Thermodynamics Problem Solving in Physical Chemistry

Study Guide and Map

Kathleen E. Murphy

• Publisher: CRC Press
• Year: 2020
• Print ISBN: 9780367231477
• eBook ISBN: 9781000030280
• Topic: Physical Sciences
• Subtopic: Chemistry
• Index: Chemistry

Thermodynamics Problem Solving in Physical Chemistry: Study Guide and Map is an innovative and unique workbook that guides physical chemistry students through the decision-making process to assess a problem situation, create appropriate solutions, and gain confidence through practice solving physical chemistry problems.

The workbook includes six major sections with 20 - 30 solved problems in each section that span from easy, single objective questions to difficult, multistep analysis problems. Each section of the workbook contains key points that highlight major features of the topic to remind students of what they need to apply to solve problems in the topic area.

Key Features:

• Provides instructor access to a visual map depicting how all equations used in thermodynamics are connected and how they are derived from the three major energy laws.
• Acts as a guide in deriving the correct solution to a problem.
• Illustrates the questions students should ask themselves about the critical features of the concepts to solve problems in physical chemistry
• Can be used as a stand-alone product for review of Thermodynamics questions for major tests.

Workbook

1

Gases and Gas Laws

Key Points – Gas Laws

Ideal gas:	Van der Waals	Virial equation
$P_{\text{ideal}}=\frac{nRT}{V}$	$P_{VdW}=\frac{nRT}{V-nb}-\frac{n^{2}a}{V_{}^2}$	$P_{\text{virial}}=\frac{nRT}{V}\left[1+\frac{nB}{V}+\frac{n^{2}C}{V^2}\right]$
$P_{\text{ideal}}=\frac{RT}{V_m}$	$P_{VdW}=\frac{RT}{V_m-b}-\frac{a}{V_m^2}$	$P_{\text{virial}}=\frac{RT}{V_m}\left[1+\frac{B}{V_m}+\frac{C}{V_m^2}\right]$

• The equation of state: $PV=nRT$ applies to “ideal gases” where there are either no interactions between particles (at low T’s and P’s) or where the attractive forces between the gas particles balance the repulsive forces. The equation can be applied to all gases, independent of chemical identity.
• Real gases show deviations from ideal behavior and introduce factors that depend on the chemical identity of the gas molecule.

The van der Waals equation introduces two important factors, the values of which depend on the chemical identity of the gas:

• A correction for the molar volume the gas particles themselves occupy, represented by the term “b”, which is subtracted from the total molar volume, appears in the first term of the equation.
• The second factor, “a”, is a measure of the attractive forces between the gas molecules, represented by the term “an²/V² or a/V_m²”, which is subtracted from the adjusted first term.
• The a and b values are tabled for each gas as van der Waals constants.

The virial equation describes gas isotherms as polynomials in V or V_m, where the second virial coefficient B, can be related to “a” and “b” from the van der Waals equation. The value of B is very temperature dependent, different for each gas and may be positive or negative. The third factor, “C”, in the equation is rarely needed to define the behavior of a gas.

• The compressibility factor, Z, is a useful parameter with which to determine when a gas is NOT acting ideally, since

Z < 1.0 The gas is not acting ideally and attractive forces dominate. Vm,obs < Videal Z = 1.0 The gas is acting ideally Vm,obs = Videal Z > 1.0 The gas is not acting ideally and repulsive forces dominate. Vm,obs > Videal

$$\begin{array}{l}Z=\frac{P\overline{V}}{RT}=\frac{P{V}_m}{RT}\\ Z=1+\frac{B}{V_m}\\ Z=1+B^{\prime }P+C^{\prime }{P}^2\end{array}$$

The values of Z vary with T and can be determined by comparing observed values of P, V or other gas properties with those predicted by the ideal gas law.

$$Z=\frac{V_{m,\text{obs}}}{V_{m,\text{ideal}}}=\frac{{\overline{V}}_{\text{obs}}}{{\overline{V}}_{\text{ideal}}}\text{OR}Z=\frac{P_{\text{obs}}}{P_{\text{ideal}}}$$

The ideal gas law allows for the determination of molecular weights or molar masses of gaseous species, as well as the density of a gas at any P and T combination, if the chemical identity o...

Table of contents

• Cover
• Half-Title
• Title
• Copyright
• Contents
• Preface
• Author
• Workbook
• Final Answers
• Index