Chem 444 Spring 2011
Homework Set #4
1)
A chemical reaction takes place in a container of cross-sectional area
100 cm2. As a result of the reaction, a piston is pushed out through 10
cm against an external pressure of 1.0 atm. Calculate the work (in J)
do
Chem 444 Spring 2011
Homework Set #5
1)
a) McQ&S, 20-3
b) McQ&S, 20-4
2)
McQ&S, 20-22
3)
McQ&S, 20-25
4)
Calculate the increase in entropy (J/K) when 2.00 mol of a monatomic
ideal gas (Cv = 3/2 nR) are heated from 300 K to 600 K and
simultaneously expande
Lets look at the sign conventions. The force (pressure) is measured from
the point of view of the external world, the volume (or length) from the
point of view of the system.
w = PV
Initial
Initial
Final
P + V + so work is negative (energy
leaves system
P
Liquid-liquid Solutions
We will extend our knowledge of phase equilibria to multi-component
systems. We must first consider partial molar quantities (initially for
two components).
G now becomes a function of two numbers of moles G (T , P, n1 , n2 )
G
j
of alcohol
Non-ideal Solutions
Intermolecular interactions between different molecules usually are not
the same as the interaction in pure liquids.
1-propanol
EtOH
MeOH
For these three alcohols in water
there are large deviations from ideal
behavior as xR
Two-component phase diagrams in general (Temperature-Composition)
This includes both solid-solid and solid-liquid ones.
These are very important both in chemical and mechanical engineering
practice, and in geology (where they may be at a (constant) high t
Chemical Equilibrium Reacting Multicomponent Systems(26.1-3)
We have been gradually building up to this point:
1) Multiphase single component systems
2) Multiphase multi component systems
3) Now components can react!
Starting with gases consider the gener
One area where activities are very important for equilibrium involves
electrolytes.
Consider CH 3COOH ( aq ) + H 2O ( l ) H 3O + ( aq ) + CH 3COO ( aq )
HAc
Ac
at 298K and P=1bar, K c = 1.74 105 in molarity units
Consider solution that is 0.1 molar in
Microscopic Connection to the Equilibrium Constant
Once again lets return to our generic reaction
v A A ( g ) + vB B ( g ) vY Y ( g ) + vz Z ( g )
A
We showed earlier: dA = SdT PdV + dn for a single component system
n T ,V
A
A
at constant T,V dA =
Kinetic theory of gases
The theory of reactions rates, as well as such things as diffusion,
viscosity, and thermal conductivity, begins with the theory of the
distributions of the velocities of particles in a gas.
Your book treats this in a long convolute
Kinetics, Rate Laws
We began by looking at the the overall ruling principles of kinetics: how
fast molecules move (from Stat Mech) and then went on to look at (in the
roughest hard sphere sense) how fast they collide. Then we looked at a
possible mechanis
What if the reaction is really fast with respect to mixing, so we cant do
conventional measurements? We can get Kc, but can we do more?
Yes. We use relaxation methods (T-jump, Temperature-Jump) studies.
By applying an electric discharge or a laser pulse w
Lets review Transition State Theory.
We consider a reaction . a simple reaction, that is one in which
two molecules collide in the gas phase to make two other
molecules . that is at equilibrium.
Reaction A+B
AB
C+D
AB = activated complex or transition sta
Standard Entropy values
We discussed standard states and standard Enthalpy values in the
last lecture.
Standard Enthalpies of different chemicals require comparison to
the standard states of the elements, to get heats of formation.
Not so standard Entropi
Enthalpy and Standard States, Hesss Law
Most (but not all) chemical reactions are conducted in open vessels,
under constant atmospheric conditions. Changes in enthalpies can be
measured for these reactions.
r H - Enthalpy change for reaction H products H
Is a process spontaneous?
The First Law tells us whether energy is absorbed or released in a
chemical or mechanical process. It can also tell us whether or not a
purely mechanical system can have a spontaneous change.
Consider a weight sitting on a shelf.
U
(T ln(Q)
+ (const ) = k B
+ (const )
T
T
V
is a very simple expression. There is an even simpler one, as explained
S = k B ln Q +
in McQuarrie. Q is for a system that is isothermal : in a heat bath (and constant volume).
Take that bath away and the
Note the complicated T
dependence of the heat capacity of
the solid Benzene. This comes
about due to the different
temperature dependence of the
intermolecular and intramolecular
vibrations. The lower heat
capacity of the gas shows the
weak intermolecular
A different way is to plot the error in the ideal gas law, called the compressibility
factor (ratio of real to ideal molar volume) for lines of constant T vs P
Notice these look somewhat similar in shape, as do the 3D plots shown before.
Since every subst
Problem 1
1a) [4pts] Tell what phases are present in the regions marked W, X, Y, Z
W : Al(s) + liquid
X : Compound A(s)+ Liquid
Y : Compound A(s) + Compound B(s)
Z : Ca(s) + Compound B(s)
1b) [4pts total; 2pts each]
A: From the chart above, we know that t
Thermodynamics of monatomic crystals
We will derive the thermodynamics of monatomic crystals (except the electronic
contribution of metals and semiconductors) from stat mech.
We treat a mole of atoms in a cube, considered as a simple cubic crystal (the ac
Non-ideal gas stat mech, done classically
Consider an atomic gas dilute enough that only two atoms ever interact at once.
We calculate the molecular" partition function of a two-atom system in a box.
( 2mkBT )3
qClassical =
Z 2 where Z2 is the configurati
Statistical Mechanics of Condensed Phases and Highly non-Ideal Gases
1. van de Waals (or Redlich-Kwong) equations of state qualitatively predict gases,
liquids, and critical points
2. Lennard-Jones potential curve qualitatively explain full vdW or R-K equ
Phase Equilibria
Phase diagram for benzene,
P vs T diagram
From this diagram, we can analyze the degrees of freedom of the
system. Within a region of single phase, pressure and temperature
can freely vary. Along a phase boundary line, P=P(T), i.e. the two
Water
Why it is so unique
The properties of water are dominated by the hydrogen
bond.
What determines these properties?
To see that, we should look to the simplest example, the
gas phase water dimer.
Almost but not quite linear H bond
Almost but not qui
Last time we found that the "speed" distribution F(u) in a gas is
3/ 2
2 m
2 mu 2 /( 2 k B T )
F (u ) =
k T u e
B
From this we can obtain easily the following quantities :
Average speed < u > =
0
Root mean square speed
Most probable speed u mp =
8k
Reaction Mechanisms
We can find rate laws experimentally, but we also want to use our basic
understanding of chemistry so that the observed rate laws make sense.
Consider these two reactions:
H 2 ( g ) + I 2 ( g ) 2 HI ( g ) , v ( t ) = k [ H 2 ] [ I 2 ]
Chain Reactions
Chain reactions are common to chemistry and primarily involve free
radicals. From our earlier discussions, what looked like a simple
reaction: H 2 ( g ) + Br2 ( g )
2 HBr ( g )
had an unexpectedly complicated rate law:
1/ 2
k [ H 2 ] [ Br2
.
Problem 1
[0] H sub = H
f usion
+H
vap
We know H vap is around 51.5 kJ/mol so lets calculate H
ing the Clapeyron equation
f usion
us-
H
usion T2 T1
fR
= ln( P2 )
T2 T1
P1
P2 T2 T1
Hf usion = R ln( P1 ) T2 T1
354
Hf usion = R ln( 0.00014 ) 354300
P1
300