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    RATE EQUATIONS AND REACTION MECHANISMS

    1. Reaction mechanism: Aseries of steps which are proposed to explain how the reactants change to theproducts.

    2. A proposed mechanism mustagree with:(i) The balanced equation i.e.

    when the steps are added together they should give the overallequation/reaction in terms of reactants and products.

    (ii) The mechanism must agreewith the reaction kinetics or the rate expression.

    3. In most mechanisms there isone slow or rate determining step and one or more fast steps which do notaffect the rate. The slow rate-determining step can be derived form therate expression . The partial order of any species appearing in the mechanismafter the rate determining step will be zero order confirming it has no effecton the rate.

    Mechanism for the hydrolysis of halogenoalkanes There are two possible mechanisms for the hydrolysis of halogenoalkanes. The chemical equation does not give any information about the mechanism of the

    reaction. The mechanism can be deduced by finding the order of reaction with respect to each

    reactant. Only substances involved in (or before) the rate-determining step appear in the rate

    equation.

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    The order with respect to a reactant indicates the number of that particles of thatreactant involved in the rate-determining step.

    Examples: S N1 and S N2 mechanisms of the hydrolysis of halogenoalkanes

    (a) SN1 mechanism (Nucleophilicsubstitution Unimolecular)

    The term unimolecular indicates that there is only one species involved in the slowrate determining step.

    Consider the reaction between 2-bromo-2-methylpropane, (CH 3)3CBr, a tertiaryhalogenoalkane and OH - from aqueous sodium hydroxide solution:

    (CH3)3CBr + OH- (CH3)3COH + Br-

    Rate = k [ halogenoalkane]

    The reaction is FIRST order with respect to (CH 3)3CBr and zero order with respectto the OH - . Only (CH3)3CBr is taking part in the slow rate determining step of thereaction. The OH - are involved in a relatively fast step following the rate determiningstep and do not affect the rate.

    Energy profile diagram for a two-step reaction

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    The activation energy fort he production of theintermediate is greater than the activationenergy fort he intermediate going to theproducts. This means that the first step is

    rate-determining step.

    The second activation energy isgreater, so the second step is therate determining step.

    (Unstable) Intermediate product : formed in the slow rate determining step whichthen reacts further to form the products.

    Reactions which involve a single intermediate are ususally referred to as two-stepreactions.

    Note that each step has its own transition state and activation energy.

    (b) SN2 mechanism: ( Nucleophilic substitution Bimolecular)

    The term bimolecular refers to the molecularity of the reaction i.e. the number ofspecies involved in the slow rate-determining step.

    Consider the reaction between bromoethane, CH 3CH2Br, a primary halogenoalkane andhydroxide ions, OH - from aqueous sodium hydroxide solution:

    CH3CH2Br + OH- CH3CH2OH + Br-

    Rate = k [CH3CH2Br] [OH -]

    The reaction is FIRST order with respect to both CH3CH2Br and + OH-. Both ofthese species must be taking part in the slow rate-determining step of the reaction.The reaction must happen by a straightforward collision between them.

    Energy profile diagram for a one step reaction

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    Transition step : This often represents a condition where old bonds are half brokenand new ones are half formed. This transition state breaks down directly to the finalproducts without forming a more stable intermediate, which could then be involved ina futher step.

    There is one transition state for each step. The transition state is formed whenreacting particles have required activation energy E A. The activation energy is thedifference in energy between the reactants and the transition state.

    (c) While the mechanismsproposed for the alkaline hydrolysis of primary and tertiary halogenoalkanes areconsistent with the experimentally determined orders of reaction and theoverall equation for the reaction, the reaction between propanone and iodine isnot clear.

    Propanone will react with iodine in the presence of acid as follows:

    CH3COCH3(aq) + I 2(aq) CH3COCH2I (aq) + HI(aq)

    Experiments are performed to deduce the order with respect to each reactant.The relative concentrations are shown below.

    ExperimentNo.

    [CH3COCH3] [I 2] [H+] Relative rate

    H+

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    1 1 1 1 22 1 2 1 23 2 1 1 44 1 1 2 4

    Deduce the order of reaction with respect to each of the substances given inthe table and give the rate equation for the reaction.

