JEE Main & Advanced Chemistry Chemical Kinetics Rate Law : Molecularity And Order Of A Reaction

Rate Law : Molecularity And Order Of A Reaction

Category : JEE Main & Advanced

Molecularity is the sum of the number of molecules of reactants involved in the balanced chemical equation. Molecularity of a complete reaction has no significance and overall kinetics of the reaction depends upon the rate determining step. Slowest step is the rate-determining step. This was proposed by Van't Hoff.

Example :     \[N{{H}_{4}}N{{O}_{2}}\,\to {{N}_{2}}\,+\,2{{H}_{2}}O\]     (Unimolecular)

                     \[NO\,+\,{{O}_{3}}\,\to \,N{{O}_{2}}\,+\,{{O}_{2}}\]            (Bimolecular)

    \[2NO\,+\,{{O}_{2}}\,\to \,2N{{O}_{2}}\]               (Trimolecular)

The total number of molecules or atoms whose concentration determine the rate of reaction is known as order of reaction.

Order of reaction = Sum of exponents of the conc. terms in rate law

For the reaction \[xA+yB\to \text{Products}\]

The rate law is \[\text{Rate}={{\text{ }\!\![\!\!\text{ A }\!\!]\!\!\text{ }}^{\text{x}}}[B{{[}^{y}}\]

Then the overall order of reaction. \[n=x+y\]

where x and y are the orders with respect to individual reactants.

  • If reaction is in the form of reaction mechanism then the order is determined by the slowest step of mechanism.

           \[2A+3B\to {{A}_{2}}{{B}_{3}}\]

           \[A+B\to AB(\text{fast})\]

           \[AB+{{B}_{2}}\to A{{B}_{3}}(\text{slow})\]              (Rate determining step)

           \[A{{B}_{3}}+A\to {{A}_{2}}{{B}_{3}}(\text{fast})\]

           (Here, the overall order of reaction is equal to two.)

  • Molecularity of a reaction is derived from the mechanism of the given reaction. Molecularity can not be greater than three because more than three molecules may not mutually collide with each other.
  • Molecularity of a reaction can't be zero, negative  or fractional. order of a reaction may be zero, negative, positive or in fraction and greater than three. Infinite and imaginary values are not possible.
  • When one of the reactants is present in the large excess, the second order reaction conforms to the first order and is known as pesudo unimolecular reaction. (Table 11.1)

 

Order and molecularity of some reaction

S.

No.

Chemical equation

Molecularity

Rate law

Order w.r.t.

First reactant

Second reactant

Overall

1.

\[aA+bB\to \]product

a + b

\[\left( \frac{dx}{dt} \right)=k{{[A]}^{a}}{{[B]}^{b}}\]

a

b

a + b

2.

\[aA+bB\to \]product

a + b

\[\left( \frac{dx}{dt} \right)=k{{[A]}^{2}}{{[B]}^{0}}\]

2

zero, if B is in excess

2

3.

\[2{{H}_{2}}{{O}_{2}}\xrightarrow{Pt,\Delta }2{{H}_{2}}O+{{O}_{2}}\]

2 (Bimolecular)

\[\left( \frac{dx}{dt} \right)=k[{{H}_{2}}{{O}_{2}}]\]

1*

­­-----

1

4.

\[C{{H}_{3}}COO{{C}_{2}}{{H}_{5}}+{{H}_{2}}O\xrightarrow{{{H}^{+}}}\]

\[C{{H}_{3}}COOH+{{C}_{2}}{{H}_{5}}OH\]

2 (Bimolecular)

\[\left( \frac{dx}{dt} \right)=k[C{{H}_{3}}COO{{C}_{2}}{{H}_{5}}]\]

1*

Zero, if H2O is in excess

1

5.

\[\underset{\text{Sucrose}}{\mathop{{{C}_{12}}{{H}_{22}}{{O}_{11}}}}\,+{{H}_{2}}O\xrightarrow{{{H}^{+}}}\]

 \[\underset{\text{Glucose}}{\mathop{{{C}_{6}}{{H}_{12}}{{O}_{6}}}}\,+\underset{\text{Fructose}}{\mathop{{{C}_{6}}{{H}_{12}}{{O}_{6}}}}\,\]

2 (Bimolecular)

\[\left( \frac{dx}{dt} \right)=k[{{C}_{12}}{{H}_{22}}{{O}_{11}}]\]

1*

Zero, if H2O is in excess

1

6.

