Explain a substances tendency related to the change in gibbs energy for phase changes
A substance will have a tendency to change to a lower gibbs energy
- if phase #1 has a higher gibbs energy than phase #2 the substance will have a tendency to spontaneously change to phase #2
this is why water freezes as ice at T less than 0 C
Fundamental gibbs equation
dG = VdP -SdT
- shows how gibbs energy relates to temperature and pressue if one of the variables is held constant
Fundamental gibbs equation at constant P
dG = -SdT
- as entropy increases gibbs energy decreases as more free energy is associated with the entropy of the system and less is available to do work or drive a process
Fundamental gibbs equation at constant T
dG= VdP
- where gibbs energy increases with increasing pressure as the stored energy of the system increases and more energy is availible to do work or drive processes
True or false?
Molar entropy increases with phase (s–l–g)
True! this is essential for understanding the fundamental Gibbs equation at constant pressure
When two phases are in equilibrium their molar gibbs energies are —
equal
True or false?
The forward and reverse reactions are equal only for the liquid to vapor phase boundary.
False, at all phase boundaries, at any point along the line the foward and reverse rates are equal
Dynamic equilibrium
Two phases in equlibrium transitioning into the other are occuring at an equal rate
Vapor pressure
pressure of the vapor when in equilbrium with the liquid phase
- increases with increasing temperatue as more molecules leave the liquid phase and join the vapor phase
Clapeyron equation
dP/dT= delta trs. H/T* delta trs. V
- an exact expression for the slope of a tangent line to the phase boundary
Chemical potential=
molar gibbs energy
Chemical potentials of substances in equlibrium at a phase boundary must be —
equal
The slope of a phase boundary is—
dP/dT
Describe the solid liquid phase boundary
Usually very steep, positive, and linear
Clapeyron equation for the solid liquid phase boundary
pf = pi + delta trs. H/ delta trs. V * ln(T2/T1)
- ln(T2/T1)= T2-T1/T1 when T2 is close to the value of T1
Describe the vapor liquid phase boundary
not usually as steep as the solid liquid boundary, it is also not linear because there is a logarithmic relationship
Clausius- Clapeyron equation
d(lnP)=delta trs H* dT/RT^2
- lets us predict how the vapor pressure varies with temperature
- pf = pi *e^x
- x= - delta trs H/ R(1/Tf-1/Ti)
liquid vapor phase boundary
Supercritical fluid
forms when the pressure is increased at a temperature past the critical temperature and the vapor will not condense into a liquid despite increased pressure
boiling temperature
the temperature when vapor pressure of a liquid is equal to the external pressure
Solute
what is dissolved, in smaller quantities
‘B’
Solvent
what the solute is dissolved in, in larger quantities
‘A’
Chemical potential for an ideal gas
start with fundamental gibbs equation for derivation
uj = uj (o) + RTln(pj)
True or false?
Chemical potential of an ideal gas increases with increasing partial pressure in the mixture?
True! There is a logarithmic relationship
Raoults law
for ideal solutions when partial vapor pressure of a substance in a mixture is proportional to the mole fraction and its vapor pressure as a pure liquid
pj= xj x pj*
P=PA+ PB
