NT 4-3. A river containing a biodegradable compound flows through two well-mixed
ID: 1713005 • Letter: N
Question
NT 4-3. A river containing a biodegradable compound flows through two well-mixed lakes separated by a long stretch of river, as indicated in the schematic diagram below. Review the data on the river and lakes and then answer the question that follows. Q = 250m3/min Co 12.00 mg/L River L=35.2 km V = 0.55 m/s C,-? Lake 1 1.6 million m Lake 2 = 1.33 million m Definitions: C conc. of compound L = length V = avg. velocity Q flowrate = volume Assumptions: Complete mixing occurs in each lake; No longitudinal mixing occurs in the river; Biodegradation of the compound occurs in both lakes and the river and exhibits first-order kinetics First-order reaction rate coefficient (k) has a value of 0.46/ day. The condition of the river-lake system is steady-state. Question: What is the concentration of biodegradable compound leaving Lake 2 (C3). 3 pts.Explanation / Answer
Given: Q= 250m3/min; C0=12 mg/lt; Vol1=1.6*10^6 m3; L=35.2km; V=0.55m/s; Vol2=1.33*10^6 m3
Formula; C=C0*e-k*t where C= concentration of compound; C0= initial concentration; k=first order rate coefficient; t= time
To find c1; C1=C0*e-k*t
C1=12*e-(0.46*4.4) where t=Vol/Q( in days)
C1=1.55mg/lt
To find C2; C2=C1*e-k*t
C2=1.55*e-(0.46*0.74) where t=L/V (in days)
C2=1.1 mg/lt
To find C3; C3=C2*e-k*t
C3=1.1*e-(0.46*3.69) where t=Vol/Q ( in days)
C3=0.2 mg/lt
Therefore concentration of bio-degradable compound leaving Lake 2= 0.2mg/lt
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