\[{{(C{{H}_{3}})}_{3}}CCl+O{{H}^{-}}\to \]

 \[{{(C{{H}_{3}})}_{3}}COH+C{{l}^{-}}\]

2 (Bimolecular)

\[\left( \frac{dx}{dt} \right)=k[{{(C{{H}_{3}})}_{3}}CCl]\]

1*

Zero, if OH does not take part in slow step

1

7.

\[C{{H}_{3}}Cl+O{{H}^{^{-}}}\to \] \[C{{H}_{3}}OH+C{{l}^{-}}\]

2 (Bimolecular)

\[\left( \frac{dx}{dt} \right)=k[C{{H}_{3}}Cl][O{{H}^{-}}]\]

1

1

2

8.

\[{{C}_{6}}{{H}_{5}}{{N}_{2}}Cl\xrightarrow{\Delta }\] \[{{C}_{6}}{{H}_{5}}Cl+{{N}_{2}}\]

1 (Unimolecular)

\[\left( \frac{dx}{dt} \right)=k[{{C}_{6}}{{H}_{5}}{{N}_{2}}Cl]\]

1

----

1

9.

\[C{{H}_{3}}CHO\xrightarrow{\Delta }C{{H}_{4}}+CO\]

1 (Unimolecular)

\[\left( \frac{dx}{dt} \right)=k{{[C{{H}_{3}}CHO]}^{3/2}}\]

1.5

----

1.5

10.

\[{{H}_{2}}{{O}_{2}}+2{{I}^{-}}+2{{H}^{+}}\to \]\[2{{H}_{2}}O+{{I}_{2}}\]

5

\[\left( \frac{dx}{dt} \right)=k[{{H}_{2}}{{O}_{2}}][{{I}^{-}}]\]

1

1

(H+is medium)

2

11.

\[2{{O}_{3}}\to 3{{O}_{2}}\]

2 (Bimolecular)

\[\left( \frac{dx}{dt} \right)=k{{[{{O}_{3}}]}^{2}}[{{O}_{2}}]\]

1

-1 with respect to O2

1

           *Pseudo-unimolecular reactions.

 

 

Rate constant and other parameters of different order reactions

Order

Rate constant

Unit of rate constant

Effect on rate by changing conc. to m times

(Half-life period) T50=

0

\[{{k}_{0}}=\frac{x}{t}\]

conc. time–1

(mol L–1 s–1)

No change

\[\frac{a}{2{{k}_{0}}}\]

1

\[{{k}_{1}}=\frac{2.303}{t}{{\log }_{10}}\left( \frac{a}{a-x} \right)\], \[C={{C}_{0}}{{e}^{-{{k}_{1}}t}}\]

\[N={{N}_{0}}{{e}^{-{{k}_{1}}t}}\], \[{{k}_{1}}=\frac{2.303}{({{t}_{2}}-{{t}_{1}})}{{\log }_{10}}\frac{(a-{{x}_{1}})}{(a-{{x}_{2}})}\]

time–1 (s–1)

m times

\[\frac{0.693}{{{k}_{1}}}\]

2

\[{{k}_{2}}=\frac{1}{t}\left[ \frac{1}{(a-x)}-\frac{1}{a} \right]\]\[=\frac{x}{ta(a-x)}\] (for the case when each reactant has equal concentration) \[{{k}_{2}}=\frac{2.303}{t(a-b)}{{\log }_{10}}\left[ \frac{b(a-x)}{a(b-x)} \right]\](for the case when both reactants have different concentration)

conc–1 time–1

(mol L–1) s–1

L mol­–1 s–1

m2 times

\[\frac{1}{{{k}_{2}}a}\]

3

\[{{k}_{3}}=\frac{1}{2t}\left[ \frac{1}{{{(a-x)}^{2}}}-\frac{1}{{{a}^{2}}} \right]\]

conc–2 time–1

(mol L–1)–2  s–1

L2 mol­–2 s–1

m3 times

\[\frac{3}{2{{k}_{3}}{{a}^{2}}}\]

n

\[{{k}_{n}}=\frac{1}{(n-1)t}\left[ \frac{1}{{{(a-x)}^{n-1}}}-\frac{1}{{{(a)}^{n-1}}} \right]\]; \[n\ge 2\]

conc(1–n) time–1

(mol L–1)(1–n) s–1

L(n–1) mol­(1–n) s–1

mn times

\[\frac{{{2}^{n-1}}-1}{(n-1){{k}_{n}}{{(a)}^{n-1}}}\]

 


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