memory aid for final

Lecture 3- Thermochemistry ∆H>0 = Exothermic ∆H<0 = Endothermic ∆ r H º = ∑ ࠵?࠵? ! º #$%& − ∑ ࠵?࠵? ! º $’()* for reaction at different T : ∆ r H º (T 2 ) = ∆ + ࠵? º (࠵? , ) + ∫ ∆ $ ࠵? # º ࠵?࠵? - ! - " ∆ $ ࠵? # º = ∑ ࠵?࠵? #! #$%& − ∑ ࠵?࠵? #! $’()* Lecture 1-Real/Perfect Gas P j =X j P ࠵? = . # . # ° ࠵? ! = . / ࠵?࠵? ! = ࠵?࠵?࠵? ࠵? ! ° = 1- # Low p =attraction Z<1 Virial expansion : ࠵?࠵? ! = ࠵?࠵?(1 + ࠵? ࠵? ! + ࠵? ࠵? ! 2 ) Boyle T: B&C=0 ࠵?࠵? ! = ࠵?࠵?( ࠵? ! ࠵? ! − ࠵? − ࠵? ࠵?࠵?࠵? ! ) Lecture 2-1 st Law ∆U isolated =0 ∆U =q+w w =-p∆V adiabatic: q=0…∆U=w Constant p : w=-pdV … ∆U=q+(-pdV) Constant v : ∆U=q v = C v ∆T Reversible Expansion : w=-p∆V Isothermal Reversible : ࠵? = −࠵?࠵?࠵?࠵?࠵?( . % . & ) Enthalpy : H=U+pV -> perfect gas -> U+nRT Constant p : ∆࠵? = ࠵? # = ࠵? # ∆࠵? Molar heat capacity : ࠵? #! = ࠵? 3! + ࠵? = ࠵? + ࠵?࠵? = 4 - ! Reversible Adiabatic : ࠵? 5 = ࠵? 6 ; . % . & < ,/) ࠵? = 4 ’ /1 = 4 ’# 1 Repulsive >Attractive Lecture 4 -2 nd & 3 rd Law Clausius Inequality : ࠵?࠵? = &8 - → ࠵?࠵? ≥ &8 - Isolated system : dS ≥ 0 Heat from hot source -> cold sink ∆S tot =0 Isothermal Expansion : ∆࠵? *%* = ∆࠵? 9:9 (࠵?࠵?࠵?ℎ) + ∆࠵? 9;$ (࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?) ∆࠵? 9:9 = ࠵?࠵? ln ; . % . & < ∆࠵? 9;$ = −࠵?࠵? ln ; . % . & < Carnot cycle : Hot Isotherm: ∆࠵? , = 8 ( - ( ࠵? < = ࠵?࠵?࠵? < ln . ) . * Adiabat: ∆࠵? 2 = 0 Cold Isotherm: ∆࠵? = = 8 + - + ࠵? ) = ࠵?࠵?࠵? ) ln . , . - Adiabat: ∆࠵? > = 0 8 ( - ( + 8 + - + = 0 ࠵? = −࠵?࠵?࠵? ln . % . & = −࠵? = −(࠵? < + ࠵? ) ) Boltzmann : ࠵? = ࠵? ln ࠵? → ࠵? = ࠵?࠵?࠵?࠵?࠵? ࠵? = # ࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵? ࠵? ! = ࠵? ln ࠵? ∆S with heating : ࠵?O࠵? 5 P = ࠵? # ln - % - & ∆S phase transition : 8 - ./0 = ∆ ./0 @ - ./0 <0=Exothermic T and ∆V : ∆࠵? *%* = ࠵?࠵? .! ln - % - & + ࠵?࠵? ln . % . & T and ∆p : ∆࠵? *%* = ࠵?࠵? #! ln - % - & − ࠵?࠵? ln . % . & ∆ r S = ∑ ࠵?࠵? ! º #$%& − ∑ ࠵?࠵? ! º $’()* Lecture 5- Gibbs and Helmholtz Closed sys heating @Constant p : dq p =dH ࠵?