Question

Question 3: n a batch reactor, the concentration of BoD decreases as the outcome of water treatment. The BOd values of water (a concentration) at different times were measured and the results are reported in the following table a. Graphically detemine the order of the reaction. b. caleulate the rate constant of the reaction (report its unit too) c. f allowable concentration of BoD is 3o mg/l, determine (mathematicaluly) how much time is required to reach this BOD Level (Hint: use k value obtained from part b) Reaction time BOD (day) mg/liter 0 1000 700 4 490 240 8

Answer 1

a) As we can see from the table, the value of BOD decreases as time increases. So we can conclude that the graph would have a negative slope.

  

1200 1000 800 E 600 t) time (days)

And the rate of change of organic matter with time is directly proportional to the organic matter present in the mixture at that time.

  

(dL_t/ dt) $\propto$ - L_t

by integrating we get L_t=L*e^-kt .......(1)

as we can see that it follows logarithmic relation, the order would be first order reaction.

b) from eq (1)

BOD_t= L_o(1-e^-kt) where L_o is initial bod

when t = infinity , ultimate BOD is achieved. then L_o=BOD_t

=> 700= (1-e^-k*2)*1000

=> k=0.6 / day   

c) if BOD_t = 30 mg/lit

30=1000*(1-e^-0.6*t)

calculate t from above equation