Summary 5.4 Chemical kinetics

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5.4 (a) Rate equations
For a reaction between A and B : A + B ------> Products
If the rate of reaction depends upon the conc. of A and B. The relationship is:
Reaction Rate proportional to [A]^m[B]ⁿ
Reaction Rate = k[A]^m[B]ⁿ  This known as a rate equation and k is the rate constant. The indices m and n are usually integers, often 0, 1 or 2, and are characteristic of the reaction.
Task 5.4a Make up 4 other rate equations which might apply to this reaction.

5.4 (b) Rate constant and order of reaction
If the reaction Rate = k[A]^m[B]ⁿ  then reaction is of order m with respect to A and of order n with respect to B. The overall order of reaction is (m+n). The proportionality constant k is called the rate constant for the reaction. The rate constant and order of reaction are experimentally determined.
Task 5.4b For the following reactions and rate equations state the order with respect to each reactant and the overall order. 
2I^-(aq) + S₂O₈^2-(aq) ---> I₂(aq) + 2SO₄^2-(aq)
                peroxodisulphate(VI)
Rate = k*[I^-]*[S₂O₈^2-]
2H₂O₂(aq) --> 2H₂O + O₂(g)
Rate =k*[H₂O₂]
BrO₃^-(aq) + 5Br^-(aq) + 6H⁺(aq) --> 3Br₂(aq) +3H₂O(l)
Rate = k[BrO₃^-][Br^-][H⁺]²

5.4 (c) Rate equations from experimental data
Rate equations are of the form rate = k[A]^m where k is a proportionality constant. A graph of rate of reaction against [concentration] ^m is plotted and the gradient of the graph will give you the constant of the reaction k.  A data table may yield a rate equation.
E.g.  A reacts with B to form C.  From the table below find the rate equation and calculate the rate constant.

5.4 (d) Activation energy and rate constant
Some bonds in a molecule must break before it can react and form new bonds.  Energy is needed to break these bonds is called the activation energy.  Reactant molecules must be given enough energy to pass the activation energy barrier to react.  The activation energy and the rate constant are linked by the Arrhenius equation.
k=Ae^-Eact/RT
where k=rate constant,  e = the base of natural logarithms, A is a constant for any given reaction, Eact = the activation energy,   R = the gas constant,  T = the temperature in K.
The Arrhenius equation shows that the rate constant (k) decreases if the activation energy (Eact) increases.  
A reaction will have a small rate constant if it has a large activation energy.
The activation energy for a reaction can be calculated as follows.
ln k = ln Ae^-Eact/RT
ln k = ln A + ln e^-Eact/RT
ln k = ln A - Eact/RT
log k=log A - Eact/2.3RT
log k=log A - Eact/2.3R * 1/T
If k is calculated for different values of T then a plot of log k against 1/T gives a line of gradient = - Eact/2.3R.
Task 5.4d 

5.4 (e) The rate determining step in a reaction
Reactions often occur in several steps, one of which, the rate determining slow step, is likely to control the overall rate of reaction. e.g. for an S_N1 reaction two steps are involved
RX -------> R⁺ + X^-     step 1   slow
R⁺ + OH^- -----> ROH      step 2   fast
The rate depends on the slow step 1.          rate = k[RX]    first order
E.G. RX=(CH₃)₃CBr

For an S_N2 reaction there is a rate determining slow step involving two species     
RX + OH^- ------> HO--R--X
rate = k[RX][OH^-]      second order
E.G. RX = CH₃Br

5.4 (f) Mechanisms and kinetic data
The mechanism for a reaction can be proposed with help from kinetic data but some speculation is needed.
1. The rate equation gives us information about what reacts in the rate determining step. 
2. Sensible products must be suggested for the rate determining step.
3. If more molecules of reactant remain and more product molecules are still to be formed more steps must be proposed.
e.g. What is the mechanism for the following reaction 
CH₃CH₂I  + NH₃ -----> CH₃CH₂NH₂ + HI
if  rate = k[CH₃CH₂I]
CH₃CH₂I is a halogenoalkane so likely to take part in a nucleophilic substitution.  NH₃ is a nucleophile because of its lone pair of electrons on the nitrogen atom.  The rate equation shows that it is first order so the slow step in the mechanism must involve only CH₃CH₂-I.
                  
CH₃CH₂---I     -----> CH₃CH₂⁺  +  I^-
A nucleophilic attack by ammonia is now possible in a fast step;
   
NH₃ + CH₃CH₂⁺   ----->  CH₃CH₂NH₃⁺
a final fast step might be loss of hydrogen ion;
                       
CH₃CH₂H₂N----H⁺ -----> CH₃CH₂NH₂  +  H⁺

For the reaction  2ICl(g) + H₂(g) ----> 2HCl(g) + I₂(g)
Experiments show that rate = k[ICl(g)][H₂(g)]
so the rate determining step involves 1 molecule of ICl and one of H₂
ICl(g) + H₂(g) ----> products
possible products are HCl because it is a product of the overall reaction and HI because the elements hydrogen and iodine are left over.
ICl(g) + H₂(g) ----> HCl(g) + HI(g)   slow step
check full equation to see what is unaccounted for one molecule of ICl still has to react so
ICl(g) + HI(g) ----> HCl(g) + I₂(g)     fast step
The kinetic data has led to a 2 step mechanism for the reaction.
Task 5.4f Propose possible mechanisms with reasons for the following reactions:
2H₂O₂(aq) --> 2H₂O + O₂(g)
Rate =k*[H₂O₂]
CH₃COCH₃(aq) + I₂(aq) --> CH₃COCH₂I(aq) +HI(aq)
rate k*[CH₃COCH₃(aq)][H⁺(aq)]
Possible mechanism
5.4 (g) The transition state
When particles collide the breaking of bonds and the formation of new bonds may take place at the same time.  Half way through the process an intermediate called the transition state is formed.  The transition state has more energy than the the reactants.  The transition state has more energy than the products. e.g. for the reaction between a hydrogen molecule and a chlorine radical.
H-H + Cl^.      <=>      H- - - H - - - Cl      ---->     H^. + H-Cl
reactants energy = E  transition state energy > E   products  energy < E 
for exothermic reaction
Animation of transition state
Enthalpy level diagrams can show transition states.

Individual reactions can be described by enthalpy level diagrams.

Task 5.4g.1 Draw an enthalpy level diagrams for an S_N2 reaction between bromoethane and cyanide ion.
Task 5.4g.2 Draw an enthalpy level diagram for an S_N1 reaction between 2-iodo-2-methylpropane and hydroxide ion.

5.4 (h) Experimental techniques for following reactions
Reactions can be followed by

* sampling, quenching and titrating (suitable for acid base reactions)
* measuring gas volumes (suitable for reactions involving a change in gas volume)
* polarimetry (suitable for reactions involving optically active substances)
* measuring conductivity (suitable for reactions producing or consuming ions)
* colorimetry (suitable for reactions involving coloured substances)
* dilatometry (suitable for reactions involving reactions in which liquids change volumes)

5.4 (i) Presenting and interpreting kinetics graphs
From a graph of concentration against time the initial slope of the graph is the initial rate of reaction.
A graph of rate against concentration will be a straight line through the origin if the rate is proportional to the concentration.
Task 5.4(i)

5.4 (j) Half-life
The time taken for the reaction to go to half completion is called the half-life of the reaction t_1/2. The half life of a 1st order reaction is independent of the initial concentration.  1st order reactions have a constant half life. t_1/2 = 0.69/k  where k = the rate constant for the reaction
Task5.4j