Review for the 2nd Exam
The examination is scheduled for Tues., Oct. 30. The exam will have two sections, like on
the last examination. During the problem solving part, you will again be provided with a
sheet of equations that you may need to solve a particular problem but you may be asked to
derive an eqn. in one or more instance. There will be more eqns. than you need. The
equations and constants that you will be given are listed below. Remember if you set up the
problem correctly you will get major credit, so you may want to set up the problems
without using your calculator and then go back at the end and punch in the numbers.
The review sheets follow. They are words and concepts that should be very familiar to you.
As before, I will take the multiple choice questions from these sheets. Also the problem
solving part will be problems based on concepts taken from the assigned homework, given
on a quiz, and listed on the review sheets. Look over the sheets and ask questions about
them at the review.
Review
Definitions: (The meanings of these words and phrases should be very familiar.
System
Work
Reversible
Heat
Criteria for Exactness
Heat Capacity
Heat
Specific Heat
Law of Conservation of Energy
1st Law of Thermodynamics
Isothermal
Isochoric
Isobaric
Adiabatic
Reversible
State Variable
Path Dependent
Closed System
Expression for dH for Ideal Gas
Isenthalpic
Expression for dU for Ideal Gas
Internal Energy
Molar Internal Energy
Enthalpy
Exothermic
Endothermic
Hess' Law
Enthalpy of Formation
H= U + PV
Standard State for Entropy
dU = q + w
Cp = Cv + nR
Cpm = Cvm + R
Gibb Free Energy of Formation
2nd Laws of Thermodynamics
Carnot Heat Engine & Assumptions
dS = dqrev / T
dS > dqirr / Tsurr
State Function
State Variable
Entropy is a State Function
Srev cycl = ∫cycle dqre /T = 0
S = k ln W
Absolute zero
Efficiency and Carnot Efficiency
3rd Law of Thermodynamics
Absolute Entropy
Heat Engine
A = U-TS
spontaneity criteria based the system
G = H - TS
Gibbs Energy of Reaction
H = U + PV
Gibbs-Helmholtz Eqn
Standard State Conditions
partial molar volume
G = H - TS
Gibbs Duhem eqn.
Phase equilibria
critical point
Chemical Potential
(phase 1) = (phase 2) etc
Clapeyron Eqn
liquid-vapor equilibrium curve
Vaporization
slope of liquid-solid equil line
Raoult’s Law
Graph of Pressure vs mole fraction
nonideal solution
intermolecular interactions of solvent
 = o + RT ln(p/po)
 = o + RT ln a
partial molar Gibbs free energy
Fundamental Law of Thermo
Gibbs Phase rule
triple point
Phase Diagram
reversibility and phase changes
Claussius Clapeyron
Sublimation
Fusion
solution chemical potential, 
Henry’s Law
ideal solution
intermolecular interaction of solute
Colligative properties
activity
Trouton's Rule
Calculations: (you should be familiar with the following in terms of calculations)
Use of Heat Capacity to Determine the Enthalpy Change
Expression for dH and dU for ideal gas
Use of Expressions for Work, Heat, U,H, S, G for different process types (i.e.
adiabatic, reversible, isothermal, etc.) The new one was the adiabatic reversible case.
Calculation of the maximum non PV work and max PV work.
Use of the 2nd Law to test if a process is realizable (spontaneous).
Derivation and use of Equations used to calculate the entropy changes for various processes.
Calculation of the Standard Gibbs Energy of Reaction
Relation of Exactness and State Function and Deriving Maxwell’s Relations
Writing out a differential given information on its variables.
Calculations to find G at a different temp. (either Gibbs Helmholtz or G = H - TS
(what are the assumptions))
Calculations to find G at a different pressure
Use of the definition of the Chemical Potentials
Expression for the molar Gibbs free energy of a gas
Partial Molar volume
Clapeyron or Claussius Clapeyron Eqn to Phase equilibria
Ideal Solutions Calculations and use of Henry's and Raoults Laws, Plot of P vs x A
Overview
General statements that define natural processes talk about the observed efficiencies in
converting heat into work, the direction of heat flow, and the fact that the disorder of the
universe seems to be increasing. The Carnot efficiency tells about the maximum efficiency
realizable for a process which converts heat to work. The expression for the Second Law of
Thermodynamics Stot > 0 for an irreversible process is strictly applicable to the system and the
surroundings. HOWEVER, new thermodynamic state variables, named the Helmholtz Free
Energy and Gibbs Free Energy, were defined to allow one to determine the spontaneity of a
process based on the system properties and the mechanical variables. Thus (dA)T,V < 0 and
(dG)T,p < 0 (closed; PV). Which property tells about the max non PV work? Which tells about the
maximum amount of work the system can do
Know how the expression for the Fundamental Equation of Thermodynamics. It is
essentially a combination of the 1st and 2nd Laws. Remember it was derived based on a
reversible process, but is it applicable to any process within the restrictions of its derivation?
