\[Selectivity = \frac{n_D}{n_U}\]

where \(n_D\) is the moles of desired product formed, and \(n_U\) is the moles of undesired product formed. Note that other definitions of selectivity are also used.

\[Yield = \frac{n_D}{n_{D,max}} * 100%\]

where \(n_{D,max}\) is the moles of desired product that would form if all the limiting reactant were consumed and no undesired reactions occurred.

For a batch reactor:

\[\xi = \frac{n_i – n_{i0}}{\nu _i}\]

where \(\xi\) is the extent of reaction (dimensionless) – note that many textbooks define \(\xi\) so that it has unites of moles, \(n_i\) is the number of moles of component \(i\) at any time, \(n_{i0}\) is the number of moles of component \(i\) initially, and \(\nu _i\) is the stoichiometric coefficient of component \(i\).

For a continuous, steady-state reactor:

\[\xi = \frac{\dot n _i – \dot n _{i0}}{\dot{\nu} _i}\]

where \(\dot n _i\) is the molar flow rate of component \(i\), \(\dot n _{i0}\) is the molar flow rate of component \(i\) at reactor inlet, and \(\nu _i\) is the stoichiometric coefficient of component \(i\) per time.

\[f = \frac{n_{i0} -n_i}{n_{i0}} = \frac{\dot n _{i0} – \dot n _i}{\dot n _{i0}}\]

where \(f\) is the fractional conversion of component \(i\).

\[K = \Pi P^{\nu _i} _i\]

where \(K\) is the equilibrium constant for a gas-phase reaction, \(P_i\) is the partial pressure of species \(i\), and \(\Pi\) represents a product (e.g., for reaction A + 2B \(\rightarrow\) C, \(K = \frac{P_C}{P_A P^2 _B}\)