Phase – homogeneous part of a substance. Phase transition – spontaneous change of one phase into another. Transition Temperature – T at which two phases are in equilibrium.  G tr = 0. The chemical potential of each component is the same in each Phase (in which it is present). Metastable phases – thermodynamically unstable phases that persist due to slow transition kinetics. Vapor pressure – The pressure of the vapor of a component that is in equilibrium with a condensed phase containing that component. P vp = f(T) Component – A distinct chemical entity in a system. P T.. solid liquid gas sc fluid

Critical T – T at which density of liquid = density of vapor and surface disappears. Phase above T c and P c is supercritical fluid (has density of liquid with flow properties of gas). Triple point – T and P at which solid, liquid, and vapor phases are all in equilibrium with each other. A single value of P & T. Degrees of freedom (f) – the minimum # of variables that must be specified such that all variables of the system have only a single possible value. P T.. solid liquid gas sc fluid

Triple point – T and P at which solid, liquid, and vapor phases are all in equilibrium with each other. A single value of P & T. P T.. P = 1 atm Melting point – T at which the liquid & solid phases coexist in equilibrium. T mp = f(P). If P = 1 atm, then normal melting point (nmp). If P = 1 bar then standard melting point.. Boiling point – T at which the vapor pressure of a liquid = external P. T bp = f(P). If P = 1 atm, then it is called the normal boiling point (nbp).. solid liquid gas sc fluid

Chemical Potential (c = 1)  = G m = (dG/dn) T,P phase 1 (  1 ) phase 2 (  2 ) For phase change (1 →2) dG =  p  p dn p =  1 dn 1 +  2 dn 2 since dn 1 = - dn 2 …. dG = (  2 –  1 ) dn 2 A substance will move from The phase with the higher  to the phase with a lower . at equilibrium,  G = 0, and  1 =  2. Then dn 2 is (+) and dG will only be (–) if (  2 –  1 ) is negative and ….  2 <  1. Any absent phase must have a higher value of  than the phases that are present. Otherwise that phase would be forming.

p = # of phases PHASE RULE c = # of components (c ind ) r = # of reaction equilibria a = # other relationships f = c ind - p + 2 c ind = c – r - a f = # of degrees of freedom Degrees of freedom (f) – the minimum # of variables that must be specified such that all variables of the system have only a single possible value.

PHASE RULE c = # of components (c ind ) r = # of reaction equilibria a = # other relationships f = c ind - p + 2 c ind = c – r - a Pure H 2 O (l) how many components? H 2 O ↔ H + + OH - c = 3, r = 1 Charge balance [H + ] = [OH - ] a = 1 f = = 2 c ind = 3 – 1 – 1 = 1 6.1

One component (pure substance)  = G m = (dG/dn) T,P Degrees of freedom (f) – the minimum # of variables that must be specified such that all variables of the system have only a single possible value. A substance will move from The phase with the higher  to the phase with a lower . At equilibrium,  G = 0 and  1 =  2. Phase rule f = c ind - p + 2 c ind = c – r - a P T.. solid liquid gas sc fluid

P T vapor liquid solid scf P atm TcTc PcPc f = = 2 f = = 1f = = 0 P atm nmpnbp Triple point

P T vapor liquid solid scf f = = 2 f = = 1f = = 0 P atm nmpnbp Triple point f = c ind - p + 2 c ind = c – r - a

P T vapor liquid Ice I K K K atm K atm H2OH2O (dG/dP) T = V & d  G =  V dP Higher P favors smaller V (dG/dT) P = -S & d  G = -  S dT Higher T favors greater S ice skating

P T I II V liquid III VI VII VIII Water Phase Diagram at High P Which solid is more dense? a) VIII b) VI c) V d) I Which solid has the lowest entropy? a) II b) V

Sulfur Phase Diagram Rhombic Monoclinic Liquid Gas P T Which solid is more dense? a) rhombic b) monoclinic

P T vapor liquid solid P atm CO K atm 194.7K 304.2K 72.9 atm scf

P T vapor liquid solid scf slope = (dP/dT)  s =  l  s + d  s =  l + d  l

d   = d   apply Gibbs equation for dG m (= d  ) d  = -S m dT + V m dP sub into above for each phase -S m,  dT + V m,  dP = -S m,  dT + V m,  dP isolate T and P terms dP/dT =  S tr /  V tr  S tr =  H tr /T dP/dT =  H tr /T  V tr Clapeyron Equation (e.g. H 2 O) (S m,  - S m,   dT = (V m,  – V m,  ) dP rearrange Clausius-Clapyeron Equation for solid/liquid  vapor assume  V m = V(gas) = RT/P  H m = cst over T d(lnP)/dT ~ -  H m /RT 2 d(lnP)/d(1/T) = -  H m /R   =    and   + d   =    + d    meaning of phase transition line

substancenbp (K)  H vap (J)  S vap (J) water , methanol , ethanol , IPA , acetone , chloroform33431, benzene , toluene , CO 2(sub) , Trouton’s Rule:  S tr =  H tr /T &  S vap ~ 85 J mol -1 K -1 - marked deviations occur for substances with stronger intermolecular forces Clausius-Clapyeron Equationd(lnP)/d(1/T) = -  H m /R What is the vapor pressure of water at 300K? Which has higher vapor pressure at 300K? Water or IPA?