Batch Systems

Let us define the following variables:

Thus, we can use the above definitions to describe the total moles in a batch system:

Let us assume a reaction between reactants A and B to produce products C and D occurring in a constant volume batch reactor. With A as the limiting reactant and the basis of the reaction:

A table used to compute the changes and remaining quantities of each substance in the reaction in a constant volume batch reactor can be developed as follows:

Using the mole fraction definition of Θ, for a constant volume batch reactor:

This formula is for an arbitrary species i ≠ A, Species A is the limiting reagent and i in the numerator represents the stoichiometric coefficient of species i. For the ± , the addition represents generation of products and the subtraction is for the consumption of reactants.

The stoichiometric coefficient is defined as follows where for a substance I with stoichiometric number i. It is positive for products and negative for reactants:

In a gas-phase reaction, the constant-volume condition tends to exist when n moles of reactant form n moles of product and when there is no change in temperature or pressure (i.e., ideal gas law states that volume is unchanged).

In liquid-phase reaction, the solvent dominates the solution, hence the density of the solute insignificantly impacts the system hence making most liquid-phase reactions essentially constant-volume.