Download Homework Assignment #5 - MSU College of Engineering

Homework Assignment #4
ENE 802
Physico-Chemical Processes in Environmental Engineering
Fall 2003
Dr. Susan J. Masten
Due: Nov. 26, 2003
1.
The hydrolysis of methyl bromide (CH3Br) at 25 oC in a buffered aqueous solution (pH 7.0)
containing 5 mM Br-occurs by the following reaction:
CH3Br + H2O  CH3OH + Br- + H+
To what extent is CH3Br ultimately converted to CH3OH when assuming that CH3Br is
initially present at low concentrations (i.e., [CH3Br] < 2 M)? In the literature you have
found the following data (all for 25 oC):
Species
CH3Br (g)
CH3OH (aq)
H2O (l)
H+ (aq)
Br- (aq)
2.
Gof
(kJ mol-1)
Po
(atm)
Cwsat (1 atm)
(mol L-1)
- 28.2
- 175.4
- 237.2
0
- 104.0
2.1
1.6 x 10-1
Yesterday, a train derailment resulted in the spill of approximately 13,000 gal of the soil
fumigant sodium metham (Vapam) (http://www.alanwood.net/pesticides/metam.html) to the
Sacramento River, 70 km upstream from Shasta Lake, California’s largest reservoir. The
spill killed almost all aquatic life in the river.
In an aqueous environment, metham (which is highly soluble) hydrolyzes to form methyl
isothiocyanate (H3C-N=C=S)
Rate constants for this reaction are ka  300 M-1s-1, k’n  1 x 10-8 M-1s-1. Metham also
undergoes indirect photolysis to form methyl isothiocyanate, with a pseudo-first-order rate
constant of approximately 1 x 10-4 sec-1.
The California Regional Water Quality Control Board urgently needs your advice, both as
to the maximum concentrations of metham that will be encountered at different points
along the Sacramento River, and as to the total load that will enter Shasta Lake.
a) Calculate the maximum concentration (in M) of Na+ (which behaves as a conservative
tracer) and metham that will be encountered, both at the town of Dunsmuir (10 km
b)
c)
d)
e)
f)
3.
downstream from the spill) and at the point where the Sacramento River reaches
Shasta Lake (70 km downstream from the spill).
How important are the processes of hydrolysis and indirect photolysis in attenuating the
peak concentration of metham between Dunsmuir and Shasta Lake? Quantify your
answer.
What are the half-lives for hydrolysis and indirect photolysis? The pH of the water is
8.1
How important are these two processes collectively in attenuating the total load of
metham between Dunsmuir and Shasta Lake?
Data are currently not available as to Henry’s Constant for metham. Would you
recommend measuring this parameter or do you believe that you can neglect air-water
exchange of metham? Explain your conclusion – it would be great if you could
estimate the Henry’s Constant.
Estimate the total mass of methyl isothiocyanate (in moles) that will be transported into
Shasta Lake, ignoring losses from any processes (such as air-water exchange) that
might remove this compound during its transport in the Sacramento River. Do you
think this is a reasonable estimate – or do you think that other processes would be
important in the removal of methyl isothiocyanate? If so, which processes are
important and why?
(This incident actually occurred on July 14, 1991.)
If ion exchange is used to reduce the Ag+ concentration of a waste stream from 5.7 mg/L to
0.43 mg/L, determine the effluent pH. The initial pH is 8.3. Use a polystyrene base DVB
8% cross linked resin, sodium form, sulfonic acid. Since the 2 exchangeable ions are
monovalent, assume that the activity coefficients of RAg and RH are equal (i.e., RAg = RH)
Ag
in the expression for the selectivity coefficient. The selectivity coefficients are, K Na
=
H
8.51 and K Na
= 1.27.
4.
MSU has decided to treat the water used by the university for cooling and heating
purposes with ion exchange (i.e., the cold water lines will not be treated). The water supply
for the university is groundwater obtained from wells that are approximately 400 ft. deep.
The raw water has the following characteristics:
total iron:
total manganese
total hardness:
temperature:
1.3 mg/L
0.5 mg/L
440 mg/L as CaCO3
50 oC
The desired effluent hardness is 85 mg/L as CaCO3. The flow is to be calculated based
upon the following criteria:
25,000 resident students at 50 gal/capita/day
34,000 non-resident students and faculty/staff at 25 gal/capita/day.
