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CHM110H5 Lecture Notes - Rate Equation, Collision Frequency, Collision Theory

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Chapter 14- Chemical Kinetics
Nerosanth Selvarajah
14.1- The Rate of a Chemical Reaction
The rate of a reaction describes how fast the concentration of a reactant or product changes with time
A + B C + D
Rate of Formation = ∆[C]/ ∆t Rate of Disappearance = -∆[A]/t
Rate of disappearance is a negative quantity because concentration decreases with time
oThe concentration at the end of a time period is less than t was at the start of the period
14.2 Measuring Reaction Rates
To determine rate of reaction, we need to measure changes in concentration over time
Reaction rate is not constant; the lower the remaining concentration of the reactant, the more slowly the
reaction proceeds
Instantaneous Rate of Reaction- is the exact rate of a reaction at some precise point in the reaction. It is
obtained from the slope of a tangent line to a concentration-time graph
Initial Rate of Reaction- is the rate of a reaction immediately after the reactants are brought together
14.3 Effect of Concentration on Reaction Rates: The Rate Law
Rate Law/ Rate Equation-for a reaction relates the reaction rate to the concentrations of the
Rate= k[A]m[B]n [Pg. 578]
Term order is related to the exponents in the rate law
The overall order of reaction is the sum of all the exponents: m + n + …
Rate constant (k)- is the proportionality constant in a rate law that permits the rate of a reaction to be
related to the concentrations of the reactants
oits values depend on the specific reaction, presence of a catalyst and temperature
othe larger the value of k, the faster a reaction goes
order of the reaction establishes the general form of the rate law & the appropriate units of k
if reaction is first order in one of the reactants, doubling the initial concentration of that reactant causes the
initial rate of reaction to double
ozero order in reactant- no effect on initial rate of reaction
ofirst order in reactant- initial rate of reaction doubles
osecond order in reactant- initial rate of reaction quadruples
othird order in reactant- initial rate of reaction increases eightfold
order of reaction (indicated through rate law) establishes units of rate constant, k [k = M-2 min-1
14.4 Zero-Order Reactions
zero-order reaction has a rate law in which the sum of the exponents, m + n+… is equal to 0
oreaction proceeds at a rate that is independent of reactant concentrations
Rate of Reaction = k [A]0 = k = constant
concentration-time graph is a straight line with a negative slope
rate of reaction which is equal to k and remains constant throughout the reaction is the
negative of the slope of the line
units of k are the same as units of rate of a reaction: mol/L*t = M/s
Integrated Rate Law- expresses the concentration of a reactant as a function of time
[A]t = -kt + [A]o
14.5 First-Order Reactions
First-order reaction has a rate law in which sum of the exponents, m + n + …is equal to 1
ln ([A]t / [A]o) = -kt or ln [A]t = -kt + ln[A]o
an easy test for a first-order reaction is to plot the natural logarithm of a reactant concentration versus time
& see if graph is linear k = -slope
Half-Life of a reaction is the time required for one-half of a reactant to be consumed; time during which the
amount of reactant or its concentration decreases to one-half of its initial value
t1/2 = ln 2 / k
Half-life is constant for a first-order reaction; it is also independent of the initial concentration
In Reactions involving gases, Rates are often measured in terms of gas pressure
Radioactive decay is a first-order process
14.6 Second-Order Reactions
Equation of Straight Line Graph:
1/ [A]t = kt + 1/[A]0
Half life depends on both the rate constant & the initial concentration [A]0
oHalf –life is not a constant; its value depends on the concentration of reactant at the start of each
half-life interval
Because the starting concentration is always one-half that of the previous half-life, each
successive half-life is twice as long as the one before it
t1/2 = 1/ k[A]0
Pseudo-First-Order Reaction- a second-order reaction that is made to behave like a first-order reaction by
holding one reactant concentration constant
14.7 Reaction Kinetics: A Summary
14.8 Theoretical Models for Chemical Kinetics
Collision Theory:
Collision Theory- the number of molecular collisions per unit time; typical collision frequency is of the order
of 1030 collisions/second
Only a fraction of the collisions among gaseous molecules lead to chemical reaction
Cannot expect every collision to result in a reaction
Activation Energy- a reactions minimum energy above the average kinetic energy that molecules must
bring to their collisions for a chemical reaction to occur
Rate of a reaction will depend on the product of the collision frequency & the fraction of activated molecules
