A mass balance for a chemical in a completely mixed reactor can be written as

Vdc/dt = F – Qc – kVc2

where V = volume (12 m3), c = concentration (g/m3), F = feed rate (175 g/min), Q = flow rate (1 m3/min), and k = a second-order reaction rate (0.15 m3/g/min). If c(0) = 0, solve the ODE until the concentration reaches a stable level. Use the midpoint method (h = 0.3) and plot your results.

Challenge question: If one ignorer the fact that concentrations must be positive, find a range of initial conditions such that you obtain a very different trajectory than was obtained with c(0) = θ. Relate your results to the steady-state solutions.