30: Gas-Phase Reaction Dynamics
- Page ID
- 62260
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- 30.1: The Rate of Bimolecular Gas-Phase Reaction Can Be Estimated Using Hard-Sphere Collision Theory and an Energy-Dependent Reaction Cross Section
- This page covers collision frequency in bimolecular gas-phase reactions using the Hard Sphere Model, linking collision frequency to reaction rates and introducing a new reaction cross-section that considers energy requirements. It highlights the model's temperature and energy thresholds while noting deviations from the Arrhenius equation.
- 30.2: A Reaction Cross Section Depends Upon the Impact Parameter
- This page critiques the flawed assumption that all collisions between Q and B particles result in reactions, noting that proper alignment is essential. It discusses the need to modify the reaction cross-section using the line-of-centers model, which takes collision angles into account. Effective collisions depend on the impact parameter, leading to a lower energy available for the reaction than the total kinetic energy.
- 30.3: The Rate Constant for a Gas-Phase Chemical Reaction May Depend on the Orientations of the Colliding Molecules
- This page discusses a revision of the hard-sphere model for particle collisions, highlighting that not all collisions lead to reactions due to insufficient energy and the importance of proper orientation, particularly for non-spherical particles. The traditional model's assumption of spherical particles overestimates effective collisions, leading to inaccuracies in the reaction rate constant \(A\).
- 30.4: The Internal Energy of the Reactants Can Affect the Cross Section of a Reaction
- This page discusses modifications to the collision model to account for the internal energy of polyatomic gas particles, including electronic, vibrational, and rotational components. It notes that molecules in high vibrational states could react without additional translational energy, influencing the reaction cross-section \(\sigma_r\).
- 30.5: A Reactive Collision Can Be Described in a Center-of-Mass Coordinate System
- This page discusses modeling bimolecular reactions of ideal gases with a center-of-mass coordinate system for enhanced accuracy in reaction kinetics. It explains how reactant molecules' kinetic energy is calculated before collisions, distinguishing between the kinetic energy of the center of mass and the relative motion of reactants. The model emphasizes that only the latter impacts the reaction outcome and addresses the conservation of mass and energy throughout the reaction process.
- 30.6: Reactive Collisions Can be Studied Using Crossed Molecular Beam Machines
- This page discusses crossed molecular beam experiments, which involve colliding gas-phase atom or molecule beams to study chemical reaction dynamics. Key features include detecting collisions, analyzing product velocities and angles, and using mass spectrometry for energy insights. Originating from Herschbach and Lee, the method has been enhanced with tools like quadrupole filters and supersonic nozzles, broadening its application.
- 30.7: Reactions Can Produce Vibrationally Excited Molecules
- This page discusses the center of mass reaction model utilized to examine energy distribution in the reaction between fluorine and deuterium. It highlights that for the reaction to be successful, the vibrational energy of \(\ce{DF(g)}\) must be under 165 kJ/mol. The analysis shows that \(\ce{DF(g)}\) can occupy vibrational states ranging from \(v = 0\) to \(4\) while adhering to this energy limitation.
- 30.8: The Velocity and Angular Distribution of the Products of a Reactive Collision
- This page discusses the speed distribution of DF molecules formed from the collision of F and D2, highlighting the connection between products' vibrational energy and their velocity. It notes that vibrational states influence translational energy and speed, analyzing data from crossed molecular beam experiments to explore angular distribution and velocity.
- 30.9: Not All Gas-Phase Chemical Reactions are Rebound Reactions
- This page describes two gas-phase reaction types: rebound reactions, where products bounce back (e.g., \(\ce{D_2}\) with \(\ce{F}\)), and stripping reactions, where products like \(\ce{KI}\) move in the same direction as reactants (e.g., \(\ce{K}\) and \(\ce{I2}\)). Stripping reactions show larger experimental collision cross-sections than predicted and involve electron transfer prior to collision.
- 30.10: The Potential-Energy Surface Can Be Calculated Using Quantum Mechanics
- This page covers Potential Energy Surfaces (PES), which illustrate the potential energy of atomic systems based on their configurations, favoring stable structures at energy minima. It discusses PES in the context of exchange reactions involving hydrogen and deuterium, detailing specific reaction pathways and highlighting transition states.