Batch Reactor Simulation and Concentration Kinetics

This tool allows users to simulate the concentration evolution in a batch reactor over time. Users can calculate the concentration of reactants and products, study the effect of reaction rate constants, initial concentrations, temperature, and order of reaction. The tool supports first-order, second-order, and custom reactions, and enables parametric studies for reaction kinetics.

The calculations are based on the following equations:

For a first-order reaction \( A \rightarrow B \):

\[ \frac{dC_A}{dt} = -k C_A \]

\[ C_A(t) = C_{A0} \exp(-k t) \]

For a second-order reaction \( 2A \rightarrow B \):

\[ \frac{dC_A}{dt} = -k C_A^2 \]

\[ C_A(t) = \frac{C_{A0}}{1 + k C_{A0} t} \]

For a general n-th order reaction:

\[ \frac{dC_A}{dt} = -k C_A^n \]

\[ C_A(t) = \left( C_{A0}^{1-n} - (1-n) k t \right)^{\frac{1}{1-n}}, \quad n \neq 1 \]

Temperature dependence of the rate constant (Arrhenius equation):

\[ k(T) = k_0 \exp\left( -\frac{E_a}{R T} \right) \]

The tool can also simulate multiple reactions in parallel or series and allows interactive adjustment of reaction parameters to study the dynamic behavior of concentrations over time.