Properties of Solutions

Concentration Terms Dilute - not a lot of solute. Concentrated - a large amount of solute. Concentration can be expressed quantitatively is many ways: Molarity Molality Percentage Mole fraction

Molarity and Molality The molarity is the number of moles of solute in 1 litre of solution. M = moles of solute / V sol’n (litres) The molality is the number of moles of solute in 1 kg of solvent. M = moles of solute / kg solvent Conversion between the two requires the solutions density.

Partial Molar Thermodynamic Properties Define a partial molar thermodynamic property as Euler’s Theorem

The Chemical Potential We define the chemical potential of a substance as

The Wider Significance of  Shows how all the extensive thermodynamic properties depend on system composition

Thermodynamics of Mixing Spontaneous mixing of two or more substances to form solutions Gibbs energy of the solution must be less than  G(pure components)

The Gibbs Energy of Mixing

The Enthalpy and Entropy

The Ideal Solution T  mix S/n T  mix G/n T  mix H/n 0 kJ/mol XAXA

The Volume and Internal Energy of Mixing

Ideal Solution Def’n For an ideal solution

Raoult’s Law Consider the following system

Raoult’s Law #2 The chemical potential expressions

Raoult’s Law: Depression of Vapour pressure VP of solution relates to VP of pure solvent P A = X A P * A Solutions that obey Raoult’s law are called ideal solutions.

Raoult’s Law Example The total vapour pressure and partial vapour pressures of an ideal binary mixture Dependence of the vp on mole fractions of the components.

An Ideal Solution Benzene and toluene behave almost ideally Follow Raoult’s Law over the entire composition range.

Henry’s Law Henry’s law relates the vapour pressure of the solute above an ideally dilute solution to composition.

The Ideal Dilute Solution Ideal Dilute Solution Solvent obeys Raoult’s Law Solute obeys Henry’s Law

Henry’s Law #2 The chemical potential expressions  J O(H) is the Henry’s law standard state. It is the chemical potential of J in the vapour when P J = k J.

Henry’s Law #3 The Standard State Chemical potential for Henry’s Law When the system is in equilibrium The chemical potential expressions reduce to Henry’s Law

Henry’s Law in terms of molalities The Standard State Chemical potential for Henry’s Law When the system is in equilibrium The chemical potential expressions reduce to Henry’s Law in terms of molalities

Chemical Potentials in terms of the Molality The chemical potential expressions  o J,m = chemical potential of the solute in an ideal 1 molal solution

The Gibbs-Duhem Equation The Gibbs-Duhem gives us an interrelationship amongst all partial molar quantities in a mixture

Colligative Properties

All colligative properties Depend on the number and not the nature of the solute molecules Due to reduction in chemical potential in solution vs. that of the pure solvent Freezing point depression Boiling Point Elevation Osmotic Pressure

Boiling Point Elevation Examine the chemical potential expressions involved

Boiling Point Elevation #2 The boiling point elevation

Freezing Point Depression Examine the chemical potential expressions involved

Freezing Point Depression #2 Define the freezing point depression

Osmosis

The movement of water through a semi-permeable membrane from dilute side to concentrated side the movement is such that the two sides might end up with the same concentration Osmotic pressure: the pressure required to prevent this movement

Osmosis – The Thermodynamic Formulation Equilibrium is established across membrane under isothermal conditions  - the osmotic pressure

The Final Equation The osmotic pressure is related to the solutions molarity as follows

Terminology Isotonic: having the same osmotic pressure Hypertonic: having a higher osmotic pressure Hypotonic: having a lower osmotic pressure

Terminology #2 Hemolysis: the process that ruptures a cell placed in a solution that is hypotonic to the cell’s fluid Crenation: the opposite effect

The Partial Molar Volume In a multicomponent system

Volume Vs. Composition The partial molar volume of a substance slope of the variation of the total sample volume plotted against composition. PMV’s vary with solution composition

The PMV-Composition Plot The partial molar volumes of water and ethanol at 25  C. Note the position of the maxima and minima!!

Experimental Determination of PMV’s Obtain the densities of systems as a function of composition Inverse of density – specific volume of solution

Example with Methanol. Plot volumes vs. mole fraction of component A or B Draw a tangent line to the plot of volume vs. mole fraction. Where the tangent line intersects the axis – partial molar volume of the components at that composition

The Solution Volume vs. Composition

The Mean Molar Volume Define the mean mixing molar volume as V * J – the molar volume of the pure liquid V m = V/n T

The Mean Molar Volume Plot V A- V A * V B- V B *

Infinite Dilution Partial Molar Properties The value of a partial molar thermodynamic property in the limit of zero volume is its infinite dilution value E.g., for the volumes

The Definition of the Activity For any real system, the chemical potential for the solute (or solvent) is given by

Activities of Pure Solids/Liquids The chemical potential is essentially invariant with pressure for condensed phases

Pure Solids and Pure Liquids For a pure solid or a pure liquid at standard to moderately high pressures or a J = 1

Activities in Gaseous Systems The chemical potential of a real gas is written in terms of its fugacity

Define the Activity Coefficient The activity coefficient (  J ) relates the activity to the concentration terms of interest. In gaseous systems, we relate the fugacity (or activity) to the ideal pressure of the gas via

Activities in Solutions Two conventions Convention I Raoult’s Law is applied to both solute and solvent Convention II Raoult’s Law is applied to the solvent; Henry’s Law is applied to the solute

Convention I We substitute the activity of the solute and solvent into our expressions for Raoult’s Law

Convention I (cont’d) Vapour pressure above real solutions is related to its liquid phase mole fraction and the activity coefficient Note – as X J  1  J I  1 and P J  P J id

Convention II The solvent is treated in the same manner as for Convention I For the solute, substitute the solute activity into our Henry’s Law expression

Convention II (cont’d) Vapour pressure above real dilute solutions is related to its liquid phase mole fraction and activity coefficient Note – as X J  0  J II  1 and P J  P J id

Convention II - Molalities For the solute, we use the molality as our concentration scale Note – as m J  0  J (m)  1 and a J (m)  m J