CIVE 2334 HOMEWORK PROBLEMS FALL 2021 HOMEWORK #1 (Air Pollution, Water Pollution) 1. The National Ambient Air Quality Standard (NAAQS) for sulfur dioxide (SO2) is 0.144 ppmv (24-hr average). What is...

CIVE 2334 HOMEWORK PROBLEMS FALL 2021

HOMEWORK #1 (Air Pollution, Water Pollution)
1. The National Ambient Air Quality Standard (NAAQS) for sulfur dioxide (SO2) is 0.144 ppmv (24-hr
average). What is the concentration in ug/m3 assuming an air temperature of 25 degrees C?
0.053 ppmv
Temperature of 25 °C + 273.15 = 298.15 K
Pressure of 1 atm
Molar mass (MM) of NO2 = 46,0055 g/mol
Using the formula :
[m3mg]=22.4ppmv∗mol∗ molar mass∗T(K)273.15K∗1atmP(atm)
[m3mg]=22.40.053∗1mol∗46.0055g/mol∗298.15273.15K∗1atm1atm=0.0997≈0.1 m3mg
Hence, the NO2 concentration in mg/m3 at a temperature of 25 °C and a pressure of 1
atm is 0.1 mg/m3.
CIVE 2334 HOMEWORK PROBLEMS FALL 2021


2. A water sample contains 10 mg NO3-/L. What is the concentration in
3. Formaldehyde (CH2O) is commonly found in the indoor air of improperly designed and constructed
buildings. If the concentration of formaldehyde in a home is 0.7 ppm, and the inside volume is 800 cubic
meters, what mass (in grams) of formaldehyde vapor is inside the home? Assume T=298K, P=1 atm.
CIVE 2334 HOMEWORK PROBLEMS FALL 2021
4. A water quality analysis of a well water used for drinking water in a rural home found an arsenic
concentration of 0.5 micromolar. This value seems very small to you. But you need to see if it still
exceeds the drinking water standard of 10 ppbm. Is the well water violating the standard (and therefore
the water would require treatment)?
Conc of PPB by mass = 10 ppb
Mass of the solution = 100g
= wb/w x 10^6
= wb/100 x 10^6
Wb = 15 x 100 / 10^6 = 1.5 x 10^-3
Percent mass of solution = wb/w x 100
= 1.5 x 10^-3 x 100 / 100
= 1.5 x 10^-3 %
5. Find out what air or water pollutants are being released in your hometown. Go to the EPA’s Toxics
Release Inventory website, https://www.epa.gov/toxics-release-inventory-tri-program
a. Go to the search engine at the bottom of the webpage, “Learn More About TRI in Your
Community: Get Location-Based Factsheets and Information on Specific Facilities”. Search the zip
code of your hometown (or current residence if there are no hits for your hometown). Browse the
site—lots of interesting facts on who is releasing what chemicals to the environment. If there are
not companies listed at this zip code, either try another zip code or instead search by metropolitan
area and enter in the name of any city.
https://www.epa.gov/toxics-release-inventory-tri-program
CIVE 2334 HOMEWORK PROBLEMS FALL 2021

b. Go to the section “Top five facilities by total disposal or other releases”. Click on one of the
company names.
c. Review this TRI Facility Report for this company.
d. Report, in a list or table, the company name, what toxic chemicals are used/treated/released
there, and what lbs of what chemical(s) was released in the most recent year for data, if these
chemicals were air or water releases. Much of this information can be found under the “chemicals”
or “releases” tabs.
CIVE 2334 HOMEWORK PROBLEMS FALL 2021

