5 - Jacobus van't Hoff (1852-1911) First Chemistry Nobel...

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1 François-Marie Raoult (1830-1901 ) Jacobus van’t Hoff (1852-1911) First Chemistry Nobel Laureate (1901) [] 1 so A solvent lution A # moles of solute Molarity: A (unit : ) Volume of solut # moles of solute Molar fraction: x ( ) (unitle # moles of solute Molality: m i ss) Total (u mass of solven # of mol t on es A A o A tt n mol n l L V n n m == 1 weight of solute % by wieght = 100 (unitless) weight of solution nit : ) mol Kg × Commonly used measures of composition Simple one-component systems Mixtures of non-reactive substances (for example – liquid solutions) We will focus on the dependence of thermodynamic functions on the COMPOSITION
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2 The partial molar volume 22 + 96.5ml - 50.0m EtOH 50.0ml EtOH . mixt l H O H O ur e ⎡⎤ ⎢⎥ ⎣⎦ (,, , ) B AA A B AB B n V nV T Px VTPxx x =+ 0 20 1 C atm ⎛⎞ ⎜⎟ ⎝⎠ Molar volume of a component depends on T, P and the composition (an intensive property!) Why does the partial molar volume depend on the composition? In pure water, each water molecule is surrounded by other water molecules. In pure ethanol, each ethanol molecule is surrounded by other ethanol molecules. In a water-ethanol mixture, each molecule is surrounded by a both water and ethanol molecules, with the relative proportions dependent on the composition. Since water-water, water-ethanol and ethanol- ethanol interactions are different, the packing of the molecules will depend on the composition. In fact, the effect of the different interactions is not limited to packing, and will show up in other partial molar quantities (partial molar energy, enthalpy, free energy, etc.), which are generally all expected to depend on the composition.
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3 The partial molar Gibbs free energy of components in a mixture (,, , ) B AA A B AB B n G nT P x TPx x x µ =+ The chemical potential of a component depends on T, P and the composition (An intensive property!) , B B G G = = (, ) Gn G T P P == The molar Gibbs free energy of a pure substance The chemical potential () The Fundamental equation of chemical thermodynamics 0 BB d dG VdP SdT n dn =−+ + Constant T and P 0 d n G dn d = +≤ A changes in composition will be spontaneous if it decreases G The rest of this course will be dedicated to the consequences of this equation.
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4 The chemical potential of a component in a gas mixture ' Consta ' nt () l n ( ) ( ) ln ; 1.0bar (standard pressure Dalton's law: ; ) A ideal T P AA A j A A A A ga A A A A P A Bj A s A j B A A dP P dG n RT G P G P n RT P nRT dG VdP S P P GP dT VdP G n PP P P Px P nn dP P P P P ° ° ° °° ° = ⎯⎯⎯⎯→ ⎡⎤ =+ = = ⇒= + ⎢⎥ ⎣⎦ ⇒=+ = × + () () l n l l n nl n ; ( ) A A A AAA A A A nR T P PG P n P PP PR T R T P P P P P T µ µµµ ° ° ° ° ° ° == = + ⎤⎡ = + = Mixing of ideal gases (constant T and P) The unmixed state ( ): l n l n Similarly: ( ) ln ln ln A Pu P A A BB u uR T P u P R T P P T P P Gu n u n u T P P T P P µµ = ° ° →+ + ++ [] [] [] The mixed state ( ): l n () l n ln ln ( ) ln Similarly: ( ) ( ) ln ( ) ( ) ln ln l n l A A A A A B A A B B B m mR T P m P R T x P P RT P P RT x u RT x mu R T x G m nm nu R T n x n x Gu nRT x x x ° ° + = + + =++ + + n B x
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5 - Jacobus van't Hoff (1852-1911) First Chemistry Nobel...

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