Design an ion exchange treatment system which could be used to remove the hardness
from this water. Describe (you do not need to design) any treatment you might need
before ion exchange.
A strong acid cation exchange column is to be used in the sodium mode for the removal
the hardness ions. Sodium chloride (10% aq. solution) is to be used as the regenerant.
The manufacturer’s specifications give the following information:
a) Softening capacity:
Salt (lb/ft3)
Capacity
(in kgrains (as
CaCO3) per ft3
4
17.8-19.5
6
21.5-23.1
10
27.5-28.1
18
31.5-32.2
b) Leakage: A maximum of 0.75% of the untreated water hardness
c) Bed depth: 30-48 in.
d) Back-wash bed expansion: at backwash rate of 6.0 gpm/ft2, 75%
e) Effective size of the resin beads: 0.45 mm
f) Operating conditions:
Operation
Service
Backwash
Regeneration
Rinse
Rate
2-5 gpm/ft3
6-8 gpm/ft2
at 50-75 oC
0.25-1.0 gpm/ft3
1-5 gpm/ft3
Solution
Water
Water
Time (min)
---5-15
10-20% NaCl
Water
30-60
10-40
The time for rinse should be sufficiently long as to pass 20-35 gal water/ft3 resin
through the column.
In designing the system you are to determine the hardness leakage, the bypass fraction (if
used), the quantity of water to be treated each day, the number of columns required, the
cross-sectional area and volume of each column, the exchange capacity of each column,
the service time of operation, the weight of salt and volume of salt solution, the
regeneration flow rate and cycle time required.
5.
A water at pH 6.7 contains 8.9 x 10-4 M total carbonate (CT). For coagulation, 30 mg/L alum
(MW = 594 g/mole) is added.
a)
b)
What will be the final pH if the system is closed (i.e., no gas transfer is allowed)?
How much lime (CaO) is required to maintain the pH at 6.7?
Rework the above problem if the system were in equilibrium with the air.
( PCO2 Error! Switch argument not specified.= 0.00033 atm)
(KH = 10-1.45 at
25°C)
6.
You are to chemically treat a wastewater to remove suspended solids using coagulation
followed by sedimentation. The wastewater has the following characteristics:
Q = 5 x 105 m3/day
Total suspended solids (TSS) = 260 mg/L
Alk = 220 mg/L as CaCO3
Temperature = 15 oC
pH = 8.2
You performed a jar test to determine the mean velocity gradient required to induce
coagulation resulting in a decrease in 95% of the turbidity. A dosage of 100 mg/L ferric
chloride was required. The flocculation apparatus you used is described below:
4 flat rotary paddles
Cd = 1.20
Paddle dimensions: 12.5 cm long and 2.5 cm wide
Velocity of paddles: 35 cm/sec
Relative velocity between water and the paddles: 75% of the paddle velocity
Volume of water in flocculation basin = 45 L
Based upon the design criteria obtained from the jar tests, along with “conventional
wisdom”, you decided to design a flocculation system that has a retention time of 45 min.
(a) What torque must be applied if the paddles are to rotate at 2.5 rpm?
(b) If the collision efficiency factor is 0.5, what is the value for the volume fraction of
colloidal particles per unit volume of suspension, ?
7.
You are to design a dissolved air flotation system to treat a waste stream, of 300 gpm,
having a temperature of 103 oF. This waste stream contains significant quantities of
nonemulsified oil and non-settleable suspended solids. The concentration of oil and
grease, as measured by the hexanes extractable test, was found to be 125 mg/L and the
suspended solids concentration was 140 mg/L. Since the oil material is of mineral origin
and not easily biodegraded, it was deemed necessary by the Michigan DNR that you must
reduce the effluent levels of suspended solids to 20 mg/L and the oil and grease to 25
mg/L. Note: Cs = 18.6 mg/L at 103 oF.
Laboratory studies provided the following additional information:
optimum alum dosage: 50 mg/L
pressure: 50 psig
f = 0.5
sludge: 3% by weight
Calculate: (a) the recycle rate, (b) the surface area of the flotation unit, and (c) sludge
quantities generated in lb dry weight/day and in gal/day.