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1. Order of Reactions

It is simplistic to assume that changing the concentration of a reactant will affect the rate of reaction.  We have observed that some reactions show that changing the concentration of reactants have no impact on the rate of the reaction.  In addition, there are those where doubling the concentration of the reactants, actually caused the rate of reaction to increase by four times.
The study of order of reactions help us to decide the effect of the concentration of the reactants on the rate of a chemical reaction.  Given a generic rate equation:
rate = k[A]n[B]m
where A and B are the reactants;  n and m are order of reaction for A and B respectively;  k = rate constant which is independent of concentration but affected by temperature.
In addition:        k = Ae-Ea/RT [This is Arrhenius equation;  A = Arrhenius constant, Ea = activation energy, R = gas constant]
In the GCE "A" level syllabus, we focus on:
(1)    Zero Order.  (e.g. where n = 0).  This implies that changing of the concentration of A have no effect on the rate.
(2)    First Order.  (e.g. where n = 1).  This implies that rate and concentration of A are directly proportional.
(3)    Second Order.  (e.g. where n = 2) .  This implies that rate is directly proportional to the square of the concentration of A.
The following concentration - time graphs and rate - concentration graphs help to show how we can recognise (i) Zero Order, (ii) First Order and (iii) Second Order graphically.
Concentration-time graphs:
Rate-concentration graphs:
Zero Order Reaction:
(1)    Rate of reaction is independent to the change in concentration.
First Order Reaction:
(1)    Rate of reaction is directly proportional to the change in concentration of the reactant.
(2)    Half-life is constant.  [Time taken for [rxt] to be halved is constant.]
(3)    t1/2 = ln 2 / k.  (t1/2 = half-life)  [k is dependent on Temperature (as it is affected be Ea but it is independent of concentration.]
Second Order Reaction:
(1)    Rate of reaction is directly proportional to the change in the square of the concentration of the reactant.
(2)    Half-life is not constant.
Pseudo - First Order Reaction:
(1)    Given that the following rate equation: rate = k[X][Y].
(2)    If X is in large excess or whose concentration does not quite change at the end of the reaction, [X] is a constant.
(3)    Hence, rate of reaction is affected by Y.  This implies =>  rate = k'[Y];  where k' = k[X].
(4)    Thus, this implies that reaction is now psuedo-first order.
(1)    Like first order reaction, (using the above situation), half-life of Y = t1/2 = ln 2 / k'
(2)    Since, k' = k[X], therefore t1/2 = ln 2 / k[X].
(3)    Hence, unlike a first order reaction, a pseudo first order reaction's half-life is dependent on concentration of the other reactant (which we have taken to be constant).
Significance of Order of Reactions:
Together with the rate equation, the order of reaction tells us the number of a particular species present in the slow step (also known as the rate determinating step) of a chemical reaction.
For example:  2X + Y -> A + D           it is found that the reaction has the following rate equation;  

                        rate = k[X][Y];

where X and Y are the reactants of the reaction
n = 1 and m = 1;  this implies that in the slow step of the reaction, there is one X and one Y in it.