HOMEWORK (Risk Assessment)
1. Consider a carcinogenic VOC with the dose-response curve shown in Figure P4.1 in the Masters & Ela
textbook.
If 70-kg people breathe 20 m3/day of air containing 10-3 mg/m3 of this VOC throughout their entire 70-
year lifetime, find the cancer risk (you first need to find the potency). You may assume typical exposure
values for air inhalation.
2. Suppose a city’s water supply has 0.2 ppb (1ppb=10-3 mg/L) of polychlorinated biphenyls (PCBs) in it.
Using the PCB oral slope factor (7.7 (mg/kg-d)-1 and the EPA recommended exposure factors given in
Table 6.14 below,
(a) What would be the individual lifetime cancer risk for an adult male residential consumer?
(b) In a city of 1 million people, use this risk assessment to estimate the number of extra cancers
per year caused by the PCBs in the water supply. “Extra” cancers refers to cancers caused by
PCBs (as opposed to other causes such as smoking, etc.)
(c) Assume the average cancer death rate in the United States in 193 per 100,000 per year. How
many cancer deaths would be expected in a city of 1 million? Do you think the incremental
cancers caused by PCBs in the drinking water would be detectable?
CIVE 2334 HOMEWORK PROBLEMS FALL 2021
3. It has been estimated that about 75 million people in the Ukraine and Byelorussia were exposed to
an average of 0.4 rem of radiation as a result of the Chernobyl nuclear accident. Human exposure to
radiation is often measured in rems (roentgen-quivalent man) or millirems (mrem). The cancer risk
caused by exposure to radiation is thought to be approximately 1 fatal cancer per 8,000 person-rems of
exposure (for example, this is like saying when 8000 people are exposed to 1 rem each, one person will
die of cancer caused by this exposure).
(a) How many extra cancer deaths might eventually be expected from this exposure?
(b) If the normal probability of dying of cancer from all causes is 0.22 (that is, 22% of any
population of people will die of cancer), how many cancer deaths would you normally expect
among those 75 million people?
4. A man works in an aluminum smelter for 10 years. The drinking water in the smelter contains 0.070
mg/L arsenic and 0.560 mg/L methylene chloride. His only exposure to these chemicals in water is at
work. Recall the total HI (i.e. the total overall risk) is the sum of individual HI values.
CIVE 2334 HOMEWORK PROBLEMS FALL 2021

(a) What is the hazard index (HI) associated with this exposure?
(b) Does the HI indicate this is a safe level of exposure?
(c) What is the incremental lifetime cancer risk for the man due solely to the water he drinks at
work and does it seem to be an acceptable risk according to the EPA’s standard of acceptable
risk?
Answer: Risk = CDI ×potency = 2.85×10-4 (mg/kg-day) ×0.01 (mg/kg-day)-1 = 2.9×10-6
5. Calculate a risk-based groundwater standard (in ppb) for the chemical 1,2-dichloroethane for a
residential homeowner where the person’s well used for drinking water is contaminated with 1,2-
dichloroethane. Assume the risk is for an average adult who weighs 70 kg. The state where you work has
determined that an acceptable risk is one cancer occurrence per 106 people. Use the values for route of
intake, exposure frequency, exposure duration, and averaging time provided for residential use in the
following table 6.14. Assume an oral slope factor for 1,2-dichloroethane of 9.2x10-2 per (mg/kg)/day.
CIVE 2334 HOMEWORK PROBLEMS FALL 2021
HOMEWORK (Environmental Chemistry)
1. Consider the following reaction representing the combustion of propane:
?3?8 + ?2 ??2 + ?2?
(a) Balance the equation.
(b) How many moles of oxygen are required to burn 1 mol of propane?
(c) How many grams of oxygen are required to burn 100 g of propane?
(d) At standard temperature (0 degrees C) and pressure, what volume of oxygen (in cubic
meters) would be required to burn 100 g of propane? If air is 21 percent oxygen, what
volume of air at STP would be required?
CIVE 2334 HOMEWORK PROBLEMS FALL 2021

