KINETICS OF CHAIN REACTIONS

What are chain Reactions?

Chain reactions are a specific class of reactions in which highly reactive atoms or free radicals are produced as intermediates, carrying out the reaction rapidly for a long time.

The first studied reaction in 1934 by Frank O Rice and then after Karl F. Herzfeld (1892-1978) is referred to as chain reactions. The steady-state approximation has proved highly useful in accounting for their rate laws.

Chain reactions are between the H2 and Br2 to form HBR, for which a five-step mechanism has been proposed.

\[\displaystyle Step:1:B{{r}_{2}}\underset{{}}{\overset{{\mathop{k}_{1}}}{\longrightarrow}}2Br(Chain\text{ }Initation)\]
\[\displaystyle \text{Step:2: }Br+{{H}_{2}}\underset{{}}{\overset{{\mathop{k}_{2}}}{\longrightarrow}}HBr+H(\text{Chain Propagation)}\]
\[\displaystyle \text{Step:3: H+B}{{\text{r}}_{2}}\underset{{}}{\overset{{\mathop{k}_{3}}}{\longrightarrow}}HBr+Br(\text{Chain Propagation)}\]
\[\displaystyle \text{Step:4: H+HBr}\underset{{}}{\overset{{\mathop{k}_{4}}}{\longrightarrow}}{{H}_{2}}+Br(\text{Chain Retardation)}\]
\[\displaystyle \text{Step:5: 2Br}\underset{{}}{\overset{{\mathop{k}_{5}}}{\longrightarrow}}B{{r}_{2}}(\text{Chain Termination)}\]

Where k1, k2, k3, k4 and k5 are the rate constants for the different steps.

In these reactions, the reactant is converted to products, and the intermediate is regenerated. The regenerated intermediate allows the cycle to be repeated over and over again. Discuss the step briefly below;

STEP – I: CHAIN INITIATION

In this step, the bromine molecule acquires energy as a result of collision to dissociate into two Br atoms. It is the chain Initiation step. It produced the chain reactive Br atoms.

STEP – II & III: CHAIN PROPAGATION

 This step chain consumes Br, converting H2 and Br2 into HBr and regenerating Br.

STEP – IV : CHAIN RETARDATION OR (CHAIN INHIBITATION)

In this step, the chain is inhibited by the product HBr’s destruction and decreases the formation rate.

STEP – V: CHAIN TERMINATION

This step is the reverse of the chain initiation step. These steps remove Br atoms, converting them back to Br2 molecules.

The reactive species H and Br chain carriers are responsible for propagating the chain.

 The rate law for the formation of HBr from H2 and Br2 in the temperature range 500 – 1500k is found to be given by,

\[\displaystyle r=\frac{{d\left[ {HBr} \right]}}{{dt}}={{k}_{2}}{{\left[ {B{{r}_{2}}} \right]}^{{\frac{1}{2}}}}\]

Rice and Herzfeld accounted for the rate law by using a steady-state approximation for [H] and [Br], according to,

\[\displaystyle \frac{{d\left[ H \right]}}{{dt}}=\frac{{d\left[ {Br} \right]}}{{dt}}=0\]
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Bhoomika Sheladiya

BSc. (CHEMISTRY) 2014- Gujarat University
MSc. (PHYSICAL CHEMISTRY) 2016 - School of Science, Gujarat University

Junior Research Fellow (JRF)- 2019
AD_HOC Assistant Professor-(July 2016 to November 2021)

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