CBSE Class 12 Chemistry Chemical Kinetics Notes Set 06

Revision Notes

Rate of a Chemical Reaction and Factors Affecting Rate of Reactions

• Chemical Kinetics: It is the branch of physical chemistry which deals with study of the rate of chemical reaction and the mechanism by which the reaction occurs.

• Rate of Reaction: The rate of reaction is the change of concentration of any reactant or product with time, for a reaction.
  \( \text{A} + \text{B} \rightarrow \text{C} \)
  Rate of reaction, \( \text{A} = \frac{\text{Decrease in concentration of A}}{\text{Time taken}} = \frac{-\Delta[\text{A}]}{\Delta t} \)
  Similarly, \( \text{B} = \frac{-\Delta[\text{B}]}{\Delta t} \)
  and for product \( \text{C} = \frac{+\Delta[\text{C}]}{\Delta t} \)
  where, [A], [B] and [C] are molar concentrations of the reactants and the product respectively.
• Unit of rate of reaction: \( \text{mol L}^{-1} \text{s}^{-1} \) or \( \text{mol L}^{-1} \text{min}^{-1} \) (in liquid), \( \text{atm s}^{-1} \) or \( \text{atm min}^{-1} \) (in gaseous form).
• Instantaneous rate of reaction: Instantaneous rate is defined as the rate of change in concentration of any one of the reactant or product at a particular time.
  \( \text{Instantaneous rate} = \frac{dx}{dt} = \frac{-d[\text{A}]}{dt} = \frac{-d[\text{B}]}{dt} = \frac{+d[\text{C}]}{dt} \)

• Average rate of reaction: The rate of reaction measured over a long time interval is called average rate of a reaction. Average rate \( = \frac{\Delta x}{\Delta t} \), where, \( \Delta x \) = change in concentration in given time and \( \Delta t \) = time taken.

• Factors affecting the rate of a chemical reaction:
  • (i) Concentration of reactants: Rate of reaction is directly proportional to the concentration of the reactants. Thus, to increase the rate of a reaction the concentration of the reactants has to be increased.
  • (ii) Temperature: The rate of a reaction increases with the increase in temperature. Increase in temperature increases the kinetic energy of the molecules which results in the increase in rate of reaction.
  • (iii) Pressure: Pressure affects the rate of only gaseous reactions. Increase in pressure decreases volume and increases concentration. Increase in concentration increases the rate of reaction.
  • (iv) Presence of catalyst: The rate of many reactions is greatly affected by the presence of a catalyst. In the presence of a catalyst, the activation energy of a reaction decreases due to which the reaction proceeds at a faster rate.
  • (v) Nature of the reactants: In a chemical reaction, some bonds are broken while some new bonds are formed. Thus, if the molecules are simpler, then less bonds will rupture and the rate of reaction becomes fast while in complex molecules, more bonds will rupture and consequently the rate of reaction decreases.
  • (vi) Surface area of the reactants: In some heterogeneous reactions, the reaction takes place at the surface of the reactant. Thus in such reactions, the reaction rate is greatly affected by the surface area. Marble powder reacts faster than marble chips.
  • (vii) Effect of radiations: The reactions which are initiated by the radiations of particular wavelengths are termed as photochemical reactions. These reactions generally proceed at a faster rate than normal thermal reactions.
  • (viii) Effect of physical state: Rate of reaction depends upon physical state of the reactant, e.g., \( \text{I}_2\text{(g)} \) reacts faster than \( \text{I}_2\text{(s)} \). \( \text{AgNO}_3\text{(aq)} \) reacts with NaCl but \( \text{AgNO}_3\text{(s)} \) does not react with NaCl.
• Rate law: Rate law or rate equation is the expression which relates the rate of reaction with concentration of the reactants. The constant of proportionality ‘\( k \)’ is known as rate constant. The rate law states that the rate of reaction is directly proportional to the product of molar concentration of reactants and each concentration is raised to some power which may or may not be equal to stoichiometric coefficients of reacting species.
  \( \text{Rate} = k[\text{A}]^m [\text{B}]^n \)
• Rate constant: Rate constant is also called specific reaction rate. When concentration of both reactants are unity (one), then the rate of reaction is known as rate constant. It is denoted by ‘\( k \)’.
• Molecularity: Total number of atoms, ions or molecules of the reactants involved in the reaction is termed as molecularity. It is always a whole number. It is never more than three. It cannot be zero.
  Example:
  \( \text{NH}_4\text{NO}_2 \rightarrow \text{N}_2 + 2\text{H}_2\text{O} \) (Unimolecular reaction)
  \( 2\text{HI} \rightarrow \text{H}_2 + \text{I}_2 \) (Bimolecular reaction)
  \( 2\text{NO} + \text{O}_2 \rightarrow 2\text{NO}_2 \) (Trimolecular reaction)
• Elementary reaction: An elementary reaction is a chemical reaction in which one or more of the chemical species react directly to form products in a single reaction step and with a single transition state.
• For a complex reaction generally, molecularity of the slowest step is same as the order of the overall reaction.
• Initial rate of reaction: The rate at the beginning of the reaction when the concentrations have not changed appreciably is called initial rate of reaction.
• Rate determining step: The slowest step in the reaction mechanism is called rate determining step.

Order of a Reaction, Integrated Rate Equations and Half-life of a Reaction

• Order of reaction: Order is defined as the sum of powers of concentration of the reactants in the experimentally derived rate equation or rate law expression. Order of reaction is experimentally determined and is not written from the balanced chemical equation. Order of reaction can be whole number, zero or fractional.

