CHEM 1412 Concept Review: Chemical Kinetics

Rate of Reaction

For any reaction of the general form “ $LaTeX: aA+bB\longrightarrow cC+dD$ $aA+bB\longrightarrow cC+dD$ ”, the average rate of reaction can be expressed by the following equation:

$LaTeX: Rate=-\frac{1}{a}\left(\frac{\Delta\left[A\right]}{\Delta t}\right)=-\frac{1}{b}\left(\frac{\Delta\left[B\right]}{\Delta t}\right)=\frac{1}{c}\left(\frac{\Delta\left[C\right]}{\Delta t}\right)=\frac{1}{d}\left(\frac{\Delta\left[D\right]}{\Delta t}\right)$ $Rate=-\frac{1}{a}\left(\frac{\Delta\left[A\right]}{\Delta t}\right)=-\frac{1}{b}\left(\frac{\Delta\left[B\right]}{\Delta t}\right)=\frac{1}{c}\left(\frac{\Delta\left[C\right]}{\Delta t}\right)=\frac{1}{d}\left(\frac{\Delta\left[D\right]}{\Delta t}\right)$

Where a, b, c, and d are coefficients, ∆t is the change in time (∆t = t_final – t_initial), and ∆[A] is the change in concentration of reactant “A” which is calculated using the following equation: . In a similar way, ∆[B], ∆[C], and ∆[D] represent changes in concentrations of other reactants and products and can be calculated in the same way.

As such, it is important to be aware of the following terminology, their corresponding equations, and how they relate to rate of reaction.

Rate of Disappearance (or Consumption):
a measure of how fast a reactant is used up or “disappears” in the course of a reaction.

Rate of Appearance (or Formation):
a measure of how fast a product is formed in the course of a reaction.

Example equation:

$LaTeX: Rate_{disappearance\:of\:A}=-\left(\frac{\Delta\left[A\right]}{\Delta t}\right)$ $Rate_{disappearance\:of\:A}=-\left(\frac{\Delta\left[A\right]}{\Delta t}\right)$

Example equation:

$LaTeX: Rate_{appearance\:of\:C}=\left(\frac{\Delta\left[C\right]}{\Delta t}\right)$ $Rate_{appearance\:of\:C}=\left(\frac{\Delta\left[C\right]}{\Delta t}\right)$

Since… $LaTeX: Rate_{RXN}=-\frac{1}{a}\left(\frac{\Delta\left[A\right]}{\Delta t}\right)$ $Rate_{RXN}=-\frac{1}{a}\left(\frac{\Delta\left[A\right]}{\Delta t}\right)$ ,

Therefore… $LaTeX: Rate_{RXN}=\frac{1}{a}\left(Rate_{disappearance\:of\:A}\right)$ $Rate_{RXN}=\frac{1}{a}\left(Rate_{disappearance\:of\:A}\right)$

Since… $LaTeX: Rate_{RXN}=\frac{1}{c}\left(\frac{\Delta\left[C\right]}{\Delta t}\right)$ $Rate_{RXN}=\frac{1}{c}\left(\frac{\Delta\left[C\right]}{\Delta t}\right)$ ,

Therefore… $LaTeX: Rate_{RXN}=\frac{1}{c}\left(Rate_{appearance\:of\:C}\right)$ $Rate_{RXN}=\frac{1}{c}\left(Rate_{appearance\:of\:C}\right)$

Important Note: For all of these different expressions of rate, the rates are always given as POSITIVE values. Since the change in reactant concentration will always be negative, negative signs appear in rate expressions corresponding to reactants in order to cancel the negative from the change in reactant concentration.

Rate Laws and Orders of Reaction

Rate Law: An equation that gives the relationship between the rate of a reaction and the concentration of reactants. The generic expression for a rate law of a reaction of general form “ $LaTeX: aA+bB\longrightarrow cC+dD$ $aA+bB\longrightarrow cC+dD$ ”, is:

$LaTeX: Rate=k\left[A\right]^m\left[B\right]^n$ $Rate=k\left[A\right]^m\left[B\right]^n$

Where k is the rate constant, m is the order of the reaction with respect to A, n is the order of reaction with respect to B, and [A] and [B] are the concentrations of reactants A and B respectively.

Reaction Mechanism: the series of individual chemical steps (reactions) by which an overall reaction occurs.

Because the rate law is based on the reaction mechanism and not the overall balanced chemical equation, rate laws MUST be determined experimentally.

Order of Reaction: the order of reaction with respect to a given reactant is the power or exponent to which that reactant’s concentration is raised in the rate law for the reaction. For example, in the generic rate law already given (), the order of reaction with respect to reactant “A” would be “m”. The order of reaction with respect to “B” would be “n”. The overall order of reaction is the sum of all the individual orders of reaction. For example, with our generic rate law, the overall order of reaction is “m + n”.

Integrated Rate Law: an equation derived from the rate law and rate expression which is used to show how concentration of a reactant changes with time for a given chemical reaction. The equations for the integrated rate laws are different for each order of reaction. A summary of those equations and related information are as follows:

CH 13 img 1.png

The Arrhenius Equation

$LaTeX: k=Ae^{-E_a/RT}$ $k=Ae^{-E_a/RT}$ , which can be rearranged into… $LaTeX: \ln k=-\frac{E_a}{R}\left(\frac{1}{T}\right)+\ln A$ $\ln k=-\frac{E_a}{R}\left(\frac{1}{T}\right)+\ln A$ or $LaTeX: \ln\left(\frac{k_2}{k_1}\right)=\frac{E_a}{R}\left(\frac{1}{T_1}-\frac{1}{T_2}\right)$ $\ln\left(\frac{k_2}{k_1}\right)=\frac{E_a}{R}\left(\frac{1}{T_1}-\frac{1}{T_2}\right)$

Where A is a constant known as the frequency factor, E_a is the activation energy, R is the ideal gas constant (8.314 J/mol▪K), and T is the temperature in Kelvins. k₁ and k₂ refer the rate constants for a given reaction at two different temperatures T₁ and T₂.

Activation Energy: The minimum energy needed by the reactants to allow them to reach a transition state and follow through with the reaction. It can also be thought of as an energy barrier that must be overcome to react.

Transition State: a high energy intermediate state that occurs as reactants transform into products.