19 Kinetic & Thermodynamic Control

Learning Objectives

By the end of this section, you should be able to:

Understand kinetic and thermodynamic control


Reactants can sometimes give rise to a variety of products.

Consider the nitration of nitrobenzene:

The relative portion of the products before reaching equilibrium is given by the ratio of the rates of production.

[latex]A+B→P_{1}[/latex] where [latex]r_{P1}=k_{r1}[A][B][/latex]

[latex]A+B→P_{2}[/latex] where [latex]r_{P2}=k_{r2}[A][B][/latex]

Here, before equilibrium:


This is called kinetic control, and it is dictated by reaction rates.
As opposed to thermodynamic control, which is dictated by reaction equilibrium (after a long time):


Say we have the system:

If [latex]k_{e1},k_{e2}\text{<<}k_{r1},k_{r2}[/latex]

Then at any time before the equilibrium reaction start severely affecting product concentration, the reaction simplifies to:


The reaction is kinetically controlled: the amount of products depends on the rates of reaction.

Proof to show: [latex]\frac{[P_{1}]}{[P_{2}]}=\frac{k_{r1}}{k_{r2}}[/latex]

Say that both [latex]P_{1}[/latex], [latex]P_{2}[/latex] start at a concentration of 0. We can express the change in concentration for [latex]P_{1}[/latex] and [latex]P_{2}[/latex] at any time before [A][B] reaches 0. Note that once [A][B] reaches 0, the equilibrium reaction starts to dominate as we no longer have forward reactions that consume A and B to produce P1 and P2.



If [latex]k_{e1},k_{e2}>>k_{r1},k_{r2}[/latex]

Then at any given time, this reaction simplifies to:


The reaction is thermodynamically controlled : the amount of products depends on the equilibrium state.

Proof to show: [latex]\frac{[P_{1}]}{[P_{2}]}=\frac{k_{e1}}{k_{e2}}[/latex]:
At equilibrium:

Forward reaction rate: [latex]\frac{d[P2]}{dt}=k_{e2}[P1][/latex]

Reverse reaction rate: [latex]\frac{d[P1]}{dt}=k_{e1}[P2][/latex]

At equilibrium, the forward and reverse reaction rates are equal:

k_{e2}[P1] & = k_{e1}[P2]\\
\frac{[P_{1}]}{[P_{2}]} & = \frac{k_{e1}}{k_{e2}}




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Foundations of Chemical and Biological Engineering I Copyright © 2020 by Jonathan Verrett is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License, except where otherwise noted.

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