30: Gas-Phase Reaction Dynamics
- Page ID
- 11826
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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
- A simple model for gas-phase reactions considers the reaction to occur between two hard, spherical particles. Although an oversimplification, this model allows us to develop an equation describing the reaction kinetics that we can improve upon with further modifications of the model.
- 30.2: A Reaction Cross Section Depends Upon the Impact Parameter
- In the previous section, it was assumed that all collisions with sufficient energy would lead to a reaction between the Q and B particles. This is an unrealistic assumption because not all collisions occur with a proper alignment of the particles.
- 30.3: The Rate Constant for a Gas-Phase Chemical Reaction May Depend on the Orientations of the Colliding Molecules
- In the previous section, the simple hard-sphere model for collisions was modified to take into account the fact that not every collision of particles occurred with sufficient energy to result in a reaction. The line of centers model assumed that all colliding particles were spheres, yet we know that this is definitely not the case. Thus, we need to modify the collision model to factor in the orientation of non-spherical particles.
- 30.4: The Internal Energy of the Reactants Can Affect the Cross Section of a Reaction
- To this point, we have developed a collision model that incorporates considered the kinetic energy of the colliding particles, the cross-section of the impact of the particles, and the relative orientation of the particles. With each added factor, the model has more closely described experimentally obtained results. In this section, we will add the internal energy of the particles to the model.
- 30.5: A Reactive Collision Can Be Described in a Center-of-Mass Coordinate System
- We will apply a center-of-mass coordinate system to the bimolecular reaction of ideal gases to develop an improved model for reaction kinetics that produces theoretical values that more closely represent experimental results.
- 30.6: Reactive Collisions Can be Studied Using Crossed Molecular Beam Machines
- Crossed molecular beam experiments are chemical experiments where two beams of atoms or molecules are collided together to study the dynamics of the chemical reaction. These experiments can detect individual reactive collisions as well as determine the distribution of velocities and the scattering angle of the reaction products.
- 30.7: Reactions Can Produce Vibrationally Excited Molecules
- In this section, we discuss the distribution of a fixed total collision energy between the internal energy of the products and the translational energy of the products in the reaction of an F atom with a deuterium molecule to form a D atom and a DF molecule. Specifically, we will look at the vibrational states of the DF molecule that may be populated.
- 30.8: The Velocity and Angular Distribution of the Products of a Reactive Collision
- This section describes how data from crossed molecular beam experiments allow us to describe the velocity and angular distribution of particles produced by a simple bi-molecular collision. As noted in the previous section, the internal vibrational energy of the products will affect the velocity and distribution.
- 30.9: Not All Gas-Phase Chemical Reactions are Rebound Reactions
- In the previous section, we studied a rebound reaction in which the vast majority of DF molecules bounce off from the collision with D2 back toward the general direction from which they came. In this section, we will look at reactions in which a majority of the product molecules continue moving on after the collision in the same direction that the precursor reactant molecules were going, and reactions in which the products disperse equally in both forward and reverse directions.
- 30.10: The Potential-Energy Surface Can Be Calculated Using Quantum Mechanics
- In this final section on reaction dynamics, we will include the potential energy of the reacting molecules in our attempt to describe the path from reactants to products. This new energy term will lead us to the development of the transition state, the energy barrier between the reactants and the products.