# Lecture 29: Arrhenius Equation and Reaction Mechanisms Overview

The Arrhenius Equation - A frequency factor ﻿$\rightarrow$﻿ Broken into 2 terms

﻿$K = A [e^{-\frac{Ea}{RT}}] = pz [e^{-\frac{Ea}{RT}}]$﻿

﻿$P =$﻿ Probability Factor

﻿$z =$﻿ Collision Frequency

﻿$\ln K = \ln (pz) - \frac {Ea}{Rt}$﻿

﻿$\ln \frac{K_{T_1}}{K_{T_2}} = \frac{Ea}{R} (\frac{1}{T_2} - \frac{1}{T_1})$﻿

﻿$\ln \frac{K_{T_2}}{K_{T_2}} = \frac{\Delta H ^ \circ}{R} (\frac{1}{T_2} - \frac{1}{T_1})$﻿

Reaction Mechanism - The balanced chemical equation provide no information about how a particular reaction occurs (it provides information about the net overall reaction) The process by which a reaction occurs.

This can produce details about the order in which bonds are broken and formed and the changes in the relative positions of atoms during the course of the reaction.

Reaction Mechanism is derived from Rate Law

Overall Reaction - ﻿$H_{2(g)} +2|C|_{(g)} \rightarrow 2 HCl_{(g)}+I_{2(g)}$﻿

﻿$(1) \ H_{2(g)} + |C|_{(g)} \rightarrow HCl + \cancel {HI}_{(g)}$﻿

﻿$(2) \ \cancel{HI}_{(g)} +|C|_{(g)} \rightarrow HCl + I_{2(g)}$﻿

The reactions in this mechanism are elementary steps meaning that they can't be broken down into simpler steps and the molecules actually interact into simpler steps and the molecules actually interact directly in this manner without any other steps.

Molecularity - The number of reactant particles in an elementary step

• Unimolecular step involves one particle
• Bimolecular step involves two particles
• Termolecular step involves three particles

﻿$\Rightarrow$﻿ Only for intermediate steps

#### Rate Laws for Elementary Steps

• Each step in the mechanism has its own rate
• Rate for an overall reaction must be determined experimentally
• But the rate law of elementary step can be deduced from the equation of the step

#### Overall Reaction

﻿$NO_{2(g)}+CO_{(g)} \rightarrow NO_{(g)}+CO_{2(g)}$﻿ Rate ﻿$\overset{obs}{=} K[NO_2]^2$﻿

﻿$(1) \ NO_{2(g)} + NO_{2(g)} \rightarrow NO_{3(g)} + NO_{(g)}$﻿ Rate﻿$﻿= K_4[NO_2]^2 _{slow}$﻿

﻿$(2) \ NO_{3(g)} + CO_{(g)} \rightarrow NO_{2(g)} + CO_{2(g)}$﻿ Rate﻿$= K_2[NO_2][CO]_{fast}$﻿

﻿$*$﻿Observation: Experimentally

﻿$*$﻿Rate observations we can see that ﻿$CO$﻿ has no influence on the rate of the reaction

• First step slower than the second step-larger activation energy
• First step in this mechanism is the rate determined step
• The rate law of this first step is the same as the rate law of the overall reaction
• The activation energy is higher ﻿$\Rightarrow$﻿ Reaction is slow (and opposite)

#### Validation of a Mechanism

1. Elementary step must sum the overall reaction
2. The rate law predicted by the mechanism must be consistent with the experimentally observed rate law