• Zero order reaction: The rate of reaction does not change with the concentration of the reactants.
  i.e., \( \text{Rate} = k [\text{A}]^0 \). Rate constant of zero order reaction is
  \( k = \frac{[\text{A}]_0 - [\text{A}]}{t} \), where ‘\( k \)’ is rate constant, \( [\text{A}]_0 \) is initial concentration of reactant.
  Unit of the rate constant \( k \) is \( \text{mol L}^{-1} \text{s}^{-1} \). Decomposition of gaseous ammonia on hot platinum, thermal decomposition of HI on gold surface and photochemical reaction between hydrogen and chlorine are examples of zero order reaction.
• First order reaction: The rate of reaction is directly proportional to the first power of the concentration of reacting substance. i.e., \( \text{Rate} = k[\text{A}]^1 \). Rate constant of the first order reaction is
  \( k = \frac{2.303}{t} \log \frac{a}{a - x} \)
  
  \( \implies \)
  \( k = \frac{2.303}{t} \log \frac{[\text{A}]_0}{[\text{A}]} \)
  where ‘\( a \)’ is initial concentration and \( (a - x) \) is the concentration after time ‘\( t \)’.
  Unit of ‘\( k \)’ is \( \text{s}^{-1} \) or \( \text{min}^{-1} \). Decomposition of \( \text{N}_2\text{O}_5 \) and \( \text{N}_2\text{O} \) are some examples.
• Second order reaction: The reaction in which sum of powers of concentration terms in rate law or rate equation is equal to 2.
  \( \therefore \text{Rate} = \frac{dx}{dt} = k[\text{A}][\text{B}] \)
  Unit of rate constant is \( \text{mol}^{-1} \text{L s}^{-1} \) or \( \text{M}^{-1} \text{s}^{-1} \), where M is molarity.

• Equation for typical first order gas phase reaction: \( \text{A(g)} \rightarrow \text{B(g)} + \text{C(g)} \)
  \( k = \frac{2.303}{t} \log \frac{p_i}{p_{\text{A}}} \)
  or
  \( k = \frac{2.303}{t} \log \frac{p_i}{(2p_i - p_t)} \)
  where \( p_i \) is the initial pressure of A at time, \( t = 0 \) and \( p_t \) is the total pressure at time \( t \).
• Half-life of a reaction: The time taken for a reaction when half of the initial value has reacted is called half-life of a reaction.
  For zero order reaction,
  \( t_{1/2} = \frac{[\text{A}]_0}{2k} \)
  where \( [\text{A}]_0 \) is initial and last concentration of reaction it means there is no change in concentration and ‘\( k \)’ is rate constant.
  For 1^st order reaction,
  \( t_{1/2} = \frac{0.693}{k} \)
• \( n^{\text{th}} \) order reaction: In general for \( n^{\text{th}} \) order reaction of the type
  A → products, where, \( \frac{dx}{dt} = k[\text{A}]^n \)
  \( k_n = \frac{1}{t(n - 1)} \left[ \frac{1}{[\text{A}]^{n - 1}} - \frac{1}{[\text{A}]_0^{n - 1}} \right] \)
  where \( [\text{A}]_0 \) is initial concentration, [A] is final concentration after time \( t \) and \( n \) can have all the values except 1.
• Half-life of a reaction of \( n^{\text{th}} \) order:
  \( t_{1/2} \propto \frac{1}{[\text{A}]_0^{n - 1}} \)
  \( t_{1/2} \propto [\text{A}] \) for zero order
  \( t_{1/2} \) is independent of [A] for 1^st order
  \( t_{1/2} \propto \frac{1}{[\text{A}]} \) for 2^nd order
  \( t_{1/2} \propto \frac{1}{[\text{A}]^2} \) for 3^rd order
  Amount of substances left after \( n \) half-lives \( = \frac{[\text{A}]_0}{2^n} \)

Integrated rate laws for the reactions of zero and first order:

• Life time: The time in which 98% of the reaction is completed is called life time.
• Catalyst: A catalyst is a substance that alters the rate of reaction without itself undergoing any chemical change at the end of reaction.
  Intermediate complex theory:
  \( \text{A} + \text{B (Reactants)} + \text{X (Catalyst)} \rightarrow \text{A} \cdots \text{B} \cdots \text{X (Intermediate complex)} \rightarrow \text{Product} + \text{Catalyst (X)} \)
  Characteristics of catalyst:
  • (i) Catalyzes only the spontaneous reaction.
  • (ii) Does not change the equilibrium constant.
  • (iii) Catalyzes both the forward and backward reactions.
  • (iv) Does not alter the free energy change (\( \Delta G \)) of a reaction.
  • (v) A small amount of the catalyst can catalyse large amount of reactions.

Mnemonics

• Concept: Zero order

  • Mnemonics: ZOR don't CCR
  • Interpretation: In zero order reaction, the rate of reaction does not change with concentration of the reactants.
• Concept: Effect of Collision
  • Mnemonics: ECFPM
  • Interpretation: Effective collisions lead to formation of product molecules.
• Concept: Catalyst
  • Mnemonics: CAR
  • Interpretation: A catalyst alters the reaction

Know the Formulae

• Integrated Rate Equations:
  • (i) For a zero order reaction:
    \( t = \frac{[\text{R}]_0 - [\text{R}]}{k} \) and \( t_{1/2} = \frac{[\text{R}]_0}{2k} \)
  • (ii) For a first order reaction:
    \( t = \frac{2.303}{k} \log \frac{[\text{R}]_0}{[\text{R}]} \) and \( t_{1/2} = \frac{0.693}{k} \)