࠵? ≥ &8 1 - ࠵? = ࠵? − ࠵?࠵? --- if Gibbs energy is decreasing at constant p, it is spontaneous Standard Gibbs Reaction: ∆ $ ࠵? = ∆ $ ࠵? − ࠵?∆ $ ࠵? ∆ r G = ∑ ∆࠵? 5 #$%& − ∑ ∆࠵? 5 $’()* Lecture 6- Exact differentials Fundamental eq : ࠵?࠵? = ࠵?࠵?࠵? − ࠵?࠵?࠵? Isothermal expansion : ∆࠵? = ࠵?࠵?࠵? ln # % # & / . % . & Perfect gas : ࠵? ! O࠵? 5 P = ࠵? ! (࠵? 6 ) + ࠵?࠵? ln # % # & Lecture 7- Phase Transitions Chemical potential : µ = ࠵? ! → ∆࠵? = ∆µ∆࠵? Phase rule : ࠵? = 2 + ࠵? − ࠵? where F=degrees of freedom, C=# of components, P= phases at equilibrium ; &A &- < # = −࠵? ! ; &A &# < - = ࠵? ! Clapeyron : &# &- = ∆ ./0 B ∆ ./0 . Fusion : &# &- = ∆ %20 @ -∆ %20 . → ࠵? 5;9 = ࠵? ∗ + W ∆ %20 @ ∆ %20 . X ln - - ∗ Vaporization : &# &- = ∆ ’41 @ -∆ ’41 . → ∆ 3(# ࠵? = ࠵? !(E) − ࠵? !(G) → ࠵? = 1- # Clausius Clapeyron : ln # # ∗ = H∆ ’41 @ 1 ; , - − , - ∗ < = −࠵? (࠵?ℎ࠵?) ࠵? = ࠵? ∗ ࠵? H)<6 Lecture 8- Mixtures A=solvent B=Solute Partial V m : V= ࠵? I ࠵? I + ࠵? J ࠵? J or ࠵?࠵? = ࠵? I ࠵?࠵? I + ࠵? J ࠵?࠵? J Partial Gibbs (µ) : ࠵?࠵? = µ I ࠵?࠵? I + µ J ࠵?࠵? J If composition variables change : if p or T vary : ࠵?࠵? = µ I ࠵?࠵? I + µ J ࠵?࠵? J + ⋯ + ࠵?࠵?࠵? − ࠵?࠵?࠵? Gibbs-Duhem : ࠵?µ J ࠵? J = −࠵?µ I ࠵? I Perfect gas ∆ !6K ࠵? = ࠵?࠵?࠵? (࠵? I ln ࠵? I + ࠵? J ln ࠵? J ) where x A = / 4 / ∆ !6K ࠵? = −࠵?࠵? (࠵? I ln ࠵? I + ࠵? J ln ࠵? J ) Liquid At equilibrium µ A(g) =µ A(l) µ I ∗ = µ I º + ࠵?࠵? ln ࠵? I ∗ ࠵? I ∗ = # * ∗ # º Raoults Law : ࠵? I = ࠵? I ࠵? I ∗ → ࠵? J = (1 − ࠵? I )࠵? J ∗ p=p A +p B If solution obeys : µ I = µ I ∗ + ࠵?࠵? ln ࠵? I Henrys Law : ࠵? I = ࠵? I ࠵? I ∆ !6K ࠵? = ∆ !6K ࠵? + ࠵?∆ !6K ࠵? Lecture 9- Phase Diagrams Ideal sol: A-A, A-B, B-B are the same Excess S : ࠵? L = ∆ !6K ࠵? − ∆ !6K ࠵? 6&’(G ∆ !6K ࠵? 6&’(G = −࠵?࠵?(࠵? I ln ࠵? I + ࠵? J ln ࠵? J ) Excess H : ࠵? L = ∆ !6K ࠵? − ∆ !6K ࠵? 6&’(G ࠵? 6&’(G = 0 Varies with comp : ࠵? L = ࠵?࠵?࠵?࠵?࠵? I ࠵? J ࠵? = ࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵? ࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵? ࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵? ࠵? < 0 ࠵?