# 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.

• 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

• 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.