# Chemical Kinetics IIT JEE Study Material

Chemical kinetics is a branch of physical chemistry that explains the rate of the chemical reactions and the mechanism by which the chemical reaction takes place including the effects of pressure, temperature, concentration, etc. The rate of the chemical reaction is defined as the change in concentration of products or reactants in a specific time interval. The Reaction Rate is measured in mol $\mathbf{L^{-1}}$ $\mathbf{s^{-1}}$ or mol $\mathbf{L^{-1}}$ $\mathbf{min^{-1}}$.

The Factors affecting the reaction rates:

1. Reaction temperature

2. Concentration of reactants

3. Presence of catalyst

4. If a catalyst or a reactant is solid then surface area also affects the reaction rates.

Chemical Kinetics IIT JEE Important Topics

A. Rates of Chemical Reactions

B. Order of reactions

C. Rate constant

D. First order reactions

E. Temperature dependence of rate constant (Arrhenius Equation)

The General Form of a Chemical Reaction:

$\mathbf{a\;A\;+\;b\;B\; \rightarrow \;c\;C\;+\;d\;D}$

The Rate of disappearance of A = $\mathbf{-\;\frac{d[A]}{dt}}$ and the Rate of disappearance of B = $\mathbf{-\;\frac{d[B]}{dt}}$

The Rate of appearance of C = $\mathbf{\frac{d[C]}{dt}}$ and the Rate of appearance of D = $\mathbf{\frac{d[D]}{dt}}$

Therefore, the rate of General Reaction:

$\mathbf{-\;\frac{1}{a}\;\frac{d[A]}{dt}\;=\;-\;\frac{1}{b}\;\frac{d[B]}{dt}\;=\;\frac{1}{c}\;\frac{d[C]}{dt}\;=\;\frac{1}{d}\;\frac{d[D]}{dt}}$

The + ve sign indicates that the concentration of compound C and D increases with time and the – ve sign indicates that the concentration of compound A and B decreases with time.

Rate Constant:

The rate law or the rate equation is the expression that relates the rate of any reaction with the concentration of the reactants.

$\mathbf{Rate\;prop\; to \;[A]^{a}.[B]^{b}\;\;or\;\;Rate\;=\;k\;[A]^{a}.[B]^{b}}$

Here, k = constant of proportionality known as the Rate Constant. The value of k is independent of the initial concentrations of the reactants and dependent on the temperature. At any fixed temperature, k is a constant characteristic of the reaction. Greater values of k indicate faster reaction rates whereas small values of k indicate slow reaction rates.

Order of Reaction:

If the rate of reaction = $\mathbf{\;k\;[A]^{a}\;\;[B]^{b}\;\;[C]^{c}}$

Then, a + b + c = order of the reaction

And, the order with respect to A, B, and C are a, b, and c respectively.

Zero Order Reaction:

In zero order reactions, the rate of reaction is independent of the concentration of the reactants.

$\mathbf{A\; \rightarrow \;Products\;\;\;and\;\;\;Rate\;=\;k\;[A]^{0}\;=\;k\;mol\;L^{-1}\;s^{-1}}$

The Time required for the completion of reaction:

$\mathbf{t\;=\;\frac{[A]_{0}}{k}\;\;and\;\;t_{\frac{1}{2}}\;=\;\frac{0.5\;[A]_{0}}{k}}$

Unit of rate constant (k) is: mol $\mathbf{L^{-1}}$ $\mathbf{time^{-1}}$

Examples of Zero Order Reaction:

1. $\mathbf{2\;HI\;(g)\;\;xr\rightarrow[Surface]{Au}\;\;H_{2}\;(g)\;+\;I_{2}\;(g)}$

2. $\mathbf{2\;NH_{3}\;(g)\;\;xr\rightarrow[Surface]{Mo\;or\;W}\;\;N_{2}\;+\;3\;H_{2}}$

First Order Reaction:

In first order reactions, the rate of reaction is proportional to the concentration of one reactant only.

$\mathbf{A\;\;\; \rightarrow \;\;\;Products}$

$\mathbf{Rate\;=\;k_{1}\;[A]\;\;or\;\;\frac{dx}{dt}\;=\;k_{1}\;(a\;-\;x)}$

A. Integrated 1st order rate equation is: $\mathbf{k_{1}\;=\;\frac{2.303}{t}\;log\;\left [ \frac{a}{a\;-\;x} \right ]}$

B. Exponential form of 1st order equation is: $\mathbf{C_{t}\;=\;C_{0}\;e^{\;-\;k_{1}\;t}}$

C. Unit of rate constant (k) is: $\mathbf{Time^{-1}}$

D. Average Life = $\mathbf{\frac{1}{k}}$ and Half Life = $\mathbf{\frac{0.693}{k_{1}}}$

Examples of First Order Reaction:

1. Mineral acid-catalyzed hydrolysis of esters.

2.$\mathbf{C_{12}\;H_{22}\;O_{11}+H_{2}\;Oxr\rightarrow[Inversion]{H^{+}\;cat. \;hy.}\;C_{6}\;H_{12}\;O_{6}\;(G)+C_{6}\;H_{12}\;O_{6}\;(F)}$

Second Order Reaction:

Case 1: When the concentrations of both the reactants are equal or two molecules of the same reactant are involved

A. Differential rate equation: $\mathbf{\frac{dx}{dt}\;=\;k_{2}\;(a\;-\;x)^{2}}$

B. Integrated rate equation: $\mathbf{k_{2}\;t\;=\;\frac{1}{a\;-\;x}\;-\;\frac{1}{a}}$

Case 2: When the initial concentrations of the two reactants are different

A. Differential rate equation: $\mathbf{\frac{dx}{dt}\;=\;k_{2}\;(a\;-\;x)\;(b\;-\;x)}$

B. Integrated rate equation: $\mathbf{k_{2}\;=\;\frac{2.303}{t\;(a\;-\;b)}\;\;log_{10}\;\frac{b\;(a\;-\;x)}{a\;(b\;-\;x)}}$

Unit of rate constant (k) is: L $\mathbf{mol^{-1}}$ $\mathbf{L^{-1}}$

Examples of Second Order Reaction:

1. $\mathbf{2\;O_{3}\;\; \rightarrow \;\;3\;O_{2}}$

2. Hydrogenation of ethane:

$\mathbf{C_{2}\;H_{4}\;+\;H_{2}\;\;\overset{100\;^{0}C}{ \rightarrow}\;\;C_{2}\;H_{6}}$

Higher Order Reaction:

A. $\mathbf{A\;\; \rightarrow \;\;Product}$

B. $\mathbf{k_{n}\;t\;=\;\frac{1}{n\;-\;1}\;\left [ \frac{1}{\left ( a\;-\;x \right )^{n\;-\;1}}\;-\;\frac{1}{a^{\;n\;-\;1}} \right ]}$ [Where, n ≠ 1 and n = order]

C. $\mathbf{t_{\frac{1}{2}}\;=\;\frac{1}{k_{n}\;(n\;-\;1)}\;\left [ \frac{2^{n-1}\;-\;1}{a^{n\;-\;1}} \right ]}$

#### Practise This Question

The points with position vectors 60^i+3^j, 40^i8^j,a^i52^j are collinear, if