Bibliography.

[L] J. D. Logan, “Applied Mathematics” or “Εφαρμοσμένα Μαθηματικά”.

[KX] Σ. Κομηνέας, Ε. Χαρμανδάρης, “Μαθηματική Μοντελοποίηση”

A chemical reaction for one reactant ([L], Chapter 1)

The reactants are transformed into products. Consider here only one reactant,

$$ A \longrightarrow \text{products}. $$

A chemical reactor with volume $V$.

Variable.

• $C$ is the concentration of the reactant (mass per unit volume) in the reactor.

Parameter.

• $\lambda$ is the flow of reactant at the entrance of the reactor (volume of supplied material per unit time).

[Thus, $\lambda C_{\rm in}$ is the mass per unit time entering the reactor.]

Assumptions.

• The supply (volume of material) at the output is equal to the supply at the input $\lambda$ (let us imagine that the pipes coming in an out of the reactor are of equal diameter).
• Reactant has uniform temperature and it is constantly homogenized → this allows us to assume that the reactant density is $C(t)$, i.e., a function of time only.
• $\lambda$ is a constant.