Lindemann Mechanism & Types of Catalysis | Physical Chemistry PDF Download

• In chemical kinetics, the Lindemann mechanism (also called the Lindemann–Christiansen mechanism or the Lindemann–Hinshelwood mechanism) is a schematic reaction mechanism for unimolecular reactions. Frederick Lindemann and J. A. Christiansen proposed the concept almost simultaneously in 1921, and Cyril Hinshelwood developed it to take into account the energy distributed among vibrational degrees of freedom for some reaction steps.
• It breaks down an apparently unimolecular reaction into two elementary steps, with a rate constant for each elementary step. The rate law and rate equation for the entire reaction can be derived from the rate equations and rate constants for the two steps.
• The Lindemann mechanism is used to model gas phase decomposition or isomerization reactions. Although the net formula for a decomposition or isomerization appears to be unimolecular and suggests first-order kinetics in the reactant, the Lindemann mechanism shows that the unimolecular reaction step is preceded by a bimolecular activation step so that the kinetics may actually be second-order in certain cases.

Activated reaction intermediates

The overall equation for a unimolecular reaction may be written A → P, where A is the initial reactant molecule and P is one or more products (one for isomerization, more for decomposition).

• A Lindemann mechanism typically includes an activated reaction intermediate, labeled A*. 
• The activated intermediate is produced from the reactant only after sufficient activation energy is acquired by collision with a second molecule M, which may or may not be similar to A. It then either deactivates from A* back to A by another collision, or reacts in a unimolecular step to produce the product(s) P.
  The two-step mechanism is then
  

Rate equation in steady-state approximation

• The rate equation for the rate of formation of product P may be obtained by using the steady-state approximation, in which the concentration of intermediate A* is assumed constant because its rates of production and consumption are (almost) equal. This assumption simplifies the calculation of the rate equation.
• For the schematic mechanism of two elementary steps above, rate constants are defined as k₁ for the forward reaction rate of the first step, k_-1 for the reverse reaction rate of the first step, and k₂ for the forward reaction rate of the second step. 
• For each elementary step, the order of reaction is equal to the molecularity.
  The rate of production of the intermediate A* in the first elementary step is simply:
  
  A* is consumed both in the reverse first step and in the forward second step. The respective rates of consumption of A* are:
  
  According to the steady-state approximation, the rate of production of A* equals the rate of consumption. Therefore:
  
  Solving for   it is found that
  
  The overall reaction rate is
  
  Now, by substituting the calculated value for [A*], the overall reaction rate can be expressed in terms of the original reactants A and M
  

Reaction order and rate-determining step

• The steady-state rate equation is of mixed order and predicts that a unimolecular reaction can be of either first or second order, depending on which of the two terms in the denominator is larger. 
• At sufficiently low pressures, k_-1[M]≪ k₂ so that d[P]/dt=k₁[A][M], which is second order. That is, the rate-determining step is the first, bimolecular activation step.
  At higher pressures, however, k_-1[M]≫ k₂ so that  which is first order, and the rate-determining step is the second step, i.e. the unimolecular reaction of the activated molecule.
• The theory can be tested by defining an effective rate constant (or coefficient) k_uni which would be constant if the reaction were first order at all pressures:
  
  The Lindemann mechanism predicts that k decreases with pressure and that its reciprocal  is a linear function of  or equivalently of 1/p. Experimentally for many reactions, k does decrease at low pressure, but the graph of 1/k as a function of 1/p is quite curved. 
• To account accurately for the pressure-dependence of rate constants for unimolecular reactions, more elaborate theories are required such as the RRKM theory.

Decomposition of dinitrogen pentoxide

• In the Lindemann mechanism for a true unimolecular reaction, the activation step is followed by a single step corresponding to the formation of products. Whether this is actually true for any given reaction must be established from the evidence.
• Much early experimental investigation of the Lindemann mechanism involved study of the gas-phase decomposition of dinitrogen pentoxide 2N₂O₅ → 2N₂O₄ + O₂. This reaction was studied by Farrington Daniels and coworkers, and initially assumed to be a true unimolecular reaction. 
• However, it is now known to be a multistep reaction whose mechanism was established by Ogg as:

N₂O₅ ⇌ NO₂ + NO₃
NO₂ + NO₃ → NO₂ + O₂ + NO
NO + N₂O₅ → 3NO₂

• An analysis using the steady-state approximation shows that this mechanism can also explain the observed first-order kinetics and the fall-off of the rate constant at very low pressures.

Activity of Catalyst

• Catalyst has an ability to increase the rate of reaction. This ability of catalyst is known as the activity of catalyst. 
• It depends upon adsorption of reactants on the surface of catalyst. Chemisorption is the main factor governing the activity of catalysts. The bond formed during adsorption between the catalytic surface and the reactants must not be too strong or too weak.
• It must be strong enough to make the catalyst active whereas, not so strong that the reactant molecules get immobilized on the catalytic surface leaving no further space for the new reactants to get adsorbed. 
• Generally for the hydrogenation reaction, from Group 5 to Group 11 metals, the catalytic activity increases. The catalytic activity is found to be highest for group 7-9 elements of the periodic table.
  

Selectivity of Catalyst

• Catalysts are highly specific compounds. They have an ability to direct the reaction to yield a particular product. The reaction with same reactants but different catalyst may yield different products. This is termed as the selectivity of catalyst. Catalysts are highly selective in nature. 
• They can accelerate a particular reaction while inhibit another reaction. Hence, we can say a particular catalyst can catalyse one particular reaction only. It may fail to catalyse another reaction of the same type. 
• For example: reaction of hydrogen and carbon monoxide yields methane when nickel is used as catalyst, methanol when a mixture of zinc oxide and chromium oxide is used as catalyst and methanal when only copper is used as catalyst.
  
  

Types of catalysts
A catalyst is a chemical compound which makes the reaction occur more quickly by reducing the reaction’s activation energy barrier. During the reaction it isn’t eaten.

• Homogeneous catalyst – Homogeneous catalysts are usually soluble metal salts or compounds that are dissolved in an effective organic solvent that is used as the medium for reaction. (here catalyst and the reactants are on the same phase)
• Heterogeneous catalyst – A heterogeneous catalyst is a functional material which under conditions of reaction continually creates active sites with its reactants. (here catalyst and reactants are on different phase).