Reaction kinetics,part-2

3.Rate laws

The rate law is an expression relating the rate of a reaction to the concentrations of the chemical
species present, which may include reactants, products, and catalysts. Many reactions follow a
simple rate law, which takes the form

ν = k [A]a[B]b[C]c    

i.e. the rate is proportional to the concentrations of the reactants each raised to some power. The
constant of proportionality, k, is called the rate constant. The power a particular concentration is
raised to is the order of the reaction with respect to that reactant. Note that the orders do not have
to be integers. The sum of the powers is called the overall order. Even reactions that involve
multiple elementary steps often obey rate laws of this kind, though in these cases the orders will
not necessarily reflect the stoichiometry of the reaction equation. For example,

H2 + I2 → 2HI ν = k [H2][I2]                                
3ClO− → ClO3 + 2Cl− ν = k [ClO−]2                 

Other reactions follow complex rate laws. These often have a much more complicated
dependence on the chemical species present, and may also contain more than one rate constant.
Complex rate laws always imply a multi-step reaction mechanism. An example of a reaction with a
complex rate law is

H2 + Br2 → 2HBr ν =[H2][Br2]1/2 / [1 + k'[HBr]/[Br2] ]  

In the above example, the reaction has order 1 with respect to [H2], but it is impossible to define
orders with respect to Br2 and HBr since there is no direct proportionality between their
concentrations and the reaction rate. Consequently, it is also impossible to define an overall order
for this reaction.
To give you some idea of the complexity that may underlie an overall reaction equation, a
slightly simplified version of the sequence of elementary steps involved in the above reaction is
shown below.

Br2 → Br + Br
Br + H2 → H + HBr
H + Br2 → Br + HBr
Br + Br → Br2                                                 

As well as having rate laws for overall reactions, we can of course also write down individual rate
laws for elementary steps. Elementary processes always follow simple rate laws, in which the
order with respect to each reactant reflects the molecularity of the process (how many molecules
are involved). For example,

Unimolecular decomposition A → B ν = k [A]

Bimolecular reaction  A + B → P ν = k [A][B]
                                     A + A → P ν = k [A][A] = k [A]2   

Multi-step processes may follow simple or complex rate laws, and as the above examples have
hopefully illustrated, the rate law generally does not follow from the overall reaction equation. This
makes perfect sense, since the overall reaction equation for a multi-step process is simply the net
result of all of the elementary reactions in the mechanism. The ‘reaction’ given in the overall
reaction equation never actually takes place! However, even though the rate law for a multi-step
reaction cannot immediately be written down from the reaction equation as it can in the case of an
elementary reaction, the rate law is a direct result of the sequence of elementary steps that
constitute the reaction mechanism. As such, it provides our best tool for determining an unknown
mechanism. As we will find out later in the course, once we know the sequence of elementary
steps that constitute the reaction mechanism, we can quite quickly deduce the rate law.
Conversely, if we do not know the reaction mechanism, we can carry out experiments to determine
the orders with respect to each reactant (see Sections 7 and 8) and then try out various ‘trial’
reaction mechanisms to see which one fits best with the experimental data. At this point it should
be emphasized again that for multi-step reactions, the rate law, rate constant, and order are
determined by experiment, and the orders are not generally the same as the stoichiometric
coefficients in the reaction equation.
A final important point about rate laws is that overall rate laws for a reaction may contain reactant,
product and catalyst concentrations, but must not contain concentrations of reactive intermediates
(these will of course appear in rate laws for individual elementary steps).

4. The units of the rate constant

A point which often seems to cause endless confusion is the fact that the units of the rate constant
depend on the form of the rate law in which it appears i.e. a rate constant appearing in a first order
rate law will have different units from a rate constant appearing in a second order or third order rate
law. This follows immediately from the fact that the reaction rate always has the same units of
concentration per unit time, which must match the overall units of a rate law in which
concentrations raised to varying powers may appear. The good news is that it is very
straightforward to determine the units of a rate constant in any given rate law.
Below are a few examples.

(i) Consider the rate law

ν = k[H2][I2].

If we substitute units into the equation,
we obtain

 (mol dm-3 s-1) = [k] (mol dm-3) (mol dm-3)

where the notation [k] means ‘the units of k’. We can rearrange this expression to
find the units of the rate constant, k.

[k] =(mol dm-3 s-1) / (mol dm-3) (mol dm-3) = mol-1 dm3 s-1

(ii) We can apply the same treatment to a first order rate law,
for example

ν = k [CH3N2CH3].

(mol dm-3 s-1) = [k] (mol dm-3)

[k] = (mol dm-3 s-1) / (mol dm-3) = s-1

(iii) As a final example, consider the rate law

ν = k [CH3CHO]3/2.

(mol dm-3 s-1) = [k] (mol dm-3)3/2

[k] = (mol dm-3 s-1) / (mol dm-3)3/2 = mol-1/2 dm3/2 s-1

An important point to note is that it is meaningless to try and compare two rate constants unless
they have the same units.

Read More»

Reaction Kinetics,part-1

1. Introduction

Chemical reaction kinetics deals with the rates of chemical processes. Any chemical process maybe broken down into a sequence of one or more single-step processes known either as elementaryprocesses, elementary reactions, or elementary steps.
Elementary reactions usually involve eithera single reactive collision between two molecules, which we refer to as a a bimolecular step, ordissociation/isomerisation of a single reactant molecule, which we refer to as a unimolecular step.
Very rarely, under conditions of extremely high pressure, a termolecular step may occur, which involves simultaneous collision of three reactant molecules. An important point to recognise is that many reactions that are written as a single reaction equation in actual fact consist of a series of elementary steps. This will become extremely important as we learn more about the theory of chemical reaction rates.

