Chapter 28, Problem 3P

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

$V\frac{dc}{dt}=F-Qc-kV{c}^2$

where $V=$ volume (12 m³), $c=$ concentration (g/m³), $F=$ feedrate (175 g/min), $Q=$ flow rate (1 m³/min), and $k=$ a second-orderreaction rate (0.15 m³/g/min). If $c\left(0\right)=0$, solve the ODE until the concentration reaches a stable level. Use the midpoint method

$\left(h=0.5\right)$ and plot your results.

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