Chemical KineticsUnit 10

• Kinetics – Kinetics – the study of the speeds of chemical reactions and the mechanisms by which reactions occur.

• Also referred to as “Reaction RatesReaction Rates”

• Rates of chemical change usually are expressed as the amount of reactant forming products per unit time.

∆[reactants]∆ time

Kinetics Kinetics

• How do reactions really occur?How do reactions really occur?– Reactant particles MUST Reactant particles MUST collidecollide!!

• Rates of chemical reactions are described in a Rates of chemical reactions are described in a model called model called collision theory.collision theory.

– Studies show most molecular collisions do NOT Studies show most molecular collisions do NOT result in a reaction…why??result in a reaction…why??

• Atoms, ions, and molecules react to form Atoms, ions, and molecules react to form products only when they collide with the products only when they collide with the proper orientation proper orientation and and sufficient energy.sufficient energy.

Collision TheoryCollision Theory

• EffectiveEffective collisions are defined by two collisions are defined by two conditions: conditions: – exactly the right exactly the right orientationorientation to react (head on to react (head on

collision is best) collision is best) – enough energy to enough energy to break bonds and form break bonds and form new new

ones ones • The minimum amount of energy required is The minimum amount of energy required is

called the reaction’s called the reaction’s activation energy.activation energy.– The activation energy is a The activation energy is a barrierbarrier that reactants that reactants

must get over to reactmust get over to react– The higher the barrier the larger the amount of The higher the barrier the larger the amount of

energy needed for the reaction to proceedenergy needed for the reaction to proceed

Collision TheoryCollision Theory

• During a reaction, a particle that is neither During a reaction, a particle that is neither reactant nor product forms momentarily, reactant nor product forms momentarily, called an called an activated complex activated complex

– if there is sufficient energy if there is sufficient energy – and if the atoms are oriented properlyand if the atoms are oriented properly

• An activated complex is a kind of An activated complex is a kind of transition molecule transition molecule which has similarities which has similarities to reactants & productsto reactants & products

– An activated complex is the arrangement of An activated complex is the arrangement of atoms at the peak of the activation-energy atoms at the peak of the activation-energy barrier.barrier.

Collision TheoryCollision Theory

• Collision theory Collision theory explains why some explains why some naturally occurring reactions are naturally occurring reactions are immeasurably slow at room temp.immeasurably slow at room temp.

– Carbon and Oxygen react when charcoal Carbon and Oxygen react when charcoal burns, but this reaction has a high burns, but this reaction has a high activation energyactivation energy

– At room temp, the collisions of oxygen and At room temp, the collisions of oxygen and carbon molecules aren’t energetic enough carbon molecules aren’t energetic enough to reactto react

– But the reaction can be helped along a But the reaction can be helped along a number of waysnumber of ways

Collision TheoryCollision Theory

• It is possible to It is possible to vary the conditionsvary the conditions of the of the reaction, the rate of almost any reaction reaction, the rate of almost any reaction can be can be modifiedmodified

o collision theory can help explain why the collision theory can help explain why the rates can be modifiedrates can be modified

• Several strategies can be used to speed Several strategies can be used to speed up reactions:up reactions:

o Increase the Increase the temperaturetemperatureo Increase the Increase the concentrationconcentrationo Decrease the Decrease the particleparticle sizesizeo Employ a Employ a catalystcatalyst

Reaction RatesReaction Rates

• IncreasingIncreasing the temperature the temperature speeds up speeds up the the reaction, while reaction, while loweringlowering the temperature the temperature slows down slows down the reactionthe reaction

• For every 10For every 10ooC increase in temperature, C increase in temperature, the reaction rate usually DOUBLES!the reaction rate usually DOUBLES!

