Units of Concentration

1
Chapter 2

• Units of Concentration

2
Units of Concentration

• Objectives
• To be familiar with different units used in
  measurement of pollutant levels in aqueous,
  soil/sediment, and atmospheric systems.
• To familiarize with typical magnitudes and units
  of concentrations that are encountered in
  environmental engineering problems.

3
Mass Concentration Units

• Mass Chemical/Total Mass
• mass fraction
• mg/kg, ppmm
• Mass Chemical/Total Volume
• concentration
• mg/L, mg/m3

4
Mass/Mass Units

• Commonly expressed as part per million (ppm),
  part per billion, part per trillion
• ppmm mg of i/kg total mass
• g of component i in 106 g total mass
• mi/mtotal x 106
• ppmm mass fraction x 106
• ppbm mass fraction x 109
• pptm mass fraction x 1012

5
Example 1

• A one-kg sample of soil is analyzed for the
  chemical solvent trichloroethylene (TCE). The
  analysis indicates that the sample contains 5.0
  mg of TCE. What is the TCE concentration in ppmm
  and ppbm?
• (Answer 5 ppmm 5000 ppbm)

6
Mass/Volume Units

• mg/L and mg/m3
• mg/m3 and mg/m3 are common units in air/
  atmosphere concentrations
• mg/L is commonly used in aqueous concentration.
  In aqueous dilute system, ppmm (mg/kg) is
  equivalent to mg/L.
• Density of water is 1 g/ml (1000 g/L) or 1kg/L

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Example 2

• A one liter of water is analyzed and found to
  contain 5.0 mg of TCE. What is the TCE
  concentration in mg/L and ppmm?
• (Answer 5 mg/L5 ppmm)

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Example 3

• What is the carbon monoxide (CO) concentration
  expressed in mg/m3 of a 10 L gas mixture that
  contains 10-6 mole of CO?
• (Answer 2800 mg/L)

9
Volume/Volume Units

• Frequently used for gas concentration
• ppmV (parts per million by volume)
• ppmV Vi/ Vtotal x 106
• volume fraction x 106
• The advantage of volume/volume unit is that the
  values do not change as a gas is compressed or
  expanded
• Air concentration expressed in mass/volume unit
  e.g. mg/m3 decreases as the gas expands
• Both ppmV and mg/m3 are common for gaseous
  concentrations

10
Mole/Mole Units

• Frequently used for gas concentration and in
  reaction calculation
• Mole fraction mole i / total mole
  ni/ntotal
• From ideal gas law
• Volume fraction Vi/ Vtotal
  (niRT/P)/(ntotalRT/P)
• ni/ntotal
• mole fraction
• For gases, volume fraction and mole fraction are
  equal, hence
• ppmV ni/ ntotal x 106

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Example 4

• A gas mixture contains 0.001 mole of sulfur
  dioxide (SO2) and 0.999 mole of air. What is the
  concentration of SO2 expressed in units of ppmV?
• (Answer 1000 ppmV)

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Example 5

• The concentration of SO2 is measured in air to be
  100 ppbV. What is the concentration in mg/m3?
  Assume the temperature is 28oC and pressure is 1
  atm.
• (Answer 260 mg/m3)

13
Example 6

• The concentration of gas phase polychlorinated
  biphenyls (PC) in the air above a lake was
  measured to 45 pg/m3. What is the partial
  pressure (in atm) of PCBs? Assume the
  temperature is 0oC and pressure is 1 atm, and the
  MW of PCBs is 325.
• (Answer 3.2 x 10-14 atm)

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Convert ppmV to mg/m3

• Using Ideal gas law
• PV n RT
• where R universal gas constant,
  8.205x103 m3-atm /mole-K,
• n number of moles, P pressure and
• T absolute temperature
• At standard conditions when P1 atm, T237.15 K
  one mole of gas will occupy a volume of 22.4 L
• of moles, n PV/RT
• Convert moles to mass, m n x molecular wt (MW)

15
Partial Pressure

• In the atmosphere, a substance will exist in gas
  phase if the atmospheric temperature is above the
  boiling point (bp) of the substance.
• The major constituents of atmosphere such as N2,
  O2, CO2, Argon (99.965) have bp above
  atmospheric temperature
• The total pressure exerted by a gas mixture
  equals the sum of the partial pressure, Pi
  exerted by each component, i of a mixture
• P ? Pi
• Pressure fraction Pi/ P (niRT / V)/(ntotalRT
  / V)
• ni/ntotal
• mole fraction or vol.
  fraction

ppmV Pi/P x 106
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Example 7

• What would be the partial pressure (in atm) of
  CO2 when the barometer reads 29.0 in Hg, the
  relative humidity is 80, and the temperature is
  70oF. The concentration of CO2 in dry air is 350
  ppmV. At 70oF the vapor pressure for water is
  0.36 Ib/in2 (psi).
• (Answer 3.3 x 10-4 atm)

