Environmental Engg

Question 1

The water in a biological wastewater treatment system must be heated from 15◦ C to 40◦C for the microorganisms to
function. If the flow rate of the wastewater into the process is 30 m3 · day−1, at what rate must heat be added to the
wastewater flowing into the treatment system? Assume the treatment system is completely mixed and that there are
no heat losses once the wastewater is heated.

Answer 1

3.14 GJ · d−1

Question 2

The discharge pipe from a sump pump in the dry well of a sewage lift station did not drain properly and the water at the discharge end of the pipe froze. A hole has been drilled into the ice and a 200-W electric heater has been inserted in the hole. If the discharge pipe contains 2 kg of ice, how long will it take to melt the ice? Assume all the heat goes into melting the ice.

Answer 2

55.5 or 56 min

Question 3

For the following conditions determine whether a CMFR or a PFR is more efficient in removing a reactive compound from the waste stream under steady-state conditions with a first-order reaction: reactor volume = 280 m3, flow rate = 14 m3 · day−1, and reaction rate coefficient = 0.05 day−1

Answer 3

CMFR = 50%; PFR = 63%

Question 4

A sewage lagoon that has a surface area of 10 ha and a depth of 1 m is receiving 8640 m3 · d−1 of sewage containing 100 mg · L−1 of biodegradable contaminant. At steady state, the effluent from the lagoon must not exceed 20 mg · L−1 of biodegradable contaminant. Assuming the lagoon is well mixed and that there are no losses or gains of water in the lagoon other than the sewage input, what biodegradation reaction rate coefficient (d−1) must be achieved for a first-order reaction?

Answer 4

k = 0.3478, or 0.35 day−1

Question 5

A railroad tank car derails and ruptures. It discharges 380 m3 of pesticide into the Mud Lake drain. As shown in Figure P-4–24, the drain flows into Mud Lake, which has a liquid volume of 40,000 m3 . The water in the creek has a velocity of 0.10 m · s−1, and the distance from the spill site to the pond is 20 km. Assume that the spill is short enough to treat the injection of the pesticide as a pulse, that the pond behaves as a flow-balanced CMFR, and that the pesticide is nonreactive. Estimate the time for the pulse to reach the pond and the time it will take to flush 99% of the pesticide from the pond.

Answer 5

Time to reach the pond = 2.3 days
Time to flush = 21.3, or 21 days

Question 6

A bankrupt chemical firm has been taken over by new management. On the property they found a 20,000-m3 brine pond containing 25,000 mg · L−1 of salt. The new owners propose to flush the pond into their discharge pipe leading to the Atlantic Ocean, which has a salt concentration above 30,000 mg · L−1. What flow rate of fresh water (in m3 ·s−1 ) must they use to reduce the salt concentration in the pond to 500 mg · L−1 within one year?

Answer 6

Q = 0.0025 m3/s

Question 7

You made up a saturated solution of calcium sulfate (CaSO4). The temperature is 25°C. You then add 5.00 × 10−3 M sodium sulfate (Na2SO4 ). What are the concentrations of calcium and sulfate after equilibrium is reached? The pKs of CaSO4 is 4.58.

Answer 7

Ca2+ = 0.0032 M,
SO2−4 = 0.0082 M

Question 8

**What is the pH of a water that, at 25◦C, contains 0.5000 mg · L−1 of hypochlorous acid? **Assume equilibrium has been achieved. Ignore the dissociation of water. Although it may not be justified based on the data available to you, report the answer to two decimal places.

Answer 8

pH 6.28

Question 9

What is the “exact” alkalinity of a water that contains 0.6580 mg · L−1 of bicarbonate, as the ion, at a pHof 5.66?

Answer 9

0.4302 mg/L as CaCO3

Question 10

The concentration of a chemical degrades in water according to first-order kinetics. The degradation constant is 0.2 day−1. If the initial concentration is 100.0 mg · L−1, how many days are required for the concentration to reach 0.14 mg · L−1?

Answer 10

32.9 days

Question 11

A water initially contains 40 mg · L−1 of Mg2+. The pH of the water is increased until the concentration of hydroxide
ion (OH−) is 0.001000 M. What is the concentration of magnesium ion in this water at this pH? Give your answer in milligrams per liter. Assume that the temperature of the solution is 25◦ C.