• Recall, temperature is directly Recall, temperature is directly proportional to average kinetic energy: proportional to average kinetic energy:

– Average KE = ½ x mass x velocityAverage KE = ½ x mass x velocity22

• At a higher temperature, there are more At a higher temperature, there are more effective collisions effective collisions – more molecules – more molecules have the velocity / energy needed to react have the velocity / energy needed to react

TemperatureTemperature

• Just sitting out, charcoal Just sitting out, charcoal does not react does not react at a measurable rateat a measurable rate– However, when a However, when a starter flame starter flame touches the touches the

charcoal, the temperature is increased so charcoal, the temperature is increased so atoms of reactants collide with atoms of reactants collide with higher higher energyenergy and and greater frequencygreater frequency

– Some of the collisions are high enough in Some of the collisions are high enough in energy that the product COenergy that the product CO22 is formed is formed

o The energy The energy releasedreleased by the by the exothermic reaction then supplies exothermic reaction then supplies enough energy to get more C and enough energy to get more C and OO22 over the over the activation-energy activation-energy barrierbarrier• Remove the starter flame:Remove the starter flame: the the

reaction will continue on its own.reaction will continue on its own.

• The more reacting particles you have in a The more reacting particles you have in a given volume, the given volume, the higher the rate of higher the rate of reaction.reaction.

• Cramming more particles into a fixed Cramming more particles into a fixed volume increases the volume increases the concentrationconcentration of of reactants:reactants:

• Increasing the concentration, increases Increasing the concentration, increases the the frequencyfrequency of the collisions, and of the collisions, and therefore therefore increasingincreasing the reaction rate. the reaction rate.

ConcentrationConcentration

• The smaller the particle size, the The smaller the particle size, the larger larger the surface areathe surface area for a given mass of for a given mass of particles. Effectively is increasing the particles. Effectively is increasing the concentrationconcentration..

• An increase in surface area increases the An increase in surface area increases the amount of the reactant amount of the reactant exposed for exposed for collisioncollision to take place… to take place…

– Which increases the collision Which increases the collision frequencyfrequency and the reaction rate.and the reaction rate.

• Methods:Methods:– Grinding the reactants into a powderGrinding the reactants into a powder– Dissolving in a solvent.Dissolving in a solvent.

Particle SizeParticle Size

•A catalyst is often the best way to speed up an reaction.

• In fact, some reactions simply will not go forward measurably without one.

•A catalyst is a substance that increases the rate of a reaction without being changed or used up during the reaction

•The key is that they permit reactions to proceed at lower activation energy than is normally required

CatalystCatalyst

•Catalysts lower the required activation energy by providing an alternative path or arrangement for the molecules to react.

•Not always understood why certain catalyst behave the way the do…they just do!

•By lowering the Ea threshold, more molecules in the system will have the required energy to surmount the barrier.

CatalystCatalyst

• The type of reactant substances also plays a role in reaction rates.

• Weak bonds = easier to break, reactants with weak bonds will react faster.

– Essentially results in a low activation energy.

• Strong bonds = harder to break, reactants with strong bonds will react slower (high Ea)

Nature of ReactantsNature of Reactants

• Reaction Reaction Rate LawsRate Laws relate the speed of a relate the speed of a reaction to the concentrations of the reactants reaction to the concentrations of the reactants (or sometimes products).(or sometimes products).

• Determined from experimentDetermined from experiment

• For equation: A For equation: A B B

– Rate = ∆[A] / ∆ t Rate = ∆[A] / ∆ t • Where ∆[A] = change in molarity of reactant AWhere ∆[A] = change in molarity of reactant A• ∆ ∆ t is the time over which the reaction occurredt is the time over which the reaction occurred

– The rate of disappearance of A is proportional The rate of disappearance of A is proportional to its molar concentration.to its molar concentration.

– Rate = k[A]Rate = k[A]• Where k is the specific rate constantWhere k is the specific rate constant

Reaction Rate LawsReaction Rate Laws

• k k is unique for every reactantis unique for every reactant

– Often expressed in Often expressed in ss-1-1 or or L / (mol * s)L / (mol * s)

– If the reaction is fast, k is large.If the reaction is fast, k is large.

