1.11 The Definition of Fractional Conversion

The fractional conversion, or simply the conversion of reactant \(A\), denoted by \(X_A\) is defined as follows: \[X_A = \frac{\text{moles of $A$ reacted}}{\text{moles of $A$ fed}}\] The fractional conversion is a measure of how far a reaction has progressed. As the name suggests, \(X_A\) varies between 0 and 1.

Batch Systems: \[X_A = 1 - \frac{N_A}{N_{A0}}\] where

\(N_{A0}\) = moles of \(A\) fed. i.e., moles of \(A\) at \(t=0\)
\(N_{A}\) = moles of \(A\) remaining at time \(t\)

Flow Systems: \[X_A = 1-\frac{F_A}{F_{A0}}\] where

\(F_{A0}\) = molar flow rate of \(A\) at the inlet
\(F_{A}\) = molar flow rate of \(A\) at the outlet

Note: It is a usual practice to choose the limiting reactant as the basis to define conversion. However, we can choose the other reactants as well to define the respective conversions.