Answer 11

0.4423 mg · L−1

Question 12

Hypochlorous acid decays in the presence of ultraviolet radiation. Assume that degradation occurs according to first-order kinetics and the rate of degradation was measured to be 0.12 day−1 (at a particular sunlight intensity and temperature). Given this, how long does it take for the concentration of hypochlorous acid to reach nondetectable levels (0.05 mg · L−1 ) if the initial concentration were 3.65 mg · L−1 ?

Answer 12

35.8 days

Question 13

A solution of acetic acid is prepared in water by adding 11.1 g of sodium acetate to a volumetric flask and bringing
the volume to 1.0 L with water. The final pH is measured to be 5.25. What are the concentrations of acetate and
acetic acid in solution? (Assume that the temperature of the solution is 25◦C.)

Answer 13

[HA] = 0.033 M
[A−] = 0.102 M

Question 14

A magnesium hydroxide solution is prepared by adding 10.00 g of magnesium hydroxide to a volumetric flask and bringing the final volume to 1.00 L by adding water buffered at a pH of 7.0. What is the concentration of magnesium
in this solution? (Assume that the temperature is 25◦ C and the ionic strength is negligible).

Answer 14

0.17 M

Question 15

Find the mass of sodium bicarbonate (NaHCO3) that must be added a 1.00 L volumetric flask containing distilled water to make a 1.0 M solution. Find the normality of the solution.

Answer 15

84 g/L

Question 16

A ferric phosphate solution is prepared by adding 2.4 g of ferric phosphate to a volumetric flask and bringing the finalvolume to 1.00 L by adding water having a phosphate concentration of 1.0 mg · L−1 .What is the concentration of soluble iron in this solution? (Assume that the temperature of the solution is 25◦C.

Answer 16

1.20 × 10−17 M

Question 17

The pH of a water is measured to be 7.5. The concentration of bicarbonate was measured to be 1.3 × 10−3 M. What
are the concentrations of carbonate, carbonic acid, and CT? Assume this system is closed to the atmosphere.

Answer 17

1.384 × 10−3 M ≈ 1.4 × 10−3 M

Question 18

The pH of a water is measured to be 7.5. What are the concentrations of carbonate, bicarbonate, carbonic acid, and CT? Assume this system is open to the atmosphere. The temperature is 25◦C. The Henry’s constant for carbon dioxide is 10−1.47 M · atm−1 at this temperature. The partial pressure of carbon dioxide is 10−3.53 atm.

Answer 18

1.70 × 10−4 M ≈ 1.7 × 10−4 M

Question 19

A soil sample is collected and the soil water is analyzed for the chemical compound 1,2-dichloroethane (DCA). The concentration in the water is found to be 12.5 g · L−1. The organic matter content of the soil is 1.0%. Determine the concentration of DCA that would be sorbed to the soil and that associated with the organic matter. DCA has a Kd of 0.724 ( g · kg−1)( g · L−1)−1

Answer 19

905 g/kg

Question 20

A 1-m3 sample of air was found to contain 80 g · m−3 of SO2. The temperature and pressure were 25.0◦ C and 103.193 kPa when the air sample was taken. What was the SO2 concentration in parts per million?

Answer 20

0.030 ppm of SO2

Question 21

A water contains 100.0 mg · L−1 CO2−3 and 75.0 mg · L−1 HCO−3 at a pH of 10 (T = 25◦C). Calculate the exact alkalinity. Approximate the alkalinity by ignoring the appropriate chemical species.

Answer 21

233 mg/L as CaCO3

Question 22

What is the pH of a water that contains 120.00 mg · L−1 of bicarbonate ion and 15.00 mg · L−1 of carbonate ion?

Answer 22

9.43

Question 23

Liquid hazardous wastes are blended in a CMFR to maintain a minimum energy content before burning them in a
hazardous waste incinerator. The energy content of the waste currently being fed is 8.0 MJ · kg−1 (megajoules per
kilogram). A new waste is injected in the flow line into the CMFR. It has an energy content of 10.0 MJ · kg−1. If the
flow rate into and out of the 0.20 m3 CMFR is 4.0 L · s−1, how long will it take the effluent from the CMFR to reach
an energy content of 9 MJ · kg−1 ?

Answer 23

t = 34.5, or 35 s

Question 24

A municipal landfill has available space of 16.2 ha at an average depth of 10 m. Seven hundred sixty-five (765) m3 of
solid waste is dumped at the site 5 days a week. This waste is compacted to twice its delivered density. Draw a
mass-balance diagram and estimate the expected life of the landfill in years.

