SIMPLE MIXTURES THERMODYNAMIC DESCRIPTION OF MIXTURES ARYO ABYOGA A ( ) GERALD MAYO L ( ) LEONARD AGUSTINUS J ( )

Simple Mixtures  Often in chemistry, we encounter mixtures of substances that can react together.  Chapter 7 deals with reactions, but let’s first deal with properties of mixtures that don’t react.  We shall mainly consider binary mixtures – mixtures of two components.

Dalton’s Law  The total pressure is the sum of all the partial pressure.  We already used mole fraction to descrice the partial pressure of mixtures of gases which refers to a total pressure

The partial molar volume is the contribution that one component in a mixture makes to the total volume of a sample H2O EtOH Add 1.0 mol H2O Volume increases by 18 cm3 mol-1 Volume increases by 14 cm3 mol-1 Molar volume of H2O: 18 cm3 mol-1 Partial molar volume of H2O in EtOH: 14 cm3 mol-1 The different increase in total volume in the H2O/EtOH example depends on the identity of the molecules that surround the H2O. The EtOH molecules pack around the water molecules, increasing the volume by only 14 cm3 mol-1 Partial molar volume of substance A in a mixture is the change in volume per mole of A added to the large volume of the mixture partial molar volume

Partial Molar Volumes  Imagine a huge volume of pure water at 25 °C. If we add 1 mol H 2 O, the volume increases 18 cm 3 (or 18 mL).  So, 18 cm 3 mol -1 is the molar volume of pure water.

Partial Molar Volumes  Now imagine a huge volume of pure ethanol and add 1 mol of pure H 2 O it. How much does the total volume increase by?

Partial Molar Volumes  When 1 mol H 2 O is added to a large volume of pure ethanol, the total volume only increases by ~ 14 cm 3.  The packing of water in pure water ethanol (i.e. the result of H-bonding interactions), results in only an increase of 14 cm 3.

Partial Molar Volumes  The quantity 14 cm 3 mol -1 is the partial molar volume of water in pure ethanol.  The partial molar volumes of the components of a mixture varies with composition as the molecular interactions varies as the composition changes from pure A to pure B.

The partial molar volume of components of a mixture vary as the mixture goes from pure A to pure B - that is because the molecular environments of each molecule change (i.e., packing, solvation, etc.) Partial molar volumes of a water-ethanol binary mixture are shown at 25 oC across all possible Compositions. The Partial molar volume, Vj, of a substance j define as :

The partial molar volume is the slope of a plot of total volume as the amount of J in the sample is changed (volume vs. composition) Partial molar volumes vary with composition (different slopes at compositions a and b) - partial molar volume at b is negative (i.e., the overall sample volume decreases as A is added)

When a mixture is changed by dn A of A and dn B of B, then the total volume changes by: When a mixture is changed by dn A of A and dn B of B, then the total volume changes by: Partial Molar Volumes If partial molar volumes are known for the two components, then at some temperature T, the total volume V (state function, always positive) of the mixture is

Partial Molar Volumes

 How to measure partial molar volumes?  Measure dependence of the volume on composition.  Fit a function to data and determine the slope by differentiation.

Partial Molar Volumes  Ethanol is added to kg of water.  The total volume, as measured by experiment, fits the following equation:

Partial Molar Volumes

 Molar volumes are always positive, but partial molar quantities need not be. The limiting partial molar volume of MgSO 4 in water is -1.4 cm 3 mol -1, which means that the addition of 1 mol of MgSO 4 to a large volume of water results in a decrease in volume of 1.4 cm 3.

Partial Molar Gibbs energies  The concept of partial molar quantities can be extended to any extensive state function.  For a substance in a mixture, the chemical potential is defined as the partial molar Gibbs energy.

Partial Molar Gibbs energies  For a pure substance:

Partial Molar Gibbs energies  Using the same arguments for the derivation of partial molar volumes,  Assumption: Constant pressure and temperature

Partial Molar Gibbs energies

Chemical Potential

Gibbs-Duhem equation

Molarity and Molality  Molarity, c, is the amount of solute divided by the volume of solution. Units of mol dm -3 or mol L -1.  Molality, b, is the amount of solute divided by the mass of solvent. Units of mol kg -1.

Using Gibbs-Duhem  The experimental values of partial molar volume of K 2 SO 4 (aq) at 298 K are found to fit the expression:

Using Gibbs-Duhem

Thermodynamics of mixing  So we’ve seen how Gibbs energy of a mixture depends on composition.  We know at constant temperature and pressure systems tend towards lower Gibbs energy.  When we combine two ideal gases they mix spontaneously, so it must correspond to a decrease in G.

Thermodynamics of mixing

Gibbs energy of mixing  A container is divided into two equal compartments. One contains 3.0 mol H 2 (g) at 25 °C; the other contains 1.0 mol N 2 (g) at 25 °C. Calculate the Gibbs energy of mixing when the partition is removed.

Gibbs energy of mixing  Two processes: 1) Mixing 2) Changing pressures of the gases.

Gibbs energy of mixing p p

Other mixing functions