Chemical Kinetics

Order and Molecularity of a Reaction, Rate Law and Specific Rate Constant

Rate Law: Rate law (or) rate equation is the mathematical expression representing the experimental rate of reaction in terms of the concentrations of reacting species (some times produced species also) that influence the rate of reaction.
For a reaction aA + bB → products
rate = k[A]x [B]y
where x is may or may not be "a"
y is may or may not be "b"
where k is rate constant, defined as the rate of a reaction when the concentrations of all the substances, appearing in the rate law are unity.

Characteristics of rate constant:
(a) It has a constant value for a given reaction at a given temperature.
(b) Its value increases with increase in temperature.
(c) Its value does not depend upon initial concentration.
(d) Faster reactions have higher values of rate constants
(e) Its units depend upon the units of time and concentration and the order of reaction.

Order of reaction:
(i) Order of a chemical reaction is the sum of the powers to which the concentration terms are raised for expressing the rate law.
rate = k [A]x [B]y
∴ order = x + y
x = order w.r.t A
y = order w.r.t B
(ii) The order of a reaction may be −ve integer, +ve integer, zero or a fraction.
(iii) it is experimental factor
(iv) It can be taken from balanced equation of reaction if it is elementary (single step) reactions otherwise the slowest step of mechanism gives the rate law and order of reaction.
a. Zero order reaction:
(i) It is a reaction whose rate remains constant throughout.
(ii) The rate is independent of concentration of reactants.
(iii) eg: \tt H_2+Cl_2\xrightarrow {h\nu}2HCl
\tt 2NH_3\xrightarrow [\Delta]{Au\ or\ Pt}2HCl
(iv) Graphs

Characteristics of zero order reaction:
(1) Rate of the reaction remains constant throughout the reaction.
(2) Half life time is directly proportional to the initial concentration and inversely proportional to the rate constant.
(3) Rate of reaction is independent of initial concentration of reactant.
(4) Whatever be the amount of substance taken and whatever be the value of half-life, nothing will be left over after 2-half lives.

1st order reaction:
It is a reaction whose rate is directly proportional to first power of molar concentration of a single reactant i.e, it is uni molecular in nature.
e.g: (i)\tt 2N_2O_5\left(g\right)\xrightarrow \Delta 4NO_{2\ \left(g\right)}+O_{2\ \left(g\right)}r=K[N2O5]
(ii) \tt 2H_2O_{2\left(l\right)}\longrightarrow 2H_{2}O_{\ \left(l\right)}+O_{2\ \left(g\right)} r=K[H2O2]
(iii) \tt NH_4NO_{2\left(s\right)}\xrightarrow \Delta N_{2\left(g\right)}+2H_2O_{\left(g\right)}
(iv)All nuclear disintegrations are first order reactions
\tt ^{226}_{88}Ra\longrightarrow^{226}_{86}Rn+^{4}_{2}He r=K[Ra]

Pseudo 1st order reaction:
A reaction is called pseudo 1st order reaction, if it follows 1st order kinetics but the molecularity is not one.

Reaction is a pseudo 1st order or pseudo uni molecular reaction if H2O is taken in large excess.
Rate r = K[CH3COOC2H5]
Another example is
\tt C_{12}H_{22}O_{11}+H_2O\xrightarrow{H^+}C_6H_{12}O_{6}(Glucose)+C_6H_{12}O_6(Fructose)

Factors Affecting order of reaction:
(a) Nature of reactants: The reaction of (CH3)3 C Br with NaOH(aq) is a first order reaction where as that of CH3CH2CH2CH2-Br is 2nd order reaction.
(b) Nature of solvents: Polarity of the solvent may change the order of reaction. If pH of solution is high, a reaction of 2nd order may become a first order reaction in the above mentioned case.
(c) Concentrations of reactants: If the concentration of all the reactants except one are in large excess, the reaction may become 1st order reaction.
(d) Mechanism of the reaction: In a multi-step reaction, the slowest step determines the rate of reaction, rate law and the order of reaction.

Molecularity of a reaction:
(i) It is the number of reacting species that collide simultaneously to bring about a chemical reaction.
(ii) Molecularities 1, 2 and 3 are quite common while higher values are very uncommon because of very rare changes of simultaneous collisions of such numbers of reactants.

Units of rate constant K:
Units of K = M1−n time−1
M=Molarity = mole litre−1

Part1:View the Topic in this Video from 10:46 to 54:15

Part2:View the Topic in this Video from 0:40 to 12:15

Part3:View the Topic in this Video from 0:08 to 12:49

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1. \tt k=\frac{2.303}{t}\log_{10}\frac{a}{(a-x)} (For first order reactions)

2. \tt k=\frac{1}{t}\left[\frac{1}{a}-\frac{1}{a-x}\right] (For second order reactions)

3. \tt k=\frac{1}{2t}\left[\frac{1}{\left(a-x\right)^2}-\frac{1}{a^2}\right] (For third order reactions)

4. For a reaction, aA + bB → product
\tt Rate=\left(\frac{dx}{dt}\right)\propto\left[A\right]^a\left[B\right]^b;\left(\frac{dx}{dt}\right)=k\left[A\right]^a\left[B\right]^b