Units - SI (International System of Units) and USCS (U.S. Customary system)
10-12 pico p
10-6 micro ?
10-3 milli m
10-2 centi c
103 kilo k
106 mega M
Significant Digits and Rounding Numbers
To round numbers:
• If the digits to the right of the digit you are rounding are greater than five, round up.
• If the digits to the right of the digit you are rounding are less than five, round down.
• If the digits to the right of the digit you are rounding are exactly equal to five, round up or down so that the digit you are rounding to is an even number. (reference: R.C. Brinker, Elementary Surveying, International Textbook Company, 1969)
Examples: Round 234.5075 to the thousandths place 234.508 Round 0.0467 to the hundredths place 0.05
To determine the number of significant digits:
Define the following terms:
leading zero - zero to left of first non-zero digit in a number trailing zero - zero to right of last non-zero digit in a number
trapped zero - zero between two significant digits (zero or non-zero) Rules of significant digits:
1. all non-zero digits are significant digits
2. all trailing zeros to right of decimal point are significant digits
3. all trapped zeros are significant digits
4. all other zeros are not significant digits
Examples: 34608 - 5 significant digits 2110 - 3 significant digits
000456 - 3 significant digits 0.000456 - 3 significant digits
0.456000 - 6 significant digits 4500.000 - 7 significant digits
Hints for problem solving
1. Write down on a single page every equation that is likely to be helpful for this problem set. Include conversion factors.
2. Read each problem several times until you understand what is being given and what is being asked. Sketch a figure if possible. Write down what you know and identify equations that will probably be useful.
a. Some people like to work backward; what do you need to determine the answer and how do you find it.
b. Some people like to work forward; if you know this, what more can you find out and does that get you closer to the final answer.
c. Do not work backward from the final numeric answer. In real life the final answer is unknown. Use the final answer only to check your work when you are finished with the problem
Chapter 1 - Conservation of Mass
1. Convert 5 miles to Mm
2. Express 13 kg/ft3 in mg/m3
3. What is the mass of 1 mole of CO2? 1 mole = mass/ molecular weight of molecule - from periodic table (Table 2.1 on page 41) add up the molecular weights of all the elements in the molecule
4. What is the mass (mg) of 2.0 moles of O2?
5. There are 2.0 moles of potassium (as K+) in 10.0 liters of water.
a. How many mg of potassium are there?
b. How many mg of water are there?
c. Express the concentration of the potassium in mg/m3.
d. Express the concentration of the potassium in ppm.
6. Convert 1 ppm to mg/L.
1 ppm = (1 g conc/ 106 g H2O) * (1000 g H2O/ 1 L H2O)* (103 mg conc/ 1 g conc)= 1 mg/L
7. Find the volume that 1 mole of ideal gas would occupy at standard temperature and pressure (STP)
PV = nRT
n= 1 mole, T = 273.15 K, P = 1 atm
V=nRT/P = 1 mol * .082056L.atm.K-1.mol-1 * 273.15K = 22.414L
1atm
8. There are 14.0 ppmv of CH4 gas (methane) present in air at 25 C and 1 atm.
a. What is the percent of methane by volume?
b. What is the molecular weight of methane gas?
c. What is the concentration of the gas in mg/m3?
9. A proposed air quality standard for ozone (O3) is 0.08 ppmv. At the elevation of Denver, the pressure is about 0.82 atm. Express the ozone standard in ?g /m3 at that pressure and at a temperature of 15oC.
10. The federal Air Quality Standard for carbon monoxide is 9.0 ppmv. Express this as a percent by volume as well as in mg/m3 at 1 atm and 25 C.
11. A wastewater treatment plant receives 10 MGD (million gallons per day) of flow. This wastewater has a solids concentration of 192 mg/L. How many kilograms of solids enter the plant every day? (from Vesilind and Morgan, 2004)
12. Two stream, each with their own chloride concentration, combine. What is the concentration of chlorides out of a stream? Assume steady state, conservative conditions.
13. A stream carries water at a rate of 3000 L/min into a pond. A second stream adds an additional flow of 1500 L/min. What is the flow out of the pond?
16. A river with 400 ppm of salts (a conservative substance) and an upstream flow of 25.0 m3/s receives an agricultural discharge of 5.0 m3/s carrying 2000 mg/L of salts. The salts quickly mix in the river. A municipality just downstream withdraws water and mixes it with enough pure water from another source to deliver water having no more than 500 ppm salts to its customers. What should be the ratio of pure water to river water, F = Q5 /Q4?
