(A)   A continuous stirred tank reactor is used to treat an industrial waste product using a reaction that destroys the pollutant under first order kinetics. This reaction rate constant k= 0.216 day^-1

The reactor volume is 500m³ and the volumetric flow rate is 500m³ day^-1 If the inlet pollutant concentration is 100 mg dm^-3 what is the pollutant concentration in the outlet assuming perfect mixing.

• Set up a labelled diagram for the system
• Set up the differential equation to show the rate of change of pollutant concentration with time
• Rearrange the equation and solve for outlet pollution concentration

(B)   The manufacturing process that generates the waste in (a) has to be shut down (No pollutant enters the tank) Determine how long it will take for the concentration of the pollutant in the tank to reach 10% of its initial steady state value.

Guidance for the above:

For part (a) the problem is a steady state system so rate of change in mass will be zero. You will need to set up an initial dC/dt equation before making this value = 0

Rate of change in pollutant mass=mass in - (mass out + mass lost through decay reaction)

Don't forget to work in units of mass so you will need a relationship that

Mass=Concentration x Volume

As a reminder of 1^st order Kinetics: loss of pollutant through 1^st order decay = kCV(Volume)

For part (b) it is none-steady state so the rate of change in mass will be changed so dC/dt will not equal Zero.

To finally solve this you will have to use  ? 1/x dx = ? n x