Answer 24

16.25, or 16 years

Question 25

The Rappahannock River near Warrenton, VA, has a flow rate of 3.00 m3 · s−1. Tin Pot Run (a pristine stream)
discharges into the Rappahannock at a flow rate of 0.05 m3 · s−1. To study mixing of the stream and river, a
conservative tracer is to be added to Tin Pot Run. If the instruments that measure the tracer can detect a
concentration of 1.0 mg · L−1, what minimum concentration must be achieved in Tin Pot Run so that 1.0 mg · L−1 of
tracer can be measured after the river and stream mix? Assume that the 1.0 mg · L−1 of tracer is to be measured
after complete mixing of the stream and Rappahannock has been achieved and that no tracer is in Tin Pot Run or the Rappahannock above the point where the two streams mix. What mass rate (in kilograms per day) of tracer must be added to Tin Pot Run?

Answer 25

263.52, or 264 kg · day−1

Question 26

As mentioned in Example 4–12, heat losses due to convection and radiation were not considered.
Using the following assumptions, estimate how long it will take for the wastewater and concrete tank to come to the desired temperature (20◦C) if radiative cooling and convective cooling are considered. Assume that the average temperature of the water and concrete tank while cooling between 85◦C (their combined temperature from Example 4–12) and 20◦C is 52.5◦C. Also assume that the mean radiant temperature of the surroundings is 20◦C, that both the cooling tank and the surrounding environment radiate uniformly in all directions, that their emissivity are the same (0.90), that the surface area of the concrete tank including the open water surface is 56 m2, and that the convective heat transfer coefficient is 13 J · s−1 · m−2 · K−1.

Answer 26

193,452 s, or 2.24 days

Question 27

The Rhett Butler Peach, Co. dips the peaches in boiling water (100◦ C) to remove the skin (a process called blanching) before canning them. The wastewater from this process is high in organic matter and it must be treated before disposal. The treatment process is a biological
process that operates at 20◦ C. Thus, the wastewater must be cooled to 20◦ C before disposal. Forty cubic meters
(40 m3) of wastewater is discharged to a concrete tank at a temperature of 20◦C to allow it to cool. Assuming no
losses to the surroundings, that the concrete tank has a mass of 42,000 kg and a specific heat capacity of 0.93 kJ ·
kg−1 · K−1, what is the equilibrium temperature of the concrete tank and the wastewater?

Answer 27

T = 358 K or 85◦C

Question 28

You are to design a membrane system for the community of Red Bull. The design flow rate is 0.100 m3 · s−1. The temperature of the water ranges from 5◦C in winter to 22◦C in summer. The membrane you have chosen has maximum TMP of 200 kPa and a resistance coefficient of 4.2 × 1012 m−1 . Based on pilot testing, the operating TMP should be no greater than 80% of the maximum TMP. Determine the required membrane area.

Answer 28

4000 m2

Question 29

Sulis Lake has a surface area of 708,000 m2. Based on collected data, Okemos Brook flows into the lake at an average rate of 1.5 m3 · s−1 and the Tamesis River flows out of Sulis Lake at an average rate of 1.25 m3 · s−1 during the month of June. The evaporation rate was measured as 19.4 cm · month−1. Evapotranspiration can be ignored because there are few water plants on the shore of the lake. A total of 9.1 cm of precipitation fell this month. Seepage is negligible. Due to the dense forest and the gentle slope of the land surrounding the lake, runoff is also negligible. The average depth in the lake on June 1 was 19 m. What was the average depth on June 30th?

Answer 29

0.81/meter

Question 30

Estimate the chronic daily intake of toluene from exposure to a city water supply that contains a toluene concentration equal to the drinking water standard of 1 mg · L−1. Assume the exposed individual is an adult female who consumes water at the adult rate for 70 years, that she abhors swimming, and that she takes a long (20 minute) bath every day. Assume that the average air concentration of toluene during the bath is 1 μg · m−3 . Assume the dermal uptake from water (PC) is 9.0 × 10−6 m · h−1 and that direct dermal absorption during bathing is no more than 80% of the available toluene because she is not completely submerged. Use the EPA lifetime exposure of 75 years.