7. An auto plant produces liquid waste containing aluminum with flow of 400 L/min. The auto plant effluent discharges into a stream which originally has a flow rate of 3.204 x 105 L/day and an aluminum concentration of 0.0020 mg/L. Below the discharge point is a town fishing spot. The fish are intolerant to aluminum concentrations above 0.100 mg/L. What is the maximum concentration of aluminum in the auto plant effluent in order to keep the aluminum concentration in the stream at or below 0.100 mg/L?
18. A lagoon is to be designed to accommodate an input flow of 0.10 m3/s of non-conservative pollutant with concentration
19. Two ponds have decay. Assuming CSTR, what is pollutant concentration leaving each pond in mg/L and ppm?
20. A polluted stream has decay and a sewage outfall. Assume the pollution is completely mixed in the lake AND assume no evaporation or other water losses or gains. Find the
Steady-state concentration. What is the OUTLET concentration?
Input rate = output rate + KCV Q1*C1 + Q2*C2 = Q3*C3 +KCV
Q1*C1 + Q2*C2 = (Q1+Q2)*C3 +KC3V
(5.0 m3/s*10.0 mg/L +0.5 m3/s*100.0 mg/L) * 103 L/m3 =
(5.0m3/s + 0.5 m3/s) C*103 L/m3 + 0.20/day* C*10.0 x106 m3*103L/m3/(24 hr/day*3600s/hr) C3 = 3.50 mg/L23. (NOT USED THIS SEMESTER) Suppose the condition of the lake (in the above problem) is deemed unacceptable and it
is decided to suddenly divert the sewage outfall completely around the lake, eliminating it as a source of pollution. The incoming stream still has Q1 = 5.0 m3/s and C1=10.0 mg/L. With the sewage outfall removed, the outgoing flow Q3= 5.0 m3/s. Assuming complete mix conditions, find the concentration of pollution in the lake one week after the diversion and find the new final steady-state concentration
24. (NOT USED THIS SEMESTER) Find Q3 and C3 0.2 days after the smaller inflow (Q2= 25 m3/s) suddenly stops flowing. Assume a non-conservative pollutant with a decay rate of K=0.3/day
Chapter 2 - Low Temperature Geochemistry
1. Balance the following stochiometric equations
CO2 + H2O ? H2CO3 (carbonic acid) CO2 + H2O ? H2CO3
SiO2 + H2O ? Si (OH)4 (quartz to silica) SiO2 + 2H2O ? Si(OH)4
C4H10 + O2 ? CO2 + H2O (butane) 2C4H10 + 13O2 ? 8CO2 + 10H2O
2. Demonstrate that mass is conserved in the following stochiometric equation: CH4 + 2O2 ? CO2 + 2H2O (methane)
3. A sample of 7.14 g of halite (NaCl) is completely dissolved in 150 g of water. What is the resulting molarity of the solution?
4. Suppose the concentration of benzene in a water sample = 0.017 mg/L. Express this concentration as mol/L. Benzene is C6H6
5. Consider a 1.67x10-3 M glucose solution (C6H12O6) that is completely oxidized to CO2 and H2O. Find the amount of oxygen (theoretical oxygen demand) required to complete the reaction.
6. Calculate the theoretical oxygen demand of 325 g of ethane, C2H6 2C2H6 + 7O2 ? 4CO2 + 6H2O
325 g * (1 moleethane / 30 g) * ( 7 moleO2 / 2 mole ethane) * (32 g / 1 moleO2) = 1.21 x 103 g
7. The hydrogen concentration in a stream is 3.5 x 10-6 mol/L. What is the pH of the stream?
8. The mineral fluorite is CaF2. What is the equilibrium concentration of the ion, fluoride, when fluorite is dissolved in water? Assume there is an unlimited supply of the solid.
9. Carbonic acid, H2CO3, completely ionizes when dissolved in water. Calculate the pH of a solution containing 52 mg/L of carbonic acid.
10. The volume of oxygen in air is about 21% by volume. Find the equilibrium concentration of O2 in water at 25 C and 1 atm. Recalculate it for Los Alamos with an elevation of 7500 ft above sea level.
11. Anaerobic digestion of an industrial waste, largely acetic acid, produces carbon dioxide and methane gas. Calculate the volume of CO2 produced daily at 20 C if there is an average daily waste production of 500 kg of CH3COOH. [there is no oxygen gas or water involved in this reaction]
12. Nitrogen in a wastewater treatment plant is in form of ammonia and ammonium. Find the fraction of nitrogen in form of ammonia (strippable) as function of pH at 25 C. The value of K is 1.82x10-5.
