(in order for Cl 2 to dissociate to two Cl atoms it must obtain energy from coll

Question

(in order for Cl2 to dissociate to two Cl atoms it must obtain energy from collisions with other gas molecules, M. The reaction is Cl2 + M ? 2Cl + M. from this equation one may expect that the rate of reaction for Cl is r = 2k[Cl2][M], but experimental studies show that r= k[Cl2] at high concentration of M. Lindmann proposed a reaction mechanism that was consistent with these experimental observations.

a) Write down the steps that are included in the lindmann mechanism for the above reaction.

b) use the steady state approximation (SSA) to show that this mechanism is consistent with the experimenta rate law at high cencentration of M,)

Explanation / Answer

a.) GENERAL MECHANISM

The schematic reaction Cl2 + M ? 2Cl + M is assumed to consist of two elementary steps:

STEP 1: Bimolecular activation of Cl2

Cl2 + M ? 2Cl + M -----------(1)

with

STEP 2: Unimolecular reaction of 2Cl

2Cl ? Product

with

Assuming that the concentration of intermediate 2Cl is held constant according to the quasi steady-state approximation, what is the rate of formation of product Product ?

SOLUTION-

First, find the rates of production and consumption of intermediate 2Cl . The rate of production of 2Cl in the first elementary step (Equation 1) and 2Cl is consumed both in the reverse first step and in the forward second step. The respective rates of consumption of 2Cl are:

d[Cl]/dt = k1[Cl2][M](forward first step) ? k?1[Cl]2[M](reverse first step) ? k2[Cl]2(forward second step)   ------(3)

According to the steady-state approximation,

d[Cl]/dt = 0 (approx) ---------(4)

Therefore the rate of production of 2Cl (first term in Equation 3) equals the rate of consumption (second and third terms in Equation 3):

k1[2Cl][M] = k?1[Cl]2[M] + k2[Cl]2 -------(5)

Solving for [Cl], it is found that

[Cl]2 = k1[Cl2][M] / k?1[M] + k2 -------(6)

The overall reaction rate is (Equation 2)

d[P] / dt = k2[Cl]2 ---------(7)

Now, by substituting the calculated value for [Cl] (Equation 6 into Equation 7), the overall reaction rate can be expressed in terms of the original reactants Cl2 and M as follows:

d[P] / dt = k1k2[Cl2][M] / k?1[M] + k2 ----------(8)

The rate law for the Lindemann mechanism is not a simple first or second order reaction. However, under certain conditions (discussed below), Equation 8 can be simplified.

THREE PRINCIPLES OF THE LINDEMANN MECHANISM

b.) Steady-state Approximation - In the steady-state approach, we write the full rate law for the intermediate Cl, and set this rate equal to zero. Hence this mechanism is consistent with with the experimental rate law at high concentration of M.

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