Answer 30

3.3 × 10−2 mg /kg day

Question 31

Estimate the lifetime average chronic daily intake of benzene from exposure to a city water supply that contains a benzene concentration equal to the drinking water standard. The allowable drinking water concentration (maximum contaminant level, MCL) is 0.005 mg · L−1. Assume the exposed individual is an adult male who consumes water at the adult rate for 63 years*, that he is an avid swimmer and swims in a local pool (supplied with city water) 3 days a week for 30 minutes from the age of 30 until he is 75 years old. As an adult, he takes a long (30 minutes) shower every day. Assume that the average air concentration of benzene during the shower is 5 μg · m−3 (McKone, 1987). From the literature, it is estimated that the
dermal uptake from water is 0.0020 m3 · m−2 · h−1. (This is PC in Table 6–6. PC also has units of m · h−1 or cm · h−1.) Direct dermal absorption during showering is no more than 1% of the available benzene because most of the water does not stay in contact with skin long enough (Byard, 1989).

Answer 31

1.74 × 10−4 mg / kg day

Question 32

The concentration of the pesticide DDT was found to be 5 g · L−1 in the water of a pond. The bioconcentration factor for DDT is 54. What is the expected concentration of DDT in the fish living in the pond?

Answer 32

270 mg/kg

Question 33

If the initial density of bacteria is 104 cells per liter at the end of the accelerated growth phase, what is the number of
bacteria after 25 generations?

Answer 33

3.4 × 10^11 cells/L

Question 34

Greenlawn Lake has a surface area 2.6 × 106 m2. The average depth is 12 m. The lake is fed by a stream having a flow rate of 1.2 m3 · s−1 and a phosphorus concentration of 0.045 mg · L−1. Runoff from the homes along the lake adds phosphorus at an average annual rate of 2.6 g · s−1. The settling rate of the lake is 0.36 day−1. A river flows from the lake at a flowrate of 1.2 m3 · s−1. What is the steady-state concentration of phosphorus in the lake? What is the trophic state of the lake?

Answer 34

20 ug/L

Question 35

Population of spotted wolves lives on the mountain Hesperides. There were 26 wolves in the year 2054 and 54
wolves counted in 2079. Assuming exponential growth, what is the net growth rate constant?

Answer 35

0.029/year

Question 36

Population of spotted wolves lives on the mountain Hesperides. There were 26 wolves in the year 2054 and 54
wolves counted in 2079. A net growth rate of 0.04 year−1 and a carrying capacity of 159, what will be the predicted
population of wolves in the year 2102?

Answer 36

91

Question 37

The initial density of bacteria is 15,100 cells per liter at the end of the accelerated growth period. What is the density of bacteria (cells per liter) after 28 generations?

Answer 37

4.053 × 10^12

Question 38

You have been conducting a water quality study of Lake Arjun, which has a surface area of 8.9 × 105 m2. The
average depth of the lake is 9 m. The lake is fed by a stream having a flow rate of 1.02 m3 · s−1 and a phosphorus
concentration of 0.023 mg · L−1 . Runoff from the homes along the lake adds phosphorus at an average annual rate
of 1.25 g · s−1 . The river flows from the lake at a flow rate of 1.02 m3 · s−1. The average phosphorus concentration
in the lake is 13.2 g · L−1 . Assume evaporation and precipitation negate each other. What is the calculated average settling rate of phosphorus?

Answer 38

1.19 × 10−5/s or
376/year

Question 39

Suppose there is a grove of 1334 Asphodel plants on Prometheus Island located in Andarta Lake. The trees are
growing with an r of 0.21 individuals/(individual × year). The carrying capacity on the island is 3250. What is the
population in 35 years, assuming a logistic growth model applies?

Answer 39

3247

Question 40

One of the congeners of toxaphene, a persistent pesticide that was used on cotton, is 1,2,3,4,7,7-heptachloro-2-norbornene. The bioconcentration factor for this chemical in fish was determined to be 11,200 L · kg−1. If the concentration is 1.1 ng · L−1 in Lake Greenway, determine the estimated concentration in fish in g · kg−1.

Answer 40

12.3 ug/L

Question 41

Farmer Tapio is raising deer. She has 110 female deer age 3–15 months. The deer require 22 MJ of metabolizable energy per day during the spring months. The deer are being fed a mixture of 50% wheat and 50% silage. The wheat contains 85% dry matter (DM) and has 12.5 MJ metabolizable energy per kilogram of DM. The silage has 30% dry matter and 10.5 MJ metabolizable energy per kilogram of DM. calculate the energy (in megajoules) converted to body tissue on a daily basis. Assume that 19% of the feed consumed is excreted as undigested material. Of the remaining 81% that is digested, 78% is used in generating metabolic waste products and heat. The remaining 22% is incorporated into tissue.

Answer 41

3.92 /day