(e) At STP, what volume of CO2 (in cubic meters) would be produced when 100 g of propane are
burned?
5.6 L of oxygen at STP are required to burn completely 2.2g of propane.
Explanation:-
The balanced chemical equation for the reaction is :-
C₃H₈ + 5O₂ → 3CO₂ + 4H₂O
_______________________________
• Molar mass of Carbon (C) = 12 g/mol
• Molar mass of Hydrogen (H) = 1 g/mol
Hence, molar mass of Propane [C₃H₈] :-
= 12×3 + 1×8
= 36 + 8
= 44 g/mol
Now, from the balnced equation :-
⇒ 44g of C₃H₈ requires 5 moles of O₂
We know that, one mole of any gas at STP occupies a volume of 22.4 L.
∴ 5 mole of O₂ will occupy a volume of :-
= 5×22.4
= 112 L
∴ 44g C₃H₈ requires 112 L O₂
∴ 2.2g of propane will require :-
= 2.2×112/44
= 0.05×112
= 5.6 L O₂
2. Suppose totally world energy consumption of fossil fuels, equal to 3 × 1017 kJ/yr, were to be obtained
entirely by combustion of petroleum with the approximate chemical formula C2H3. Combustion of
petroleum (with O2) releases an amount of energy about 43 × 103 kJ/kg (seems like a lot of moles of
CIVE 2334 HOMEWORK PROBLEMS FALL 2021

C2H3). Estimate the emissions of CO2 per year in units of kg CO2, assuming complete conversion of all C
in petroleum to CO2.
Calorific value is the amount of energy released or produced when 1 kg of fuel burns.
Given that on complete combustion of 2.4 kg of fuel 3,60,000 kJ of heat energy is produced
That is, 360000 kJ of heat for 2.4 kg
It's calorific value will be = 360000/2.4 = 150000 kJ/kg
3. Hydrochloric acid, HCl, completely ionizes to H+ and Cl- when dissolved in water. Calculate the pH of a
solution after 25 mg/L of HCl is added to water.
Answer - HCl + H2O → Cl− + H3O+
4. Hydrogen sulfide (H2S) is an odorous gas that can be stripped from solution by bubbling air through
the solution. H2S when dissolved in water is also a weak acid that can deprotonate to bisulfide ions
which are not removed by air stripping. That reaction is
?2? ?
+ + ??−
With equilibrium constant Ka=0.86x10-7.
Find the fraction of hydrogen sulfide in the H2S form at pH 6 and pH 8. At which pH would you expect to
have an easier time to strip away H2S gas?
5. Determine the equilibrium pH of aqueous solutions of the following strong acids or bases.
Remember, strong acids and bases completely dissociate. (a) 15 mg/L of HSO4-, (b) 10 mM NaOH, (c)
2,500 ug/L of HNO3.
CIVE 2334 HOMEWORK PROBLEMS FALL 2021

2500 ug = 2500 x 10-6 = 2.5 x 10-3 gm
M = 2.5 x 10-3 / 63 = 2.9 x 10-5
PH = -log [8.9 x 10-5] = 4.3
6. The chemical 1,4-dichlorobenzene (1,4-DCB) is sometimes used as a disinfectant in public lavatories.
Its odor could be particularly annoying. At 20°C (68°F) the vapor pressure is 5.3 × 10-4 atm. What would
be the concentration in the air in units of g/m3? The molecular weight of l,4-DCB is 147 g/mole.
R=0.08205Latm/moleK

The chemical 1,4-dichlorobezene (1,4-DCB) is used in an enclosed area. At 20ºC the saturated vapor
pressure of DCB is 5.3×10-4 atm. What would be the concentration of DCB in the air of the enclosed
area (in units g/m 3) at 20ºC. Molecular weight of DCB is 147 g/mole R=0.08205Latm/moleK


7. Pure toluene comes into contact with groundwater. (a) What is the concentration of toluene in the
water at equilibrium? (b) This groundwater flows slowly through the soil that has a foc value of 9%.
Estimate the concentration (in mg/kg) of toluene in the soil at equilibrium.

