Study Guide
...for taking the ACS "Physical Chemistry Thermodynamics" exam.
Test circumstances
- 50 multiple choice questions
- Score is based only on # of correct answers: no penalty for guessing, so answer every question.
- 100 minutes.
- Graphing calculators and calculators with programmable memory are not allowed. Scratch paper is allowed, but will be collected at the end of the test.
Information available to you during the test
- van der Waals equation of state,
- values of constants like $R$, $k_B$, $N_A$. Though gas constant $R=8.3145$ J/K/mole: *not* 8314 J/K/kmole, as we've been using.
- Uses the same sign convention that we have used: Work, $\delta W>0$, is positive when it's done by the system on the surroundings. Heat, $\delta Q >0$, is positive when heat from the surroundings flows in to the system.
ACS exam preparation guide
I've placed my copy of the ACS Physical Chemistry Study Guide on reserve in the Good Library. The Physical Chemistry Study Guide covers three broad areas:
- Thermodynamics
- Kinetics
- Quantum Chemistry
You will be taking the Thermodynamics exam, so you may disregard the sections on Kinetics and Quantum Chemistry.
Advice from students past
- Make sure you're familiar with rate constants! (2 comments)
- Know how to use those enthalpy / gibbs / entropy of formation
Outline of our course
Exact vs inexact differentials
- What does it mean for a variable to have an exact or inexact differential? Path independence, dependence only on initial and final conditions...
- Which thermodynamic quantities are exact or inexact.
- Pfaffian of a function $f(x,y)$ of several variables: $$df = \left(\frac{\del f}{\del x}\right)_y dx +\left(\frac{\del f}{\del y}\right)_x dy.$$
- Property of an exact differential: $$\[\frac{\del}{\del y}\left(\frac{\del f}{\del x}\right)_y \]_x = \[\frac{\del}{\del x}\left(\frac{\del f}{\del y}\right)_x \]_y .$$ You can use this to derive the Maxwell-type relations from Table 8-1.
Ideal gas
- Special behaviors of ideal gases (e.g. $U$ depends only on $T$...)
- Heat capacities of monoatomic and diatomic gases.
Processes and diagrams of processes
- Isochoric, isobaric, isothermal, adiabatic.
- Adiabatic processes for ideal gas: $Pv^\gamma=$constant.
- Identifying and characterizing processes from $P-V$ (and other) plots.
- Going back and forth between:
Process diagrams $\Leftrightarrow$ process descriptions. - Calculations of work and heat from common processes--usually involves some integration.
- The Carnot cycle, and maximum possible efficiency.
- Interpreting phase diagrams.
First and second law
- $$dU=T\,dS-P\,dV$$
- Calculating entropy changes: for typical processes, for heat reservoirs.
- Content of 2nd law regarding spontaneous processes, and system/surroundings.
Characterizing substances
- Heat capacities $C_v$ and $C_P$. Relationship to energy $U$ and enthalpy $H$.
- Mayer's relationship between $C_p$ and $C_v$, and connection to the $\gamma$ constant that shows up in adiabatic processes involving ideal gases.
- Using $\beta$ and $\kappa$.
- Heats (enthalpies) of formation, of vaporization.
van der Waals gases and phase transitions
- Can you sketch isotherms above/below the critical temperature on a $P-V$ diagram?
- The coexistence region of the phase diagram: Adding heat at constant pressure changes proportions of matter in liquid/vapor phase, but not temperature.
- Meanings behind $a$ and $b$ constants in vdW gases.
Thermodynamic potentials
- Relationships of $U$, $H$, $F$, $G$.
- Wouldn't hurt to be able to come up with the content of table 8-1.
Gibbs energy
- $G$ and chemical potential $\mu=G/n=g$.
- Relations between chemical potentials in a chemical reaction (See Carter, eq 9.48).
- Criteria for diffusive (and other) equilibria.
- Meaning of notation like $\Delta H_f^0$, $\Delta G_r^0$.
- Gibbs energy and spontaneity (direction of a chemical reaction). Neither $\Delta H_r^0$, nor $\Delta S_r^0$ alone determine direction of a reaction.
- How reaction constants change with temperature: See my equation (25) under Chemical processes and following.
- Reaction equilibrium constants, under standard conditions.
Atomic theory and equipartition of energy
- Connection of pressure with atomic phenomena.
- Finding quantities like $\bar{v}$ or $\bar{v^2}$ given a probability distribution $f(v)$.
- Equipartition of energy: $\frac{1}{2}k_BT$ for each energy degree of freedom. And how you use this to reason for a monoatomic ideal gas that: $$\frac{3}{2}k_BT=\frac{1}{2}m\bar{v^2}.$$
- You don't need to memorize the Maxwell-Boltzmann distribution, but you should have a qualitative recollection of how it changes with temperature.
Statistical mechanics
- The number of microstates $w_k$ in a macrostate labelled with index $k$.
- The basic postulate of stat. mech. that all microstates of an isolated system are equally probable.
- Relationship to Thermodynamic probability:$p_k=w_k/\Omega$.
- Degeneracy.
- Counting states in systems with a small number of energy levels.
- Counting states for assemblies of identical vs non-identical particles.
- Classical entropy: $S=k\ln w$.
Energy level diagrams
- as illustrated by particle-in-a-box, how the energy levels change with the volume of the system.
- How the population of different energy levels changes when the temperature changes.
- Connection of number of energy levels and degeneracy with system entropy.