13. Carbon dioxide dissolves in water to form carbonic acid which then disassociates into bicarbonate and hydrogen ions as follows:
CO2 + H2O ? H+ + HCO3 K = 4.47 x 10
The amount of [HCO3 ] depends on the pH. Find the fraction of carbon ions that is bicarbonate as a function of pH. What would be the bicarbonate fraction for pH = 9.2?
14. Calculate the equilibrium concentration of dissolved carbon dioxide in water at 2300 m elevation above sea level and at 20C. Carbon dioxide is 0.03% of the atmosphere15. Assume water in contact with the atmosphere, which contains 0.03% carbon dioxide. What is the concentration of bicarbonate at pH = 7 ? Assume sea level at 25 C
16. Uranium 238 has a 1/2 life of 4.5 billion year. If the oldest rocks studied contain uranium 238 which currently has a mass of 54% of the original uranium, how old are the oldest rocks (lead 206 is the daughter product) ?
17. The half-life of cesium 137 is 30 years. If there were 500 g of cesium 137, how much would remain after 16.00 years (to 3-significant digits)?
18. A radionuclide is reduced by 80% in 15 minutes. What is its half-life?
Chapter 4 - Risk Analysis
1. There is some risk to eating peanut butter from the aflatoxins that cause cancer. The Food and Drug Administration restricts aflatoxin in peanut products to 20 ppb. At this level, eating 4 tablespoons a day is estimated to cause 0.8 cancer deaths /year per 100,000 people who eat peanut butter. Assuming there are 260,000,000 people in the U.S. who eat 4 tablespoons of peanut butter every day, how many people will die of cancer each year?
What percentage of the yearly U.S. death rate from cancer would this be?
2. For every hour spent in a coal mine, a worker increases his mortality risk of dying by Black Lung Disease by 1 in 1,000,000. Suppose 600 coal miners work at the United Carbon Coal Mine for 40 hours each week, 50 weeks per year and 25 years. What percent of the coal miners will die from Black Lung Disease from working in the mine?
3. Suppose a 70 kg person drinks 2 L of water every single day for 70 years with chloroform concentration of 0.10 mg/L (drinking water standard). Chloroform has potency factor = 6.1x10-3 (mg/kg-day)-1. What is upper bound lifetime cancer risk for this person?
4. Suppose drinking water contains 1.0 mg/L of toluene and 0.01 mg/L of tetrachloroethylene (C2Cl4). An adult drinks this water for 10 years. What is the hazard index? Tetrachloroethylene is probably carcinogenic. What is the lifetime risk to one person? Is this water safe?
5. Suppose Marion's water supply has 52 ppb of carbon tetrachloride in it. Using the PCB oral potency factor (Table 4.9 of your text) and the EPA recommended exposure factors (Table 4.10).
a. What is the CDI over a lifetime?
b. What is the individual lifetime cancer risk for an adult residential consumer?
c. If 20,000 people live in Marion, estimate the number of extra cancers per year caused by the carbon tetrachloride in the water supply.d. The average cancer death rate in the U.S. is 193 per 100,000 persons per year. How many cancer deaths would be expected in Marion? Do you think the additional cancers caused by the carbon tetrachloride in the drinking water would be detectable?
6. Find the DWEL for drinking water with chloroform that would result in a 10-6 risk. Chloroform has potency factor = 6.1x10-3 (mg/kg-day) -1.
8. The cancer risk caused by exposure to radiation is thought to be approximately 1 fatal cancer per 8000 person-rems of exposure (e.g. 1 cancer death if approximately 8000 people are exposed to 1 rem each). Living in a home with 1.5 pCi/L of radon is thought to cause cancer risk equivalent to that caused by about 400 mrem/yr of radiation.
a. Estimate the annual cancers in the U.S. caused by radon gas in homes. Assume to population of the U.S. is 300,000,000 people.
9. An underground storage tank has been leaking for years, contaminating groundwater and causing contaminant concentration beneath site of 0.30 mg/L. The contamination is moving with velocity = 0.50 ft/day toward public drinking water well 1 mile away. The half-life of contaminant = 10 years. The PF for the contaminant is 0.02 kg-day/mg. What is the life time cancer risk for one person who drank the water for 10 years ?
10. A factory releases a continuous flow of wastewater into a local stream, resulting in a carcinogen concentration of 0.1 mg/L in the stream below the factory. Suppose this carcinogen has an oral potency factor of 0.30 (mg/kg-day)-1 and that it is degradable with a reaction rate coefficient, k = 0.10/day. Assume that the stream is uniform in cross-section and has a velocity of 1 mile/hr. At a distance of 100 miles downstream, the town of Upton uses this surface water as its only source of drinking water. Estimate an Upton resident's residential lifetime cancer risk caused by drinking this water.