LINDEMANN THEORY G.SURIYA PRAKASH(B843041), 2ND MSC CHEMISTRY, SCHOOL OF CHEMISTRY, MADURAI KAMARAJ UNIVERSITY. THEORIES OF UNIMOLECLAR GASEOUS REACTION It is easy to understand a bimolecular reaction on the basis of collision theory. Thus, when two molecules A and B collide, their relative kinetic energy exceeds the threshold energy with the result that the collision results in the breaking of bonds and the formation of new bonds . But how can one account for a unimolecular reaction ? If we assume that in such a reaction (A P ),the molecule A acquires the necessary activation energy by colliding with another molecule , then the reaction should obey second-order kinetics and not the first order kinetics which is actually observed in several unimoleclar gaseous reaction. 1.Lindemann theory According to this theory , a unimolecular reaction A proceeds following mechanism; A+ A K1 P A* + A K-1 A K2 P Here A* is the energized A molecule which has acquired sufficient vibrational energy to enable it to isomerize or decompose. A* is simply a molecule in a high vibrational energy level and not an activated complex. In first step what actually happen is that the kinetic energy of the second molecule is transferred into the vibrational energy of the first. . In the lindemann mechanism , a time lag exists between the energization A to A* and the decomposition (or isomerization) of prodcts . during this time lag , A* can be de-energized back to A. The rate of formation = k1 [A]2 and The rate of decomposition = K-1 [A][A*] +K2 [A*] According to study state approximation(s.s.a), d[A*]/dt = K1[A]2 _ K-1 [A][A*] – K2 [A*] = 0 …………….(1) so that [A*] = K1 [A]2 / K-1 [A]+ K2 …………………………………………(2) The rate of the reaction is given by r = - d[A] / dt = k2 [A*] ……………………………(3) sbstituting Eq. (2) in Eq. (3), r = K1 K2 [A]2 / K-1 [A] + K2 ………….(4) The rate law given by Eq.( 4) has no definite order . we can , however, two limiting cases , Case 1 ; If k-1[A] >> K2 Then the K2term in the denominator can be neglected , r = ( k1 k2 / k-1 )[A] …………………(5) which is the rate equation for a first order reaction. In a gaseous reaction , this is the high – pressure limit because at very high pressure ,[A] is very large so that k1[A]>>K2. Case 2 ; If k2 >>k-1[A] then the k-1 [A] Term in denominator can be neglected, r = k1[A]2 ……………….(6) Which is the rate equation for a second –order reaction . This is the low pressure limit. The experimental rate is defined as r = kuni [A] Where ……………………….(7) kuni is the unimolecular rate constant . Comparing eqs.(4) and (5),we have kuni = k’ = k1k2[A] /k -1[A]=K2 ……………..(8) LIMITATION OF LINEMANN THEORY Equ. 8 becomes k’ = k1 k2[A]/k-1[A] = K2 . . . K-1[A] >> K2 . . . K1 = K1 K2 [A] / K-1[A] . . K1 = K1 K2 / K-1 = K∞ …………(10) . . . . K’ = CONSTANT(K∞ ) . . ZERO ORDER REACTION Case 1; ……………(9) Case 2; k-1 << k2 k’ = k1 k2 [A] / K2 K’ = K[A] …………..(11) FIRST ORDER REACTION Plot of k’ verses [A] K ∞ ………………..........................…….... K’ [A] According to equ.(9), the plot of the first order rate constant K’ verses [A] is HYPERPOLA. The rate constant K’ is a constant in the heigher concentration range .but falls of low concentration. Application of this relationship to experimental data raises some difficulties Another difficulty with lindemann mechanism becomes evident when experimental results are in another way. Rewritting eq.(8) as, 1 /k’ = = k-1[A] + K2 / K K [A] 1 2 K-1[A]/K1K2[A] + K2 / K1K2[A] 1 /K’ = K-1 / K1K2 / + 1 K1[A] ………………..(12) Y = C + M x stright line equation Ploting 1 / K’ VS 1 / [A] give stright line . However ,deviation from linearity heave been found (fig -2.) THEORITICAL EXPERIMENTAL 1 / K’ Theoretical rate is heigher than the experimental rate . From this graph theoretical curve is stright line and the experimental line is hyperpola. 1 / [A] The variation between the two lines is one of the limitation of lindemann theory. The variation is further explained by the RRK and SLATERS theory.