Fractional-Conversion and Extent-of-Reaction Reactors Reference Page
When You Saw It, What Was the Extent of Your Reaction?

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Intro to Fractional-Conversion and Extent-of-Reaction Reactors

Chemical reactions change the composition of process streams.
Unlike mass, moles of individual species are not conserved when reactions occur.

Two common ways to describe reaction progress are:

  • Extent of reaction
  • Fractional conversion

These videos explain both approaches and show how they are used to perform reactor mole balances.

When You Saw It, What Was the Extent of Your Reaction? Part 1

Covers fractional conversion, extent of reaction, and reactors with a single reaction

Visuals

When You Saw It, What Was the Extent of Your Reaction? Part 2

Covers reactors with multiple reactions

Visuals

When You Saw It, What Was the Extent of Your Reaction? Part 3

Covers yield and selectivity

Visuals

Examples and Definitions

Definitions

Chemical Reaction
A process in which one or more substances (reactants) are transformed into different substances (products) through the breaking and forming of chemical bonds.

Reactions rearrange atoms but do not create or destroy them.

Stoichiometric Coefficients, \(\nu_i\)
Numbers that describe the relative amounts of reactants and products in a balanced chemical reaction.

For example:

\[ \mathrm{A + 2B \rightarrow C} \]

\[ \nu_\mathrm{A} = -1,\quad \nu_\mathrm{B} = -2,\quad \nu_\mathrm{C} = +1 \]

Reactants have negative coefficients and products have positive coefficients.

Extent of Reaction, \(\xi\), \(\dot{\xi}\)
A measure of how far a reaction has progressed.

The change in moles of species \(i\) is related to the extent of reaction by

\[ n_i = n_{i,0} + \nu_i \xi \]

The change in molar flow rate of species \(i\) through a reactor is related to the extent of reaction by

\[ \dot{n}_i = \dot{n}_{i,0} + \nu_i \dot{\xi} \]

Fractional Conversion, \(f\)
The fraction of a reactant that has been consumed relative to the amount initially present.

For species \(A\)

\[ f_A = \frac{n_{\mathrm{A}0} - n_\mathrm{A}}{n_{\mathrm{A}0}} \]

Fractional conversion is often easier to use when only one reaction is present.

Yield, \(Y\)
The amount of desired product formed relative to the maximum amount that could be produced from the reactant consumed.

Yield measures reaction efficiency.

Selectivity
A measure of how strongly a reaction favors the formation of a desired product over undesired byproducts.

High selectivity means most reactant forms the desired product.

Differential Balance
A balance written in terms of rates, such as mol/s or kg/s.

Differential balances are typically used for continuous reactors and lead to differential equations describing reactor behavior.

Integral Balance
A balance written in terms of total amounts, such as moles or kilograms.

Integral balances are commonly used for batch reactors or overall process calculations.

Composition or Mole Fraction
The ratio of the moles of a component to the total moles in the mixture.

\[ x_i = \frac{n_i}{\sum n_i} \]

Composition strongly affects reaction rates, equilibrium, and reactor performance.