    A suggested mechanism is as follows:

    Propanone will react with iodine in the presence of alkali as follows:

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    CH3COCH3(aq) + I 2(aq) CH3COCH2I (aq) + HI(aq)

    Experiments performed to deduce the orders with respect to each reactantreveal that the reaction first order with respect to propanone, zero order withrespect to iodine and first order with respect to hydroxide ions, which do noteven appear in the equation.

    The rate equation for this reaction therefore is:

    Rate = k [CH3COCH3] [OH-

    ]

    A likely explanation for the mechanism of this reaction is that iodine entersafter the rate-determining step.

    A suggested mechanism is as follows:

    Step 1: the base removes a proton from a CH3 group, which is the ratedetermining step.

    CH3COCH3 + OH- CH3COCH2- + H2O

    Step 2 : the lone pair of electrons on the C - of the carbanion forms a bond withan iodine atom in I 2 and I 2 bond breaks.

    CH3COCH2- + I2 CH3COCH2I + I -

    Since the reaction is first order with respect to both propanone and hydroxide ionsand zero order with respect to iodine, the first step must be the rate determiningstep. This fact can be confirmed by carrying out the same reaction but using bromineor chlorine instead of iodine, where it is found that the overall rate of reaction is thesame.

    Second or subsequent step is rate determining

    OH-

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    If the second or a subsequent step is rate determining, the derivation of the overallrate equation is more complex.

    Consider the reaction:

    A + 2b + C D + E

    Step 1 is a rapid step that is reversible:

    A + B Int

    where Int is an intermediate

    Step 2 is the slowest step and hence is rate determining:

    Int +B X

    Step 3 is faster than step 2:

    C + X D + E

    The overall rate is determined by the rate of the slowest step 2:

    Overall rate = rate of step 2 = k[B] [Int]

    Examples:

    Finding the slowest step in the reaction mechanism

    The rate expression for the reaction:

    2A (g) + 3B (g) C (g) + 2D (g)

    is found to be Rate = k [A] 2 [B]

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    (a) Does this reaction have a mechanism?

    Yes, because if there were no reaction mechanism, the rate expression of the given reaction

    would be:Rate = k [A] 2 [B]3

    But, the given rate expression is different from the rate expression we find. In that casethe reaction has a mechanism.

    b) If it has a mechanism, write the slowest step.

    Rate = k [A] 2 [B]

    So, 2A + B products.

    Finding the rate expression of a reactionThe mechanism proposed for the reaction:

    2 ICl + H2 2 HCl + I2 is as follows:

    (I) H 2 + ICl HI + HCl (slow)

    (II) HI + ICl HCl + I2 (fast)

    a) Which step is the rate-determining step?Step I

    b) What is the rate expression for this reaction?

    Rate = k [H 2 ] [ICl]

    The rate expression can be written form the rate-determining step directly. The rate of the

    reaction is directly proportional to the concentration of the reactants of the rate- determining step.

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    c) If the concentrations of H 2 and ICl are doubled, how many times will the rate of thereaction change?Increase by factor 4

    (Because the rate of reaction is directly proportional to the both of theconcentrations of H 2 and ICl.

    d) If the concentrations of HI and HCl are tripled, how many times will the rate change?HI and HCl do not appear on the rate equation, so they do not cause any change.

    Finding the rate-determining step

    The rate equation for the reaction:

    2NO (g) + Cl2 (g) 2 NOCl (g)

    is found to be Rate = k [NO] 2 [Cl2]

    which of the following mechanisms will likely belong to this reaction?

    A. 2NO (g) N2O2 (slow)N2O2 (g) + Cl2 (g) 2 NOCl (g) (fast)

    B. Cl2 (g) 2Cl (slow)

    NO (g) + Cl (g) NOCl (g) (fast)

    C. NO (g) + NO (g) + Cl2 (g) 2 NOCl (g)

    Answer: C

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    Finding the rate expression

    The reaction,

    2A + B + K L + F + 120 kJ

    has a mechanism with three steps.

    The first two steps of the mechanism are as follows:

    2A + B C + D (fast)

    C + E K + L (fast)

    a) Deduce the rate expression for the reaction.The sum of the reactions in the mechanism gives the net (overall) reaction. Therefore,the slowest step which is not given can be found by subtracting the given steps fromthe net equation.

    2A + B + K L + F (overall reaction)

    -2A + B -C + D (fast)

    -C + E -K + L (fa