Important questions in chemistry How much and how far? How fast? Reaction rates and rate laws Reaction mechanism Mechanism and temperature dependence Catalysis

Learning objectives ► Describe factors affecting rates of reaction ► Describe reaction rate in terms of reactants and products ► Determine rate of reaction from concentration over time ► Use method of initial rates to determine orders of reaction and rate constant ► Apply integrated rate law equations to determine order of reaction and rate constant ► Apply order of reaction to identifying possible reaction mechanisms ► Describe factors that affect the pre-factor in the Arrhenius rate equation ► Apply Arrhenius rate equation to determine activation energy ► Describe general principles behind the function of catalysts

Thermodynamics and kinetics ► Thermodynamics addresses the first ► Kinetics addresses the second ► They are distinct areas and have nothing to say to each other  A reaction may be favoured by thermodynamics but not happen because of kinetic obstacles

The paradox of the reaction between H 2 and O 2 ► The reaction is very favorable, and yet a mixture of hydrogen and oxygen can remain unreacted for centuries – for eternity

Underlying principles ► All molecules are in motion ► Molecules undergo collisions as a result ► Some collisions result in reactions to give products

Reaction pathway in energy ► All reactions have an energy barrier ► Molecules must have enough energy to leap ► Molecules with insufficient energy don’t make it

Thermodynamics considers the before and after Reactants at equilibrium Province of kinetics Products at equilibrium

Rate a minute ► Rate is defined as: Concentration change/time change ► In typical reaction ► Rate is measured either by measuring decrease in [reactant] or increase in [product] ► Units of rate are mol/L●s

Plot of concentration vs time ► Rate of appearance of product (or disappearance of reactant) depends on the number of moles in the equation equation

General rate of reaction ► Divide the actual rate of appearance/disappearance by the coefficient in the balanced equation ► Usually rate changes with time: the longer the time, the slower the rate – reactants are used up reactants

Comparison of instantaneous rate with an interval rate ► As Δt decreases, measured rate Δ[NO 2 ]/Δt approaches slope of curve d[NO 2 ]/dt ► Rate measured over time interval is an approximation ► Rate of reaction at the very beginning (t = 0) is the initial rate – when [product] = 0

Laws and Order ► For the typical reaction aA + bB = products ► The rate is given by the following rate law k is the rate constant m and n are orders of reaction with respect to A and B respectively

Inconstancy of rate constants ► k is for a specific reaction ► Units of k depend on overall reaction order ► k does not change with [reactants] or [products] ► k does not change with time ► k does depend on temperature ► k does depend on presence of a catalyst

Significance of orders ► Orders of reaction are usually small integer numbers 0, 1, 2 ► In complex processes ½ or other fractions, or even negative numbers can be observed ► Significance of order on relationship of concentration and rate Order of reaction m Effect on rate of doubling concentration (2 m ) None Doubles Quadruples

Overall reaction order ► Sum over individual orders Order = m + n + …+ ► Reaction order is determined experimentally and cannot be predicted from the chemical equation alone  A complete description of the reaction mechanism is required to predict reaction orders  Experimental orders are used to identify reaction mechanisms

Strategies for determining orders of reaction ► 1: Method of initial rates  At t = 0, [product] = 0  Vary concentration of one reactant, keeping other(s) constant  Compare ratios of rates at different [reactant] in turn  Reaction is second order in NO and first order in O 2

The common rate laws and units ► Rate of reaction and rate constant (k) are not the same  Rate of reaction depends on concentrations  Rate constant does not  Rate of reaction always has units of M/s  Rate constant has units that depend on rate equation

2: Integrated rate law method ► General first order dependence ► Integrate ► But ► A plot of ln[A] t vs t is linear

First order reaction and half- life ► The half-life is the time required for the concentration of the reactant to halve ► When [A] t = ½[A] 0 ► The half-life is constant since it depends on k only

Integrated rate law for second order ► General second order dependence ► In this case the plot of 1/[A] t vs t is linear

Zero-order reactions ► Uncommon but not impossible ► Integrated rate law ► Plot of [A] t vs t gives a straight line with slope -k