Phase Transitions & Thermochemistry
Thermochemistry:
Study of energy transfer as HEAT
during a chemical reaction
Exchange of energy between
system and surroundings
Calorimetry
Spring 2014
Teaching Material Prepared by L. Valenzano
1
Phase Transitions & Th
Equations of State (EOS)
Initial state
(n = const)
n,T?,P?,V1
I can change V
n,T0,P0,V0
n,T?,P2,V?
n,T3,P?,V?
I can change T
I can change P
Taking n = const I can change T,Prepared by L. Valenzano at the time BUT
P and V one
Spring 2014
Teaching Material
Changes in Entropy: Mixing
Ideal gas within adiabatic walls (q = 0 for the overall process)
1
V1 V2
n1 n2
T1 = T2
P1 = P 2
2
Vtot = V1 + V2
ntot = n1 + n2
Tf = T1 = T2
P1 = P 2
T = const
Spring 2014
U = 0
w=0
Entropy drives the
mixing!
Teaching Material P
Non-Ideal (Real) Gases
PV = nRT PV = RT
V =V
n
Molar Volume
often not good enough
for real gases
Real Ideal
low P
Ideal Real
high P
Spring 2014
Teaching Material Prepared by L. Valenzano
1
Non-Ideal (Real) Gases
What is the origin of the deviation ?
In re
Introduction: Types of Equilibrium
Thermodynamic Equilibrium (TD) is satisfied when
the following three forms of equilibrium are present
Mechanical Equilibrium
No unbalanced forces
acting on or present
within the system
(no acceleration,
no turbolence)
Th
Helmholtz & Gibbs Energies
Lets build the Helmholtz Free Energy A
Lets find conditions for material eq. in a
system held at T = const and V = const
(i.e. dT = 0, dV = 0)
We want to:
1) Work within an irreversible approach to equilibrium;
2) Define the Hel
Reprise: Exact & Inexact Differentials
f ( x, y ) = ax 3 y + by 2
f
f
df ( x, y ) = dx + dy
y
x y
x
f
= 3ax 2 y
x y
f
= ax 3 + 2by
y
x
df ( x, y ) = (3ax y )dx + (ax + 2by )dy
2
Spring 2014
3
Teaching Material Prepared by L. Valenzano
di
Using Maxwell Relationships
Maxwell Relationships are
P
T
=
S V V S
V
T
=
S P P S
P
S
=
T V V T
V
S
=
T P
P T
Spring 2014
Teaching Material Prepared by L. Valenzano
1
Using Maxwell Relationships
Example of usefulness
dH = VdP +
Natural Variable Equations
We want to address the properties of A and G
Well find relations between U, H, A, G, S
Well deal with reversible processes
occurring in closed systems
Processes composed by infinitesimal states at
equilibrium!
All the relations
Helmholtz & Gibbs Energies
Important comments:
dw = -PdV
is the only work weve considered so far,
that is mechanical work (PV work)
There are other forms of work (ex: electrical)
that MUST be included if present
dw = -PdV + dwnon-PV
Spring 2014
Note also
Helmholtz & Gibbs Energies
U
Internal Energy
H U + PV
A U TS
G H TS
Spring 2014
Enthalpy
Helmholtz Energy
Gibbs Free Energy
Teaching Material Prepared by L. Valenzano
1
Helmholtz & Gibbs Energies
U
A U TS
H U + PV
G H TS
They are sum of state functions!
T
Multi-Component Systems: Liquid/Liquid
Simplest case: 2-component systems
binary solutions
Case (1)
How many phases
do we have?
Only 1!
How many DoF?
The liquid occupies
all the volume
Spring 2014
DoF = 2 1 + 2 = 3
Teaching Material Prepared by L. Valenza
Ideal Gases: Gas Laws
All the three laws involve V
BOYLEs law
1
V = const
P
at given n, T
CHARLES law
V = const T
at given n, P
V = const
at given P, T, n
AVOGADROs law
Spring 2014
Teaching Material Prepared by L. Valenzano
1
The Ideal Gas Law
PV = nRT
E
Introduction
The ball reaches the
bottom of the hill but its
still rolling: it has kinetic
energy but not potential
energy anymore
Top of the hill: the ball
has potential energy
but no kinetic energy
The ball is rolling down:
it has both kinetic and
poten
Phase Equilibrium in Single-Component Systems
Component
Unique chemical substance having
specific properties
Systems composed only by one
component: H2O, NaCl, etc
Single-component systems are
chemically homogeneous
Spring 2014
On the other hand
Teaching
Phase Transitions
Among other causes, equilibrium can be
affected by heat
According to the direction of heat
(in/out) equilibrium will shift
One phase will increase in amount and the
other will decrease
Phase transitions!
