Chapter 5-Gibbs
Free Energy
Problems:
5.1,3,5,11; concept:5.9,19,21,22,23
1.G-energy to drive chemical reactions
-ΔpG- tabulated
(in table)
-ΔrxnG-
usually calculated
eq.1: ΔrG- ∑v*ΔfGproducts
–∑v*ΔfGreactants
-if 0, reaction
is at equilibrium
-if
negative, reactions proceeds towards right (spontaneous)
-if
positive, reaction will not proceed (non-spontaneous)
2.Phase Transitions
-Phase 1 --> Phase 2:
eq.2:ΔrxnG= n* ΔfGphase
2 – n* ΔfGphase1 (ΔG is molar)
-if ΔGf
phase 2 > phase 1, ΔGrxn is positive (non-spontaneous)
-if ΔGf
phase 1 > phase 2, ΔGrxn is negative (spontaneous)
-if ΔGf
phase 1 = phase 2, ΔGrxn is 0 (equilbrium)
-stable phase- phase with lowest ΔGf
3.Molar ΔGf vs Pressure- ΔGf,m or ΔGm =
Vm*ΔP
-ΔG is
directly proportional to changes in pressure
-larger molar volume- ΔG changes more as pressure changes for substances with larger molar volumes
eq.3:Vm=ΔG/ΔP
-solids,liquids:
final ΔGm= ΔGm,i + Vm(Pf-Pi), where pressure is in bars
-gases:
final ΔGm*(Pf)= ΔGm*(Pi)+RTln(Pf/Pi)
-reactions: ΔGrxn= ∑V*ΔGm,final (products) – ∑V*ΔGm,final
(reactants)
4.Molar ΔGf vs Temperature
-for small
changes in T, entropy values are nearly constant
eq.4:ΔGm=-Sm*ΔT
5.Phase
boundaries- on phase diagrams, show the pressure and temperature combinations
at which 2+ phases are stable
-liquid-vapor
boundary-liquid is in contact with and in equilbrium with a gas of that
composition; pressure of the vapor is its vapor pressure, which substantially
increases with temperature
-solid-vapor
boundary-solid in contact with and in equilbrium with vapor; sublimination
vapor pressure of the solid can be determined in the same way as the liquid
vapor pressure
-slope-
slope of boundary determined by thermodynamic properties
-ΔtrsH-
change of heat during transition between phases (where temperature and pressure
stay constant)
eq.5: ΔP/ΔT=ΔtrsH/T*ΔtrsV
7.Clausius-Clapeyron
equation: Δ(lnP)= ΔvapH/RT2 *ΔT
-liquid-gas boundaries
eq.6:lnP’=lnP+ΔvapH/R*(1/T-1/T’),
where P’ is final P, and T’ is final T
-Table 5.1-
log(P in kPa)=A-(B/T), where A and B are constants (see derivation on p.113)
8.Critical
point-terminal point on liquid-gas boundary curve
-highest
pressure at which liquid can be condensed
-fluid- above
critical point, state of matter is called “fluid”, no boundary
-observed
between states of matter as seen between liquid and gas
9.Normal
boiling point- boiling temperature at 1 atm
-Standard boiling
point- boiling temperature at 1 bar
-Normal
boiling point- melting temperature at 1 atm
-Standard
melting point- melting temperature at 1 bar
10. Phase Rule-
for a system at equilbrium, F=C-P+2
-F=degrees
of freedom, C=number of component, P=number of phases, 2=T+P
-components-
minimum number of species necessary to define all the phases present in a
system
-degrees of
freedom- number of intensive variables (P,T,mol fraction, etc.) that can be
changed without disturbing equilbrium
-triple
point- F=0 (C=1, P=3)
-phase
boundary- F=1 (C=1, P=2)