Module 8.1: Reaction Rates

8.1.1 Introduction

I Reaction rate: a quantity that illustrates how fast a reaction occurs through the change in concentration of the reactants or products over time

1. reaction rate is analogous to velocity in physics.

   1. average reaction rate: the change in molar concentration over a time interval $\textrm{Rate} = \frac{\Delta[\textrm{A}]}{\Delta \textrm{t}}$ (Eq. 125)

   2. instantaneous rate: the reaction rate at a given instant $\textrm{Rate} = \frac{\textrm{d}[\textrm{A}]}{\textrm{dt}}$ (Eq. 126)

   3. if the time interval approaches zero, the average reaction rate becomes the instantaneous rate.

2. in chemical kinetics, it is convention to keep all rates as positive values

3. units in chemical kinetics are very important.

   1. It is best practice to use $\textrm{mol} \textrm{L}^{-1}$ instead of $\textrm{M}$ to check for any errors

II reactants and products from the same reaction may have different rates

1. For example, in a hypothetical reaction $2\textrm{A} \rightarrow \textrm{B}$, when $2 \textrm{M} \textrm{s}^{-1}$ of $\textrm{A}$ is consumed, then $1 \textrm{M} \textrm{s}^{-1}$ of $\textrm{B}$ would be produced.

2. You nust report the species for reaction rates

3. unique rate ($\nu$): Reaction rate that can be reported without specifying the species $\nu = \frac{1}{\nu_{J}} \frac{\Delta [\textrm{J}]}{\Delta \textrm{t}}$ (Eq. 127)

4. $\nu_J$ represents the stoichiometric numbers in an equation; they possess positive values for product coefficients and negative values for reactant coefficients.

5. it is still necessary to report the chemical equation

III There are many ways to measure reaction rates:

1. spectrophotometry: measuring the absorption of light to monitor concentration

   1. spectrophotometry heavily relies on Beer-Lambert law: $\textrm{log} \frac{\textrm{I}_{0}}{\textrm{I}}= \epsilon [\textrm{J}]\textrm{L}$ (Eq. 128)

      ($\textrm{I}_{0}$ and $\textrm{I}$ are the incident and transmitted intensities, $\epsilon$ is molar absorption constant, and $\textrm{L}$ is path length)

   2. We always use this form of Beer-Lambert's law: $\textrm{A} = \epsilon[\textrm{J}]\textrm{L}$ (Eq. 129)

2. rapid reactions often use the stopped-flow technique which rapidly injects reactants into a mixing chamber and monitors the sudden change in concentration

8.1.2 Rate Laws and Reaction Order

IV The rate of a reaction is often related to the concentrations of its reactants

1. rate law: expresses the rate of reaction in terms of concentrations of the species in the overall reaction. An example of rate law for the reaction $\textrm{A} + \textrm{B} \rightarrow \textrm{P}$ is given below: $\nu = \textrm{k}_{r}[\textrm{A}]^{n}[\textrm{B}]^{m}$ (Eq. 130)

2. rate constant ($\textrm{k}_{r}$): A constant value that is independent of concentration (or pressure, if gas-phase), but dependent of temperature

   1. The rate constant will always ensure that the final units in a rate law is $\textrm{M} \textrm{s}^{-1}$

   2. If the reaction is gas-phase, then the rate constant will always ensure that the final units in a rate law is molecules $\textrm{cm}^{-3}$.

   3. If the forward reaction's rate constant is denoted $\textrm{k}_{r}$, the reverse is denoted $\textrm{k}_{r}$.

3. with these two, you can predict the rate of the reaction at any composition and any time

V Reaction are classified based on their rate law order, the power to which the concentration of a species is raised in the rate law.

1. In Eq. 117, n and m are both orders.

   1. If n = 1, then the reaction would be first-order in A.

   2. If n = 2 and m = 1, the reaction would be second-order in A, first-order in B.

   3. If n = 2 and m = 1, the reaction would be second-order in A, first-order in B.

2. orders do not have to be integers.

3. The overall order of a reaction is the sum of all of the orders (for Eq. 117, n + m)

4. approximations are very important in kinetics; always check for limiting/special cases

   1. if one concentration is nuch larger than the other; ex. $[\textrm{A}] \gt\gt [\textrm{B}]$

VI All rate laws are determined experimentally and can guide what the mechanism of the reaction is

1. reaction stoichiometry is independent of the rate law (Ref. Table 5)

8.1.3 The Determination of the Rate Law

VII The rate law is determined through:

1. isolation method: all components in a reaction are in a large excess with the exception of one (this is known as the monitored species and is the species that will be present in the concentration vs. time plot)

   1. the concentration of the monitored species makes the largest contribution to the rate of reaction

   2. the change of concentration of the large excess species is negligible compared to the monitored species; the large excess species are approximated to be constant

   3. for the reaction $\textrm{A} + \textrm{B} \rightarrow \textrm{P}$, if the rate law is $\textrm{Rate} = \textrm{kr}[\textrm{A}][\textrm{B}]^{2}$ and $[\textrm{B}] \gt \gt [\textrm{A}]$, $\textrm{Rate} = \textrm{k}_{ (r, eff) }[\textrm{A}]$, where $\textrm{k}_{(r, eff)} = \textrm{k}_{r} [\textrm{ B }]^{2}_{0}$ (Eq. 131)

   4. this is known as a pseudo first-order, and $\textrm{k}_{(r, eff)}$ is known as the effective rate constant.

   5. A pseudo second-order is formed when $[\textrm{A}] \gt \gt [\textrm{B}]$ as $[\textrm{A}]$ is now incorporated into the $\textrm{k}_{(r, eff)}$ term leaving just $[\textrm{B}]_{2}$ in the rate law.

2. initial rates: the instantaneous rate measured at the beginning of the reaction

   1. initial rates ignore the presence of products, which can hinder the overall rate of reaction (reverse reactions can occur)