First order reaction in a batch reactor

Implement first order kinetics of one species in a batch reactor.

Suggested approach:

• Write a function that computes the reaction rate for a provided concentration

• Write this function in such a way that the reaction rate coefficients can be passed as parameters.

• Provide an analytical expression of the concentration as function of time. Verify your codes with the analytical solution for the case $k = 1.0~\mathrm{s^{-1}}$, with initial concentration $c_{0} = 1.0~\mathrm{mol\cdot m^{-3}}$.

Questions:

1. Solve using forward Euler discretization

2. Solve using backward Euler discretization

3. Solve using scipy.integrate.solve_ivp