16: The Properties of Gases
- Page ID
- 11811
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- 16.1: All Dilute Gases Behave Ideally
- This page discusses ideal gases, highlighting their elastic collisions that produce pressure and deriving the ideal gas law through Newton’s laws. It notes that ideal gases cannot exist as liquids and underscores the importance of interparticle interactions in phase transitions. Additionally, it differentiates between extensive properties, which grow with system size, and intensive properties, which remain constant regardless of system size.
- 16.2: van der Waals and Redlich-Kwong Equations of State
- This page discusses the limitations of the ideal gas law at high pressures and introduces the van der Waals and Redlich-Kwong equations as alternatives for more accurate modeling of real gas behavior. The van der Waals equation adjusts for volume and intermolecular attractions using parameters \(a\) and \(b\). The Redlich-Kwong equation builds on this with temperature-dependent parameters and improved handling of mixtures.
- 16.3: A Cubic Equation of State
- This page covers the relationships between gas pressure and volume described by isotherms, including the van der Waals equation’s application to ideal and real gases, especially CO2. It highlights the critical point and calculations for critical volume and temperature.
- 16.4: The Law of Corresponding States
- This page discusses Van der Waals' theory that all real gases show similar behavior at corresponding states defined by critical parameters. He proposed a universal equation to explain gas behavior, although it has limitations at critical points. More accurate models, like Redlich-Kwong and Peng-Robertson, address these shortcomings.
- 16.5: The Second Virial Coefficient
- This page discusses the second and third virial coefficients, which describe the influence of intermolecular forces on gas behavior and pressure. As gas density rises, deviations from ideal gas behavior are noted through the virial equation of state. The second virial coefficient can be calculated using intermolecular pair potentials or the Isihara-Hadwiger formula for hard convex bodies.
- 16.6: The Repulsive Term in the Lennard-Jones Potential
- This page discusses the Lennard-Jones potential, which models the interaction energy between non-bonding atoms based on their distance, balancing attractive and repulsive forces. It emphasizes the potential's minimum at equilibrium for stability, where repulsive forces dominate at close distances and attractive forces prevail when atoms are further apart.
- 16.7: Van der Waals Constants in Terms of Molecular Parameters
- This page explains the van der Waals equation, which accounts for real gas behavior through molecular volume and intermolecular forces. Using binomial expansion, it connects pressure, volume, and temperature with coefficients a (intermolecular attraction) and b (particle volume).
- 16.E: The Properties of Gases (Exercises)
- This page covers homework exercises from Chapter 16 of McQuarrie and Simon's "Physical Chemistry," focusing on calculations involving gas mixtures, ideal gas laws, and various equations of state like van der Waals and Redlich-Kwong. It includes problems on gas behavior, critical properties, and the application of the Newton-Raphson method for solving cubic equations.
Thumbnail: Motion of gas molecules. (CC BY-SA 3.0; Greg L via Wikipedia)