Question

A recent study has shown that monochloramne, NH2Cl, “decays” in wastewater is very slow, especially in comparison with free chlorine, HOCl and OCl‐. The exposure of NH2Cl to light was found to increase the rate of decay significantly. When light was completely excluded from the sample, 20 percent decay took place in 8 hours and the data conformed to the first‐order rate law.

(a) Assuming

(1) a treatment planet is discharging effluent containing 1 mg/L NH2Cl as Cl2;

(2) a 1:10 dilution (one part effluent plus nine parts receiving water) is achieved with complete mixing;

(3) the receiving water is not exposed to light; and

(4) a level greater than 0.002 mg/L NH2Cl as Cl2, is deleterious to trout, how long after discharge will it take for the receiving water to become “acceptable” for trout?

(b) Assuming that each 12‐hour period of no light is followed by a 12‐hour period of light during which the applicable first‐order reaction rate constant is 0.3/hr, how long will it take for the receiving water to come acceptable for trout?

Answer 1

For 1st order decay, -ln(1-XA)= Kt in the absence of light

where XA =conversion =0.2 and T= time= 8 hrs

-ln(1-0.2)= K*8, K= 0.028/hr

Concentration of NH2Cl2 after dilution = 1 mg/L/10= 0.01 mg/K

this needs to be reduced to 0.002 mg/L for acceptable limits

for 1st order ,ln CA =lnCAO-Kt, ln (0.002)= ln(0.01)- 0.028*t

0.0298 t= 1.61 and t= 1.61/0.0298 hr =54 hours

b) conversion in 8 hours is 20% during no light period, for 12hour period

-ln(1-XA1)/-ln(1-XA2)= t1/t2

ln (0.8)/ ln(1-XA2)= 8/12

ln(1-XA2)= ln(0.8)*12/8=-0.334

1-XA2= 0.71

XA2= 0.29 so after 12 hour period CA = 0.71*0.01 =0.007. This becones CAO for the next 12hour period of sunlight

during the next 12 hour period, lnCA= lnCA0-Ktl

lnCA= ln(0.007)- 0.3*12

CA=0.000191 This is less than what needs to be achied as 0.002 mg/L

hence lnC(0.002)= ln(0.007)- 0.3*t

0.3*t= 1.252

t= 1.252/0.3 =4.2 hours

Time required for the concentration to drop to derided level =12 ( o light period)+ 4.2 ( Hours)= 16.2 hours

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