240_l16 - Simple Mixtures Atkins 7th, Ch. 7: Sections...

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Simple Mixtures Thermodynamic Description of Mixtures Partial Molar Quantities Partial Molar Volume Partial Molar Gibbs Energies Significance of Chemical Potential Gibbs-Duhem Equation Thermodynamics of Mixing Gibbs Energy of Mixing Other Thermodynamic Mixing Functions Chemical Potentials of Liquids Ideal Solutions Ideal Dilute Solutions Atkins 7th, Ch. 7: Sections 7.1-7.3; 8th, Ch. 5: Sections 5.1-5.3 Last updated: Dec. 11, 2006; minor correction to slide 21
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p A % p B % ... ' ( x A % x B % ...) p ' p Simple Mixtures We now go from the behavior of simple single substance systems to mixtures of substances. In general, these will still be non-reacting substances and we will be dealing mostly with the energetics of the mixing process itself and to a lesser extent with the types of nonideal interactions which can take place between different substances. We will also start to learn how to deal with liquid solutions, which will increase the arsenal of systems that we know how to deal with. Mainly, we will deal with non-reactive binary mixtures , which have components A and B, making use of the relation: x A + x B = 1 We have already used such mole fractions to describe the partial pressures of mixtures of gases which give rise to a total pressure
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Partial Molar Volume The partial molar volume is the contribution that one component in a mixture makes to the total volume of a sample H 2 OE t O H Add 1.0 mol H 2 O Add 1.0 mol H 2 O Volume increases by 18 cm 3 mol -1 Volume increases by 14 cm 3 mol -1 Large volumes Molar volume of H 2 O: 18 cm 3 mol -1 Partial molar volume of H 2 O in EtOH: 14 cm 3 mol -1 The different increase in total volume in the H 2 O/EtOH example depends on the identity of the molecules that surround the H 2 O. The EtOH molecules pack around the water molecules (i.e., solvate ) differently than how water molecules pack around water molecules: the increase in the molar volume is only 14 cm 3 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
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Partial Molar Volume, 2 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 o C across all possible compositions The partial molar volume, V J , of a substance J is defined as V J ' M V M n J p , T , n ) where n & signifies that all other substances present are constant
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Partial Molar Volume, 3 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) For a binary mixture, the composition can be changed by addition of dn A of A and dn B of B, with the total volume changing by dV ' M V M n A p , T , n B dn A % M V M n B p , T , n A dn B ' V A dn A % V B dn B 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 V ' n A V A % n B V B
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This note was uploaded on 10/24/2009 for the course CHEM 260 taught by Professor Staff during the Spring '08 term at University of Michigan.

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240_l16 - Simple Mixtures Atkins 7th, Ch. 7: Sections...

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