Spring 2014
Teaching Material Pre
Order & 3rd Law of TD
1
2
is more ordered than
Spring 2014
Teaching Material Prepared by L. Valenzano
1
Order & 3rd Law of TD
Boltzmann (late 1800s): Statistical Thermodynamics
Different definition of entropy
Statistics
System containing N molecules
with
Chemical Changes
Chemical reaction Chemical change
Chemical substances H, U
Chemical reactions H, U
rxn H = H f H i
rxn H = H products H reactants
Spring 2014
Teaching
Same for U, A, G, S Material Prepared by L. Valenzano
1
Chemical Changes
rxn H = H p
Reaction Equilibrium in Ideal Gases
Lets consider the ideal gas reaction
aA + bB cC + dD
At equilibrium
i
i
=0
that is
i
cC + d D a A b B = 0
But each chemical potential
(ideal gas, isothermal process!) is given by
Pi
i = + RT ln o
P
Therefore
o
i
Sprin
Multi-Component Systems: Liquid/Gas
Liquid/Gas solutions
non-ideal!
Raoults law does not apply!
Spring 2014
Teaching Material Prepared by L. Valenzano
1
Multi-Component Systems: Liquid/Gas
Pi xi
Ki
Pi = K i xi
Henrys Law
Henrys Law constant (depends on co
Chem. Eq.: Solutions and Condensed Phases
How are dissolved solutes, liquids and solids
represented in equilibrium constants?
For other phases (not gas) we can define the
activity ai in terms of chemical potentials
i = io + RT ln ai
For the gas phase we j
Gibbs-Helmholtz Equation
Link between G and T useful for dealing with
changes in equilibrium constants
divide by T
G H
S
G H TS
T T
differentiate wrt T
keeping P = const
T
H S
G
=
=
HT 1
T P T T P T P T
(
1
=H
T
T
( )
Spring 2014
P
+T
1
S
P
T
Chemical Potential for Pure Ideal Gas
G
( P, T )
n
G G ( P, T , n)
For a fixed amount of substance
dG = SdT + VdP
Dividing by the amount of moles
dG = d = S dT + V dP
At constant T
Spring 2014
RT
d = V dP =
dP
P
Teaching Material Prepared by L. Val
Temperature Changes
What if T const ?
T 0
We want to determine rH0 for a reaction @T1 and @T2
at P = const (standard condition, P = 1 bar)
If CP is not a function of T:
H
CP =
T P
Tf
dH = CP dT
Ti
If CP is a function of T:
C P = C P (T )
Spring 2014
H
Reaction Equilibrium
Lets consider a gas-phase reaction
A A(g) + B B(g) Y Y(g) + Z Z(g)
We define the EXTENT OF REACTION such that
=
ni ni ,0
0
i
t initial
n A = n A, 0 A
nY = nY , 0 + Y
n B = n B , 0 B
nZ = n Z , 0 + Z
Spring 2014
reactants
Teaching
Electrochemistry: Charges and Coulombs Law
Attraction/Repulsion Forces
between charged particles at distance r
q1, q2
charged particles
Coulomb (C)
q1 q2
F 2
r
Spring 2014
Units of Force?
Newton
meter (m)
We miss something
Teaching Material Prepared by L.
Reversible Isothermal Process for Ideal Gases
By definition
dw = Pext dV
For a reversible process
Pext = Pint
dwrev = PdV
How does this reduce for an ideal gas?
nRT
dwrev =
dV
V
V2
V2
nRT
T
wrev =
dV = nR dV
V
V
V1
V1
What if the process
is isothermal?
Spring 2014
Teaching Material Prepared by L. Valenzano
1
Thermodynamics
What ?
Thermodynamic System
How ?
Physical Variables Math
Laws
Why ?
To understand the behavior of matter
(gases, liquids, solids)
Spring 2014
Teaching Material Prepared by L. Valenza
Single-Component Systems: Phase Diagrams
Useful way to visualize phase transitions:
phase diagrams
Graphical representation of
relative stabilities of phases
under various conditions of
pressure, temperature, volume
3D plot (P, V, T) and 2D plot (P, T)
Sp
Fugacity
It allows us to measure non-ideality of real gases
PV = nRT
2
an
P + 2 (V nb) = nRT
V
PV
2
3
Z=
= 1 + B ' P + C ' P + D' P + .
RT
Spring 2014
PV
B C
D
Z=
= 1+ + 2 + 3 +K
RT
V V
V
Teaching Material Prepared by L. Valenzano
1
Fugacity
G
n