oSince fraction of high-energy molecules is generally small, rate of reaction is usually much smaller
than collision frequency
Higher the activation energy of a reaction, smaller the fraction of energetic collisions and the
slower the reaction
A factor that can strongly affect the rate of a reaction is the orientation of molecules at the time of their
oSometimes number of unfavorable collisions in the reaction mixture exceeds the number of favorable
Transition State Theory:
Transition State-in a chemical reaction is an intermediate state between the reactants and products
Activated Complex-is an intermediate in a chemical reaction formed through collisions between energetic
molecules. Once formed, it dissociates either into the products or back to the reactants
Formation of the activated complex is a reversible process
Reaction Profile- is a graphical representation of a chemical reaction in terms of the energies of the
reactants, activated complexes and products
Difference in energy between the activated complex and the reactants is the activation energy of the
oThus a large energy barrier separates the reactants from the products, and only very energetic
molecules can pass over this barrier
1-enthalpy change of a reaction is equal to the difference in activation energies of the forward and reverse
2-for an endothermic reaction, the activation energy must equal to or greater than the enthalpy of reaction
(and usually it is greater)
14.9 The Effect of Temperature on Reaction Rates
Arrhenius Equation:
ln (k2/k1) = (Ea/R)[(1/T1) – (1/T2)] R= 8.3145 J/mol*K
a graph of ln k vs. 1/T is a straight line
14.10 Reaction Mechanisms
a three-molecule collision is an unlikely event
Reaction Mechanism- is a step-by-step detailed description of a chemical reaction
Elementary Process- a single step in a reaction mechanism; an event that significantly alters a molecule’s
energy or geometry or produces a new molecule
Two requirements of a reaction mechanism:
oBe consistent with the stoichiometry of the overall reaction
oAccount for the experimentally determined rate law
Characteristics of Elementary Processes:
oare either unimolecular- process in which single molecule dissociates
oor bimolecular- process involving the collision of two molecules
oor termolecular- process involving simultaneous collisions of 3 molecules which is relatively rare
oexponents of the concentration terms in the rate law are the same as the stoichiometric coefficients
oelementary processes are reversible, and some may reach a condition of equilibrium in which the
rates of the forward & reverse processes are equal
ocertain molecules are produced in one elementary process and are consumed in another; thus such
intermediate molecules must not appear in the overall chemical equation or the overall rate law
oRate-Determining Step- is an elementary process that is instrumental in establishing the rate of
the overall reaction, usually because it is the slowest step in the mechanism
Reaction Intermediate- is a species formed in one elementary reaction in a reaction mechanism and
consumed in a subsequent one; as a result the species does not appear in the equation for the overall
Difference between transition state & reaction intermediate is that the transition state represents the
highest energy structure involved in a reaction(or step in a mechanism); but transition states exist only
momentarily and can never be isolated, reaction intermediates can sometimes be isolated
oTransition states have partially formed bonds, whereas reaction intermediates have fully formed
Steady-State Approximation:
In complex multistep reaction mechanisms, however, more than one step may control the rate of a reaction
Steady-state condition is in which a molecule is produced and consumed at equal rates
Smog- is the general term used to refer to a condition in which polluted air reduces visibility, causes
stinging eyes and breathing difficulties, and produces additional minor and major health problems (ex.
Industrial smog & photochemical smog)
14.11 Catalysis
Catalyst- provides an alternative mechanism of lower activation energy for a chemical reaction; the reaction
is speeded up and the catalyst is regenerated
oFormula of a catalyst does not appear in the overall chemical equation instead placed above arrow
Two basic types of catalysis- homogeneous & heterogeneous
Homogeneous Catalysis refers to a catalytic reaction taking place in a single phase
Heterogeneous Catalysis- catalyst is present in a different phase of matter than are the reactants and
oInvolve: Absorption of reactants
Diffusion of reactants along the surface
Reaction at an active site to form absorbed product
Desorption of the product
Most human enzyme-catalyzed reactions proceed fastest at about 37ºC
oIf temperature raised higher, the structure of the enzyme changes, and the active site becomes
distorted and the catalytic activity is lost