As a general rule, elementary processes involve a transition between two atomic or molecular states separated by a potential barrier. The potential barrier constitutes the activation energy of the process, and determines the rate at which it occurs. When the barrier is low, the thermal energy of the reactants will generally be high enough to surmount the barrier and move over to products, and the reaction will be fast. However, when the barrier is high, only a few reactants will have sufficient energy, and the reaction will be much slower. The presence of a potential barrier to reaction is also the source of the temperature dependence of reaction rates.
The huge variety of chemical species, types of reaction, and the accompanying potential energy surfaces involved means that the timescale over which chemical reactions occur covers many orders of magnitude, from very slow reactions, such as iron rusting, to extremely fast reactions,such as the electron transfer processes involved in many biological systems or the combustion reactions occurring in flames.
A study into the kinetics of a chemical reaction is usually carried out with one or both of two main
goals in mind:

1. Analysis of the sequence of elementary steps giving rise to the overall reaction. i.e.the reaction mechanism.

2. Determination of the absolute rate of the reaction and/or its individual elementary steps.The aim of this course is to show you how these two goals may be achieved.

2. Rate of reaction When we talk about the rate of a chemical reaction, what we mean is the rate at which reactants are used up, or equivalently the rate at which products are formed. The rate therefore has units of
concentration per unit time, mol dm-3 s-1 (for gas phase reactions, alternative units of concentration
are often used, usually units of pressure – Torr, mbar or Pa).
To measure a reaction rate, we simply need to monitor the concentration of one of the reactants or products as a function of time.
There is one slight complication to our definition of the reaction rate so far, which is to do with the stochiometry of the reaction. The stoichiometry simply refers to the number of moles of each reactant and product appearing in the reaction equation.

For example, the reaction equation for the well-known Haber process, used industrially to produce ammonia, is:

N2 + 3H2 = 2NH3

N2 has a stochiometric coefficient of 1, H2 has a coefficient of 3, and NH3 has a coefficient of 2.We could determine the rate of this reaction in any one of three ways, by monitoring the changing concentration of N2, H2, or NH3. Say we monitor N2, and obtain a rate of

-d[N2]/dt = x mol dm-3 s-1.

Since for every mole of N2 that reacts, we lose three moles of H2, if we had monitored H2 instead of
N2 we would have obtained a rate

-d[H2]/dt = 3x mol dm-3 s-1.

Similarly, monitoring the concentration of NH3 would yield a rate of 2x mol dm-3 s-1.

Clearly, the same reaction cannot have three different rates, so we appear to have a problem. The solution is actually very simple: the reaction rate is defined as the rate of change of the concentration of a reactant or product divided by its stochiometric coefficient. For the above reaction, the rate (usually given the symbol ν) is therefore

ν = -d[N2]/dt = -1/3{d[H2]/dt} =1/2d{[NH3]/dt}

Note that a negative sign appears when we define the rate using the concentration of one of the reactants. This is because the rate of change of a reactant is negative (since it is being used up in the reaction), but the reaction rate needs to be a positive quantity.

Read More»

Benzilic Acid Rearrangement

Theory and Defination :

Benzilic Acid Rearrangement is the rearrangement reactions of 1, 2-diketones to give alpha hydroxy carboxylic acids. 1, 2-Diketones can be converted into the salt of an alpha hydroxy caboxylic acid upon treatment with alkali hydroxide after acidic workup, the free  alpha hydroxy carboxylic acid is obtained.
A well-known example is the rearrangement of benzil into 2-hydroxy-2, 2-diphenyl acetic acid. The substituent should not bear hydrogen to the carbonyl group, in order to avoid competitive reactions.
 The conversion of benzil (α-diketone) into the salt of α-hydroxy acid by means of base treatment is generally referred to as the benzilic acid rearrangement or benzil-benzilic acid rearrangement. This rearrangement is normally carried out in the favored solvents of water and aqueous ethanol, and also in other aqueous organic solvents, such as in aqueous dioxane or even in solid state. This rearrangement has been reported to complete within a few hours under refluxing condition. The counterion of the base affects the reaction rate of the rearrangement when the reaction is carried out in aqueous organic solvents. The coordination of metal cation also helps this rearrangement.

General Reaction :

Illustration as below ,

 

 

 

Mechanism:

• Reaction is induced by nucleophilic addition of the hydroxide anion to one of the two carbonyl groups.
• The aryl substituent migrates with the bonding electrons to the adjacent carbon atom.
• Electrons excess at the center is avoided by the release of a pair of $\pi$-electrons from the carbonyl group to the oxygen.

Finally, a proton transfer leads to the formation of carboxylate anion. The benzilic acid rearrangement of cyclic diketones are of particular interest, since these reactions leads to ring contraction.

Example and Application: 

 

1) The reaction is general one and can take place with aromatic, heterocyclic, alicyclic, and aliphatic 1, 2 – diketones as also 1,2 quinones.

 

 

2) Doering extended the reaction to the formation of the corresponding ester by replacing the normal alkali by alkoxides. Thus benzil may directly be converted into alkyl benzilate by treatment with sodium alkoxide. 

3) The reaction may be used for the preparation of αα-hydroxy acids from the easily accessible starting materials.

Read More»