What are the best (natural) thermodynamic variables for U? Be able to show how more
Thermodynamic information comes from the definition of the exact differential and the
exactness criterion. What are Maxwell’s relations?
How are they derived from the equation for dU? What about dG? What are the natural
thermodynamic variables for dG? Be able to write out dG for these variables? These variables
are derived from the basic definition of G=H-TS. (Gsys)T,P tells us about the spontaneity of the
process, and whether the system is at equilibrium. How does it change with P and T? What is
the Gibbs Helmholtz relation? Be able to use it. Does the Gibbs free energy change very much
with a pressure change on a solid or liquid? Why?
What is the fundamental equation of chemical thermodynamics? The chemical potential
of a pure substance is  = o + RT ln(p/po) how does this change for a real gas. In general  =
o + RT ln a where a is the activity. For ideal gas a = p/po. For real gas a = f/po. What is the
fugacity coefficient? What is the activity coefficient? What is chemical potential for ideal
solution? How does the chemical potential of the pure liquid change when a nonvolatile solute is
added to it?
Constants and Equations
U = Q + W
rxno = prod n Hfo - react n Hfo dH = CpdT dU=CvdT
 S = nR ln(Vf/Vi)
S = -nR ln(Pf/Pi)
S= nCpm ln(Tf/Ti)
Strs = trs/Ttrs
S= nCvm ln(Tf/Ti)
Cpm = R + Cvm
rSo=Srxno= prodnSo -reactnSo
 = 1 - Tc/Th
o
o
 = Wnet /Qin S (T2) = S (T1) + T rCp dT/T
S = Qrev/T
o
o
o
o
Grxn = prod n fG - react n fG
Gm = Gm + RT ln(P/Po) G = H - T S
G(pf) = G(pi) + p ∫ VdP (d(G/T)/dT)P = -H/T2
G/T)f - (G/T)i = H (1/Tf - 1/Ti)
j = (G/nj)P,T,n  j = (U/nj)S,V,n
j = (H/nj)P,S,n
j = (A/nj)V,T,n
*
G = -W rev W = -pex V, W = -nRT ln(Vf/Vi), q = C V=nAVA + nBVB
VA = (∂V/∂nA)T,P,nB
G = nAGA + nBGB
GA = (∂G/∂nA)T,P,nB
dU = TdS - P dV H=U+PV G=H-TS A=U-TS dG = VdP - SdT + adna + bdnb
Go=Ho-TSo (dUsys)S,V < 0 (dSsys)U,V > 0 (dGsys)T,,P < 0
(dAsys)T,V < 0
(dHsys)P,S < 0
dH = TdS + VdP
dA = -SdT - PdV
dP/dT =trsH/trsV) dP/dT = trsS/ trsV
ln(p/p*)=(-Htrs/R) (1/T - 1/T*) p=p*exp((-trsH/R) x (1/T-1/T*)) dG=VdP-SdT + adna +bdnb
 = o + RT ln(p/po)
a = a* + RT lnxa
 = o + RT ln a Pb = xbKb
Pb=mKb'
Pa = xaPa*
Tf = iKf m
b= iKbm  = iMRT
ya = Pa/P
P = xBPA*
a = x
*
*
*
P=Pb + (Pa*-Pb )xa
P = Pa + Pb + Pc + Pd + ….
aA = pA/pA
F = C-P+2
R = 8.314 J/(mol K) R = 0.08206 L atm/(mol K) 1atm = 760 Torr 1 atm = 14.7 psi 1atm
= 101325 Pa 1 bar = 105 Pa g = 9.81 m/s2 1L = 0.001 m3 K = oC + 273.15