) Gas Ideality => No Intermolecular forces Solution Ideality => Uniformity in Intermolecular forces. (Binary: A-A, B-B, A-B all the same) Dalton’s Law

Raoult’s Law & Ideal Solutions

Thermodynamics of Mixing for an Ideal Solution

TD’s of Mixing for an Ideal Binary (A-B) Solution See Mathcad plot

Finding Minimum of ΔG mix curve

Henry’s Law (Solubility of gases in liquids) In dilution solutions, each solute is surrounded by solvent molecules (uniform environment, relatively ‘ideal.’) Positive and Negative deviations from Raoult’s Law Endothermic Mixing versus Exothermic Mixing

Phase Diagrams

The Phase Diagrams of H 2 O and CO 2 Phase Diagrams

Phase Diagrams for Multi-components For 2 components: Need 3 variables ( T, P, composition ) P T Most common plots: VP vs. constant T B. pt. vs. constant P

Phase Diagrams for Multi-components Liquidus Curve: Vapour Curve:

Phase Diagrams for Multi-components Excel Vap-line

Boiling-Point Elevation Molal boiling-point-elevation constant, K b, expresses how much  T b changes with molality, m S : Decrease in freezing point (  T f ) is directly proportional to molality (K f is the molal freezing-point-depression constant): Colligative Properties

Figure 13.22

Solubility ( Conc’n vs. T ) Derivation starting with equilibrium thermodynamics, At equilibrium (constant P & T):

Freezing Point Depression ( T vs. conc’n ) K f = molal freezing point constant, all properties of the solvent A [ units = K kg mol -1 ] Similar equation for  T b

Osmosis movement of a solvent from low solute concentration to high solute concentration across a semipermeable membrane. Colligative Properties Figure 13.23

Osmosis Osmotic pressure, , is the pressure required to stop osmosis: Colligative Properties

Application to Polymeric Solutions

Ideal and Dilute Solutions