# Chemical kinetics

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## Definition :

She is interested in the evolution over time of reaction systems. Her goal is :

• The determination and the study of reaction rates and laws that govern these reactions.
• Determining the reaction mechanism.

The formal kinetics is the formatting of the experimental results obtained in carefully controlled conditions. It led to the establishment of rate laws.

## Reaction rate :

The rate of reaction, in a given time interval, at a predetermined temperature, is equal to the change in concentration with respect to time.

It can be expressed in terms of the concentration of reactants or product concentration.

Example : AA is the reaction + bB -> cC + dD

The rate of reaction, at any moment, East :

• V = (-1/a) d[A] / dt = (-1/b) d[B] / dt ; rate of disappearance.
• V = (1/c) d[C] / dt = (1/d) d[D] / dt ; rate of onset.

The disappearance rates of appearance and are equal in absolute values, at time t.

## Order of the reaction :

In general, the rate of reaction is proportional to the concentrations of reacting species : v = k[A]a [B]b

or : k = specific kinetic constant of an evolving system, at a certain temperature,
α = partial order with respect to species A.
β = partial order with respect to the species B.
α + β = overall order of the reaction.

## molecularity :

It is the number of particles that do participate in the chemical reaction. It is indicated by the stoichiometric equation.

Note : It should not be confused with the order-molecular reaction. They are equal only if the reactions are elementary (simple).

Example : C4Hg —> 2 C2H4 : molecularity = 1 (monomolecular)

## Simple Order Reactions :

a- Reaction of zero order :
In a typical reaction A - * Products, speed is expressed by : v = – d[A] / dt = k[A]° = k. Therefore : [A] = -kt + constant.
to t = 0 [A] = [A0] = constant. The law of variation of the concentration is, with time :
[A] – [A0] = -kt —> [A0] – [A] = kt.
The constant k = ([A0] -[A])/t s'exprime in mol.Ltps-1.
In theory, the reagent is completely consumed only after an infinite time. That is why, usually defines the time of half-life fi / 2 of a reagent by the time required to consume half the usable concentration of this reagent.
The concentration is then : [A] = [A0] 12. It follows that : Xa = [A0] /2k.
Note : The graphical representation of the concentration versus time is a straight line whose slope is equal to -k.

b- order reaction 1 :
In a reaction type A -> products,
The speed is expressed by : V = – d[A] / dt = k[A]
Therefore : Ln[A] = -kt + constant.
to t = 0 ; [A] = [A0] —► Ln[A] = -kt + Ln[A0]. The law of variation of the concentration is, with time :
Ln([A]/[A0]) = -kt —► [A] = [A0]e-kt. The rate constant k = (1/t) Ln([A]/[A0]) speaks in tps-1.
The half reaction time, for which [A] = [A0] / 2, is then equal to : t1/2 = Ln2 / k = 0,693/k.
Note : The plot of the logarithm of the concentration versus time is right -k negative slope and intercept Ln[A0].

c- order reaction 2 :
In a reaction type A + A —> products,
speed is expressed by : V = – d[A] / dt = k[A]2
Therefore : d[A] / [A]2 = -Kdt - 1/[A] – 1/[A0] = kt.
to t = 0 [A] = [A0] —* k = (1/t)(1/[A] – 1/[A0]) s'exprime in mol-1Ltps-1.
Replacing the value of the concentration [A] = [A0] / 2 in the rate equation, we obtain : tn = (1/k)(1/[A0]).
Note : The graphical representation of 1/[A] over time is a line of slope + k and intercept 1/[A0].

## Determining the order of a reaction :

To establish the order of a reaction, there are two means.

1- Calculation of the rate constant k to check the corresponding equation :
If k is expressed as mol L-1tps-1, the reaction is zero order.
If k is expressed as gst-1, the reaction is of order 1.
If k is expressed in mol-1Ltps-1, the reaction is of order 2.

2- Graphic Representation :

• For a zero-order reaction, the plot of the concentration versus time gives a right -k negative slope and the intercept [A0] • For an order of reaction 1, the plot of Ln[A] over time is right -k negative slope and intercept Ln[A0], • For an order of reaction 2, the blaze 1/[A] over time is a straight line of positive slope + k and intercept l /[A0]. Course of Dr Tayeb Benmachiche Akila – Faculty of Constantine