Physical Chemistry for the Chemical and Biological Sciences

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Outline of the Course 1) Review and Definitions 2) Molecules and their Energies 3) 1 st Law of Thermodynamics Conservation of Energy. 4) 2 nd Law of Thermodynamics Ever-Increasing Entropy. 5) Gibbs Free Energy 6) Phase Diagrams and REAL Phenomena 7) Non-Electrolyte Solutions 8) Chemical Equilibrium 9) Chemical Kinetics and Rates of Processes
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Section 7.0. Non-Electrolyte Solutions & Simple Mixtures PART II (Chapter 7 in Chang Text – Most of It!)
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7.8. Real Solutions …………………….….most solutions do not behave ideally Remember …….in a solution we have two components…… solvent and solute In a real (non-ideal) solution – how do we write the chemical potentials of the solute and the solvent ??
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The Solvent Component ……the chemical potential of the solvent in an ideal solution is given by the following equation……….. 1 (l) = 1 * (l) + RT ln x 1 where x 1 = P 1 /P 1 * and P 1 is the vapour pressure of 1 when it is a component of a solution while P 1 * is the equilibrium vapor pressure of pure component 1 at T. ……for a non-ideal solution we write……….. 1 (l) = 1 * (l) + RT ln a 1 where a 1 is the activity of the solvent.
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• non-ideality is the consequence of unequal intermolecular forces between solvent – solvent and solvent – solute molecules • the solvent’s activity can be expressed in terms of vapour pressure as follows: a 1 = P 1 /P 1 * • the solvent’s activity is related to mole fraction (concentration) as follows: a 1 = 1 x 1 where 1 is the activity coefficient. 1 (l) = 1 * (l) + RT ln a 1 1 (l) = 1 * (l) + RT ln 1 + RT ln x 1
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The Activity Coefficient ( 1 ) is a measure of the degree of deviation from ideality: a 1 = 1 x 1 ….solvents obey Raoult’s Law as concentration of solute approaches zero (i.e. x 2 0 ). In this case (i.e. x 1 1 ) the activity of the solvent approaches the mole fraction….. so a 1 x 1 as x 1 1 …..in fact as x 1 1 …… 1 1.
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Solute Component • for ideal solutions the solute and the solvent obey Raoult’s Law • for ideal-dilute solutions (also referred to as non-ideal dilute solutions) the solute obeys Henry’s Law and the solvent obeys Raoult’s Law The chemical potential for the solute according to Raoult’s Law (i.e. for solute in an ideal solution ) is given by: 2 (l) = 2 * (l) + RT ln x 2 = 2 * (l) + RT ln (P 2 /P 2 *)
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The chemical potential for the solute according to Henry’s Law (i.e. for solute in an ideal-dilute solution ) is given by: [ recall: P 2 = K x 2 ] 2 (l) = 2 * (l) + RT ln (P 2 /P 2 *) = 2 * (l) + RT ln [(K x 2 )/P 2 *] = 2 * (l) + RT ln [K/P 2 *] + RT ln x 2 = 2 o (l) + RT ln x 2 = 2 o (l) + RT ln (P 2 /K) where: 2 o (l) = 2 * (l) + RT ln [K/P 2 *]
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For non-ideal solutions (beyond the dilute solution limit) the chemical potential of the solute is commonly given as follows: 2 (l) = 2 (l) + RT ln a 2 where a 2 is the activity of the solute.
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