Consecutive reaction

The concentrations of the species involved in a consecutive reaction as a function of time.

Consecutive reactions , also known as follow-up reactions , are reactions in which starting materials are converted into products via one or more intermediate stages . The overall reaction is therefore the result of several successive steps, each step having its own rate constant . Probably the simplest consecutive reaction is:

${\displaystyle \mathrm {A{\xrightarrow {k_{1}}}B{\xrightarrow {k_{2}}}C} }$

In this reaction, the concentration of educt A decreases over time, while that of intermediate B increases, passes through a maximum and finally decreases again. How large the maximum concentration of the intermediate will be at what point in time depends on the two rate constants and . The formation of the product C begins after the formation of a certain amount of intermediate product (induction period). ${\displaystyle k_{1}}$ ${\displaystyle k_{2}}$

Laws of Speed

The following equations apply for the rate of decay of and as well as for the rate of formation of : ${\displaystyle A}$ ${\displaystyle B}$ ${\displaystyle C}$

${\displaystyle v_{a}=-{\frac {d\mathrm {[A]} }{dt}}=k_{1}\cdot \mathrm {[A]} }$

${\displaystyle v_{b}={\frac {d\mathrm {[B]} }{dt}}=k_{1}\cdot \mathrm {[A]} -k_{2}\cdot \mathrm {[B]} }$

${\displaystyle v_{c}={\frac {d\mathrm {[C]} }{dt}}=k_{2}\cdot \mathrm {[B]} }$

with the rate constants of the reaction as well as the reaction and the condition: ${\displaystyle k_{1}}$ ${\displaystyle A\rightarrow B}$ ${\displaystyle k_{2}}$ ${\displaystyle B\rightarrow C}$

${\displaystyle {d\mathrm {[A]} }+{d\mathrm {[B]} }+{d\mathrm {[C]} }=0}$

The integrated speed laws are:

${\displaystyle \mathrm {[A]} _{t}=\mathrm {[A]} _{0}\cdot e^{-k_{1}\cdot t}}$

${\displaystyle \mathrm {[B]} _{t}=\mathrm {[A]} _{0}\cdot {\frac {k_{1}}{k_{2}-k_{1}}}\cdot (e^{-k_{1}\cdot t}-e^{-k_{2}\cdot t})}$

${\displaystyle \mathrm {[C]} _{t}=\mathrm {[A]} _{0}\cdot (1-{\frac {k_{2}\cdot e^{-k_{1}\cdot t}-k_{1}\cdot e^{-k_{2}\cdot t}}{k_{2}-k_{1}}})}$

1. Borderline case : ${\displaystyle k_{1}>>k_{2}}$

${\displaystyle \mathrm {[B]} _{t}\approx \mathrm {[A]} _{0}\cdot e^{-k_{2}\cdot t}}$

${\displaystyle \mathrm {[C]} _{t}\approx \mathrm {[A]} _{0}\cdot (1-e^{-k_{2}\cdot t})}$

The fast first reaction step disappears in the kinetics.

2nd borderline case : ${\displaystyle k_{1}<<k_{2}}$

${\displaystyle \mathrm {[B]} _{t}\approx \mathrm {[A]} _{0}\cdot {\frac {k_{1}}{k_{2}}}\cdot e^{-k_{1}\cdot t}}$

${\displaystyle \mathrm {[C]} _{t}\approx \mathrm {[A]} _{0}\cdot (1-e^{-k_{1}\cdot t})}$

Here, too, the quick intermediate step disappears from the kinetics.

The following always applies to both borderline cases: The slowest step determines the kinetic course of the overall reaction in successive reactions.

See also

• Follow-up reaction
• Kinetics (chemistry)

Individual evidence

1. ^ ^{A b} Santosh K. Upadhyay: Chemical Kinetics and Reaction Dynamics . 1st edition. Springer Netherlands, 2006, p. 63–65 , doi : 10.1007 / 978-1-4020-4547-9 ( springer.com [accessed June 19, 2018]).