• Reaction Rate Reaction Rate OrdersOrders

– The “order” of a reaction is the The “order” of a reaction is the powerpower to to which the concentration must be raised to which the concentration must be raised to provide for the actual rate observed.provide for the actual rate observed.

– First order reactions have rates directly First order reactions have rates directly proportional to one reactant. If reactant proportional to one reactant. If reactant concentrationconcentration doublesdoubles, , raterate doublesdoubles..

– Rate = k[A]Rate = k[A]11 (note: powers of 1 usually not shown)(note: powers of 1 usually not shown)

Reaction Rate LawsReaction Rate Laws

First Order Reaction Rates

• Second Order Rate LawsSecond Order Rate Laws

– Rate = k[A]Rate = k[A]22

– Ex.: If [A] is doubled, the rate Ex.: If [A] is doubled, the rate quadruplesquadruples..

• The General Rate LawThe General Rate Law

– The order of reaction for each reactant is the The order of reaction for each reactant is the value of its exponent. Overall order of the value of its exponent. Overall order of the reaction is the sum of exponents.reaction is the sum of exponents.

– For reaction: xA + yB For reaction: xA + yB Products Products

– Rate = k[A]m[B]n

– Overall order = Overall order = mm + + nn

Reaction Rate LawsReaction Rate Laws

Second Order Reaction Rates

• ““Method of initial ratesMethod of initial rates” determines order ” determines order by comparing rates with varying by comparing rates with varying concentrations of reactants.concentrations of reactants.

• When [A] When [A] doublesdoubles, initial rate , initial rate doublesdoubles (= first order). (= first order).

• When [B] When [B] doublesdoubles, rate , rate quadruplesquadruples(= second order).(= second order).

Rate Law: Rate = k[A]Rate Law: Rate = k[A]11[B][B]22

• Overall order of reaction: 1+2 = 3Overall order of reaction: 1+2 = 3

Determining Reaction Determining Reaction OrderOrder

Trial Initial [A] (M)

Initial [B] (M)

Initial Rate (mol/L*s)

1 0.100 0.100 2.00 x 10-3

2 0.200 0.100 4.00 x 10-3

3 0.200 0.200 16.00 x 10-3

Run # Initial [A] ([A]0)

Initial [B] ([B]0)

Initial Rate (v0)

1 1.00 M 1.00 M 1.25 x 10-2 M/s

2 1.00 M 2.00 M 2.5 x 10-2 M/s

3 2.00 M 2.00 M 2.5 x 10-2 M/s

What is the order with respect to A?

What is the order with respect to B?

What is the overall order of the reaction?

What is the rate law?

0

1

1

Rate = k[B]

• Reaction rates decline over time as the concentration of reactants decrease.

• The rate at any given point in time is called the “Instantaneous Reaction Rate”

• Equal to the slope of the tangent to the curve at any given point in time.

• Rate = slope of tangent = (y2 – y1) / (x2 – x1)

Instantaneous Instantaneous Reaction RatesReaction Rates

Br2 (aq) + HCOOH (aq) 2Br- (aq) + 2H+ (aq) + CO2 (g)

average rate = -[Br2]

t= -

[Br2]final – [Br2]initial

tfinal - tinitial

slope oftangent

slope oftangent slope of

tangent

instantaneous rate = rate for specific instance in time13.1

• If you know the rate law and reactant concentrations, you can directly calculate the instantaneous rate.

• Example:Example:

2N2N22OO55 4NO 4NO22 + O + O22

Rate = k[NRate = k[N22OO55] ] where where k = 1.0 x 10k = 1.0 x 10-5-5 s s-1-1 and and concentration of Nconcentration of N22OO55 is is 0.350 M0.350 M..

Rate = 3.5 x 10Rate = 3.5 x 10-6 -6 mol/(L*s)mol/(L*s)

Instantaneous RatesInstantaneous Rates