࠵?࠵?࠵?ℎ࠵?࠵?࠵?࠵?࠵? ࠵? > 0 ࠵?࠵?࠵?࠵?࠵?ℎ࠵?࠵?࠵?࠵?࠵? Excess V : ࠵? L = ∆ !6K ࠵? − ∆ !6K ࠵? 6&’(G ࠵? 6&’(G = 0 Pressure/composition : Total vapour pressure (x A ): ࠵? = ࠵? J ∗ + (࠵? I ∗ − ࠵? J ∗ )࠵? I Total pressure (y A ): ࠵? = # * ∗ # ) ∗ # * ∗ MN# ) ∗ H# * ∗ O: * For amount - Lever rule : ࠵? G68 ࠵? G68 = ࠵? 3(# ࠵? 3(# Azeotrope : at the point both components will evaporate as one component Lecture 10-Activities Ideal : µ I = µ I ∗ + ࠵?࠵? ln ࠵? I Not ideal : µ I = µ I ∗ + ࠵?࠵? ln # * # * ∗ Activity solvent : ࠵? I = # * # * ∗ = ࠵? I ࠵? I Solute : ࠵? J = # ) P ) = ࠵? J ࠵? J Activity coefficient : ࠵? I = ( * K * Std state : µ J = µ J º + ࠵?࠵? ln ࠵? J → ࠵? J = ࠵? J W ࠵? J ࠵? º X ࠵?ℎ࠵?࠵?࠵? ࠵? º = 1 Ideal : ∆ !6K ࠵? = ࠵?࠵?࠵?(࠵? I ln ࠵? I + ࠵? J ln ࠵? J ) ∆ !6K ࠵? = 0 Regular : ∆ !6K ࠵? = ࠵?࠵?࠵?(࠵? I ln ࠵? I + ࠵? J ln ࠵? J + ࠵?࠵? I ࠵? J ) ∆ !6K ࠵? = ࠵?࠵?࠵? ࠵?࠵? I ࠵? J Ion activity ideal: ࠵? ! 6&’(G = µ M + µ H real: ࠵? ! = ࠵? ! 6&’(G + ࠵?࠵? ln ࠵? M ࠵? H mean activity coefficient ࠵?±= (࠵? M ࠵? H ) " ! ࠵? ! = ࠵? ! 6&’(G + 2࠵?࠵? ln ࠵? ± Debeye Huckel: to calculate the mean activity coefficient of salt at low concentrations log ࠵? ± = −|࠵? M ࠵? H |࠵?√࠵? ࠵? = , 2 ∑ Q & Q º 6 ࠵? 6 2 Z= valence cation/anion A=0.509 for (aq) b=molality Lecture 11- equilibrium Gibbs energy reaction : ∆ $ ࠵? = RS RT where ࠵? = ࠵?࠵?࠵?࠵?࠵?࠵? ∆ $ ࠵? < 0 ࠵?࠵?࠵?࠵?࠵?࠵?࠵? ࠵?࠵? ࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵? ∆ $ ࠵? > 0 ࠵?࠵?࠵?࠵?࠵?࠵?࠵? ࠵?࠵? ࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵? Chem equilibrium in perfect gas : µ I = µ I º + ࠵?࠵? ln # * # º ࠵? $ = µ J º − µ I º + ࠵?࠵? ln ࠵? J ࠵? I ࠵? = ࠵? J ࠵? I = ࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵? ࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵? ∆ $ ࠵? = ∆ $ ࠵? º + ࠵?࠵? ln ࠵? ∆ $ ࠵? º = −࠵?࠵? ln ࠵? ࠵? = ࠵? ’8;6G Change in p and T : ࠵? = ࠵? H ∆/7 º 89 Van’t Hoff- how k varies with 1/T : & UV P &W " 9 X = − ∆ / @ º 1 ln ࠵? 2 − ln ࠵? , = − ∆ / @ º 1 W , - % − , - & X