Chem 444B Homework Set #7 - Solutions DUE: Friday, March 14, 2008
1) The partial molar volumes of acetone (MM=58.08 g/mol) and chloroform (CHCl3, MM=119.37 g/mol) in a mixture in which the mole fraction of CHCl3 is 0.4693 are 74.166 cm3/mol and 80.23
Liquid-liquid Solutions Ideal and Miscible(Chpt 24.1-4) We will extend our knowledge of phase equilibria to multi-component systems. We must first consider partial molar quantities (initially for two components). G ( T , P, n1 , n2 ) so G j = G j = partia
Partition Functions and Ideal Gases (Chapter 18.1, 2) As we discussed last time, for gases where the number of available eigenstates is greater than N we can write N q ( V , ) indistinguishable! Q ( N ,V , ) = N! We will explicitly determine the molecular
Going Beyond U and CV (17.6, 7, 8)
So far we have considered the energy and heat capacities of two systems: perfect gases (monatomic & diatomic) and perfect atomic crystal.
Again, looking ahead a couple of weeks, we note E j Pj ( N ,V ) = = Pressure in th
Partition Functions (17.3, 4, 5)
(Believe it or not)
There is more to life than monatomic ideal gases.
In Chapter 18 we will derive the details, but for now lets consider an ideal diatomic molecule (rigid rotor harmonic oscillator approx.). The molecular
Boltzmann Factor (17.1, 2) In Chem 442, we gave a brief introduction to temperature and the population of Quantum States. With bulk measurements of ~1023 molecules, how do we describe the distribution of these molecules in energy levels from our Q.M. solu
Why do gases attract? (16.6, 16.7) For gas molecules, repulsion is (relatively) easy to explain: electron cloud (charge density) overlap (for closed shell systems) gives rise to a strong repulsive force (~1/r12 or hard sphere). But what causes attraction?
Virial Coefficients (16.5) Recall from the past two lectures: Z = PV = Compressibility Factor RT For T Tc ( TR 1) , Z<1 at a given pressure, suggests a significant drop in V from 'ideal' behavior. 1 Expand Z as a polynomial in ( ): V B2V ( T ) B3V ( T ) P
Equations of State How far can we push it? (16.3,16.4) Consider the vdW equation of state: a P + 2 ( V b ) = RT ( PV 2 + a ) ( V b ) = RTV 2 V
PV 3 ( RT + bP ) V 2 + aV ab = 0 RT 2 a ab 3 V b + = 0 Cubic equation in V ( 3 roots ) V + V P P P Figure shows
Equations of state (Chapter 16.1, 16.2) Ideal and Non-Ideal Gases Chem 442: What did you learn (I hope!) Microscopic Properties of Matter Quantum phenomena Energy levels: atoms, diatomics, polyatomics Electronic, Vibrational, Rotational Degrees of Freedom
Partition Functions for Molecules (18.3-18.8) Moving beyond atoms to molecules, we have two more independent types of degrees of freedom: vibration and rotation. = trans + rot + vib + elec and accordingly: q ( V,T ) = qtrans qrot qvib qelec q ( V ,T ) and
Thermodynamics 1st Law (Chapter 19.1- 3) There are three basic laws of Thermodynamics developed and formulated ~ two centuries ago. It is a classical theory, developed completely independent of atomic and molecular theory. It is remarkable to note that th
More Thermodynamics (19.4-19.9)
As we have already noted for any ideal gas U=U(T) depends on temperature only. So, for an isothermal process: U=0 for an ideal gas. This implies q+w=0, or -q=w, or - q= w Furthermore, if the process is reversible: V2 and: q
Phase Equilibria(Chapter 23) We will begin to look at phase diagrams, initially for pure materials to understand the relationships between various phases. Phase diagram for benzene
Fig 23.1
From this diagram, we can analyze the degrees of freedom of the s
Standard States, Non-ideality and Gibbs-Helmholtz(22.6-8) In the last two lectures we began to develop tools for evaluating thermodynamic properties of non-ideal gases. Note that S 0 's are reported for ideal gas behavior (using stat. mech methods). This
Maxwell Relations and Non-ideality(22.3-5) There are lots of mathematical tricks and games we can play U U dU = TdS PdV = dS + dV S V V S U U T = and P = S V V S but since V T then V U U = S V S S V S V P = this is a Maxwell relation S S V
P S Similarly
(Free) Energies: Helmholtz and Gibbs(Chapter 22.1,22.2) For an isolated system, dS>0 spontaneous process occurs. But how is an open beaker isolated? It isnt, so we must consider S of the surroundings as well. Then, Suniverse= Ssurr+ Ssys>0 will determine
The Third Law of Thermodynamics(Chapter 21) Since entropy is related to motion/disorder (and is sometimes induced by heat), it will be useful to explore this connection. As we have seen: dU=TdS-PdV U U and formally we can write dU ( V , T ) = dT + dV T 2
More Entropy (20.6-8)
Applications of thermo are manifold. Lets return to our example from Lecture 13: As we complete the reversible cycle = 0 = qcyc + wcyc dU The area inside the lines is the work done by the system on the surroundings over the entire cy
Spontaneity!(20.4-5) Remember the Zeroth Law: heat flows from a warm to a cold body (spontaneously!). Consider two isolated systems A and B at different temperatures. isolated Remember what isolated means? (no heat, no matter flow) V ,T V ,T
A A B B
isola
Welcome to Entropy (20.1-3) 1st Law tells us whether energy or enthalpy is released or absorbed in a chemical process. It does not tell us whether a process will occur spontaneously. Well, what does make a process spontaneous? 1st thought: energy (or enth
Enthalpy and Chemical Reactions (19.10-12) Most (but not all) chemical reactions are conducted in open vessels, under constant atmospheric conditions. Changes in enthalpies can be measured for these reactions. (sometimes called thermochemistry, at least i
Chemistry 444
Spring 2009
Hour Exam #1
Monday, February 16, 2009
Name _
1.
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20
2.
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10
3.
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20
4.
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20
5.
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30
Total _
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100
50 minutes!
General Instructions and Information:
1. DO NOT START THE EXAM YET!
2. Calculators are not allowed for this
5.
Industrially the gas phase reduction of ethyne to ethene (selectively) is an
important process in purifying ethene feedstock before the synthesis of
polyethene. The equation is as follows:
C2H2 (g) + H2 (g) <-> C2H4 (g)
Assuming that you start with n0