CE 452 – Introduction to Environmental Engineering
Second Semester 2013
Problem Set 2 Solution
Due: Thur Feb 28
SIMPLE and APPLIED KINETICS
1. You are provided the following rate constants for the hydrolysis of a variety of organic
chemicals, Chloroform (7.13x10-10/min) and trichloroethane (1.24x10-6 /min)
a. Calculate the half-lives in years for the hydrolysis of these chemicals?
From the units of the rate constant, observe that it is for a first order reaction
0.693
t 0.5 =
k
t 0.5 Chloro = 1,850 years
t 0.5Trichlor = 1.06 years
b. Which chemical will persist longest in the environment
Chloroform because it has the larger half-life (Smaller k)
2. A treat ability study is run to investigate the rate at which a hazardous chemical can be
treated. The following data are collected at 25 oC.
Time(min)
0
3
6
12
Concentration of chemical (µ
µ M)
25
17.7
11.1
6.25
a. What is the order of the reaction?
Plot the data as C versus t and ln C versus t. Inspect which plot results in a
straight line. First order reaction
b. Use the experimental data to evaluate the rate constant, k, of the reaction (Note: be
sure to specify the units.)
The rate constant equals the slope of the line
κ = SLope = 0.12 min −1
c. What is the half-life for this reaction?
− ln 0.5 = 0.12t
t = 5.8 min
d. Predict the chemical concentration at t=10 days
[C ] f = (1.0 µg / L)e −0.12*10
[C ] f = 0.3µg / L
3. Radon is a naturally occurring gas present in many houses. Radon decays into Polonium
which has a half-life of 5 minutes. If you inhaled Polonium, what % reduction of
Polonium would occur during one breath in your lungs if you were sleeping (assume 7
breaths per minute while sleeping). Radioactive decay is a first-order process.
Find K
From
t1 / 2
0.5[C ]o
= e − K *5 min
[C ]o
K = 0.13 min −1
then
[C ] f
[C ]int
find
=e
conc after
− 0.23*
1 min
7
1
7
= 0.97 = 97%
MATERIALS BALANCE and REACTORS
4. A home washing machine removes grease and dirt from clothes in a first-order process in
which 12% of the grease on the clothes is removed per minute. The washing machine
holds 50.0L of water and has a wash cycle of 5.00 minutes before discharging the wash
water. What will be the grease concentration (in mg/L) in the discharge if the clothes
initially contain 0.500 g grease?
5. Plateau Creek carries 5.0 m3/s of water with a selenium (Se) concentration of 0.0015
mg/L. A farmer starts withdrawing 1.0 m3/s of the creek water to irrigate the land. During
irrigation, the water picks up selenium from the salts of the soil. One-half of the irrigation
water is lost to the ground and plants, and the other half is returned to Plateau Creek. The
irrigation run-off to the creek contain 1.00 mg/L of selenium. Selenium is a conservative,
nonreactive substance, and the stream does not pick up more selenium from any other
source.
a. If the farmer irrigates continuously, what will be the steady-state concentration of
selenium in the stream downstream from the farm (after the irrigation run-off
returns to the stream)?
b. Fish are sensitive to selenium levels over 0.04 mg/L. The farmer agrees not to use
more water than will keep the stream selenium level below this critical
concentration. How much water can the farmer withdraw from the stream to use
for irrigation?
6. A CSTR is used to treat an industrial waste product, using a reaction that destroys the
pollutant according to first-order kinetics, with k=0.216 d-1. The reactor volume is 500
m3, the volumetric flow rate of the single inlet and exit is 50 m3 day-1, and the inlet
pollutant concentration is 100 mg L-1.
a. Assuming the CSTR has reached steady state, what is the outlet concentration
after treatment? State your answer in units of mg/L.
C out =
C in * Qin
=
Qout + kV
100mg / L * 50m 3 / day
= 31.6mg / L
0.216
3
3
50m / day +
* 500m
day
b. A plug-flow reactor (PFR) is used to model the chemical transformation of the
waste product presented in Part a. Assume that the flow rate and the first-order
decay rate constant are unchanged (Q = 50 m3 day-1, k = 0.216 day-1). Based on
this information answer the following. What is the volume required for the PFR to
obtain the same degree of pollutant reduction as the CSTR of Part a? Report your
answer in m3.
C out = C in e − kθ
31.6 = 100mg / l * e
− ( 0.216*
V
)
50
0.316 = e −0.00432V
V = 266.3m 3
c. What is the % reduction in volume as compared to the volume of the CSTR for
the same steady-state conditions?
Percent Reduction
500 − 266.3
* 100 = 46.74%
500
CSTR Volume=500m3
PFR=266.3 m3