A/q to dalton’s alw
Partial pressure = mole fraction x Total press
XaPa = XrPr

For total pressure
Ps = XaPa + Xb
Ps = 0.5 x 37 + 0.5 x 119
Ps = 78 t0rr

Now, XaPa = YaPr
Ya = XaPa/Pt = 0.5 x 37 / 78 = 0.23
CIVE 2334 HOMEWORK PROBLEMS FALL 2021

HOMEWORK (Mass Balances, Reactors)
1. Five million gallons per day (MGD) of wastewater, with a concentration of 10.0 mg/L of a
conservative pollutant, is released into a stream having an upstream flow of 10 MGD and pollutant
concentration of 3.0 mg/L.
(a) What is the concentration in ppm just downstream?
(b) How many pounds of substance per day pass a given spot downstream?
Answer: a) 5.3 mg/L
b) 66.5.74 lb/day
2. A lake with constant volume 10 × 106 m3 is fed by a pollution-free stream with flow rate 50 m3/s. A
factory dumps 5 m3/s of a nonconservative waste with concentration 100 mg/L into the lake. There is
one outflow from the lake. The pollutant decays and has a first order reaction rate coefficient k of
0.25/day. Assuming the pollutant is well mixed in the lake, find the steady-state concentration of
pollutant in the lake.
Vlake= 106 m3
Pollution free stream: Mass of pollutant input = Qstream*conc. = (50.0 m3/s)*0 =0
Industrial effluent: Mass of pollutant input = Qeff*conc.
= (4.5 m3/s)*90mg/L = (4.5*1000 L/s)*90mg/L
=405 g/s = 405*(24*3.600) kg/day=34,992 kg/day
3. A lagoon is to be designed to accommodate an input flow of 0.10 m3/s of nonconservative pollutant
with concentration 30.0 mg/L and reaction rate constant 0.20/day. The effluent from the lagoon must
have pollutant concentration of less than 10.0 mg/L. Assuming complete mixing, how large must the
lagoon be?
Answer: 86,400 m3
4. A lagoon with volume 1,200 m3 has been receiving a steady flow of conservative waste at a rate of
100 m3/day for a long enough time to assume that steady-state conditions apply. The waste entering the
lagoon has a concentration of 10 mg/L. Assuming completely mixed conditions, what would be the
concentration of pollutant in the effluent leaving the lagoon?
Answer: 3,430 mg/L
5. Repeat problem 4 for a nonconservative pollutant with rate constant k=0.20/d.
Answer: 2,760 mg/L
6. A mixture of two gas flows is used to calibrate an air pollution measurement instrument. The
calibration system is shown below. If the calibration gas concentration Ccal is 4.9 ppmv, the calibration
gas flow rate Qcal is 0.010 L/min, and the total gas flow rate Qtotal is 1.000 L/min, what is the
concentration of calibration gas after mixing (Cd)? Assume that the concentration upstream of the
mixing point is zero.
CIVE 2334 HOMEWORK PROBLEMS FALL 2021

7. Poorly treated municipal wastewater is discharged to a stream. The river flow rate upstream of
the discharge point is Qus = 8.7 cubic meters per second. The discharge occurs at a flow of Qd = 0.9 cubic
meters per second and has a BOD concentration of 50 mg/L. Assuming that the upstream BOD
concentration is negligible. (a) What is the BOD concentration just downstream of the discharge point,
after mixing? (b) If the stream has a cross-sectional area of 10 square meters, what would the BOD
concentration be 50 km downstream? BOD is removed with a first-order decay rate constant equal to
0.20/day.
8. You are designing a reactor that uses chlorine in a plug flow reactor or a completely stirred tank
reactor to destroy pathogens in water. A minimum contact time of 30 min is required to reduce the
pathogen concentration from 100 pathogens/L to below 1 pathogen/L through a first-order decay
process. You plan on treating water at a rate of 1,000 gal/min. (a) What is the...