Question

10 ml of waste water is diluted to 1 liter, aerated and sealed. The initial dissolved oxygen level of the sample was 50mg/l. The dissolved oxygen level after 5 days and 20 days were 40 mg/l and 28 mg/l. Estimate the rate constant associated with the biological decomposition of the waste.

Answer 1

It is generally assumed that the rate at which the oxygen is consumed is directly proportional to the concentration of degradable organic matter remaining at any time.

dL_t/dt = - K_t *L_t integrate this equation from L₀ to L_t we find L_t =  L₀ exp(-K_t*t)

Where L₀ is intial oxygen concentration , L_t = Concentration at time t

K_t = rate constant

for 5 days

L_t =  L₀ exp(-K_t*t)

40 = 50 exp(-K5* 5)

K5 = 0.0446 / day

similarly

28 = 50 exp(-K₂₀* 20)

K₂₀ = 0.02899 / day