**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 : C_{4}Hg —> 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] = [A_{0}] = constant. The law of variation of the concentration is, with time :

[A] – [A_{0}] = -kt —> [A_{0}] – [A] = kt.

The constant k = ([A_{0}] -[A])/t s'exprime in mol.L^{–}tps^{-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] = [A_{0}] 12. It follows that : Xa = [A_{0}] /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] = [A_{0}] —► Ln[A] = -kt + Ln[A_{0}]. The law of variation of the concentration is, with time :

Ln([A]/[A_{0}]) = -kt —► [A] = [A_{0}]e^{-kt}. The rate constant k = (1/t) Ln([A]/[A_{0}]) speaks in tps^{-1}.

The half reaction time, for which [A] = [A_{0}] / 2, is then equal to : t_{1/2} = Ln2 / k = 0,693/k.

Note : The plot of the logarithm of the concentration versus time is right -k negative slope and intercept Ln[A_{0}].

**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/[A_{0}] = kt.

to t = 0 [A] = [A_{0}] —* k = (1/t)(1/[A] – 1/[A_{0}]) s'exprime in mol^{-1}Ltps^{-1}.

Replacing the value of the concentration [A] = [A_{0}] / 2 in the rate equation, we obtain : tn = (1/k)(1/[A_{0}]).

Note : The graphical representation of 1/[A] over time is a line of slope + k and intercept 1/[A_{0}].

**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^{-1}tps^{-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^{-1}Ltps^{-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 [A_{0}]

• For an order of reaction 1, the plot of Ln[A] over time is right -k negative slope and intercept Ln[A_{0}],

• For an order of reaction 2, the blaze 1/[A] over time is a straight line of positive slope + k and intercept l /[A_{0}].

*Course of Dr Tayeb Benmachiche Akila – Faculty of Constantine*