17
Mole/Volume Units

• Commonly used to report concentration of
  compounds dissolved in water.
• Unit of moles/liter is called Molarity, M
  (molar)
• 10-4 M solution contains 10-4 moles of
  a compound per liter of solution
• Molality, m is the number of moles of a solute
  added to exactly 1 liter of solvent. The final
  volume will be slightly higher. Not common in
  environmental engineering.
• Normality (equivalents/L) is used in defining the
  chemistry of water for acid/base and when
  oxidation/reduction take place.

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Example 8

• Convert the concentration of TCE (5 ppm) to unit
  of molarity. The molecular weight of TCE is 131.5
  g/mole.
• (Answer 3.8 x 10-5 M)

19
Example 9

• The concentration of alachor,a common herbicide
  in a river was found to range from 0.04 to 0.1
  mg/L. What is the concentration range in
  nmole/L?. The molecular weight of alachor,
  C14H20O2NCl is 270 g/mole.
• (Answer 0.15 nmol/L)

20
Normality (equivalents/L)

• Commonly used in analysis of water constituents.
• If two chemical species 1 and 2, react and they
  have the same strength on equivalent basis then
  1-ml of reactant 1 will react with 1 ml of
  reactant 2.
• In acid/base chemistry, the of equivalents /
  mole of acid equals number of moles of H, the
  acid can donate and for base equals to the number
  of moles of H that will react with one mole of
  base
• HCL has 1 equivalent/mole and H2SO4 has 2
  equivalent/mole. NaOH has 1 equivalent/mole and
  CaCO3 has 3 equivalent/mole

21
Equivalents Weight (eqv wt)

• The number of equivalent (eqv) is also related to
  how many electrons a species donates or accept.
  The number of equivalent of Na is 1 because Na ?
  Na e- and for Ca2 is 2 since Ca ? Ca2 2e-
  
• The equivalent weight (g/eqv) of a species is
  defined as the molecular weight of the species
  divided by the number of equivalents in a mole of
  species
• eqv wt MW (g/mole) ? eqv / mole

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Example 10

• What is the equivalent weight of HCL, H2SO4,
  NaOH, CaCO3, and aqueous CO2?
• (Answer 36.5 g/eqv 49 g/eqv 40 g/eqv 50 g/eqv)

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Example 11

• What is the normality of 1 M solutions of HCL and
  H2SO4?
• (Answer 1 N 2 N)

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Common Constituents

• Concentration can be reported in terms of a
  common constituent such as phosphorous (P) and
  nitrogen (N) and can include contribution of P
  and N from number of chemical compounds.
• For example, nitrogen exists in various forms
  such as ammonia (NH3 and NH4), nitrate (NO3-),
  nitrite (NO3-) etc.
• To express the concentration for the total N and
  P, the concentration for every individual form of
  P or N is calculated and added to determine the
  total P or N concentration.

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Example 13

• A water contains two nitrogen species. The
  concentration of NH3 is 30 mg/L NH3 and the
  concentration of NO3- is 5 mg/L . What is the
  total nitrogen concentration in units of mg N/L?
• (Answer 25.8 mg N/L)

26
Alkalinity and Hardness

• The hardness of water is due the divalent cations
  such as Ca2 and Mg2 which are released from
  dissolution of minerals.
• Calcium carbonate can react with the natural
  acidity in water to release hardness (Ca2) and
  alkalinity (HCO3-)
• CaCO3 H2CO3 ? Ca2
  2HCO3-
• The alkalinity and hardness of water is
  determined from the alkalinity/hardness
  contributed by all divalent cations, and
  expressed in mg CaCO3/ L
• Hard water produces scale in boilers and piping
  and has no adverse health effect

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Example 14

• Water has the following chemical composition.
• Ca2 15 mg/L
• Mg2 10 mg/L
• SO42- 30 mg/L.
• What is the total hardness in units of mg/L as
  CaCO3?
• (Answer 80)

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Particle Concentrations

• Particles present in air may reduce visibility,
  blacken, corrode, or erode buildings and
  adversely affect health.
• Total suspended solids (TSP) is determined by
  pulling a known volume of air through a filter.
  The increase in weight of filter is then divided
  by the volume of air. TSP is expressed in g/m3 or
  mg/m3
• TSP ranges around 20 mg/m3 in clean areas and
• 60 - 200 mg/m3 in urban areas.
• PM2.5 refers to particulate concentration below
  2.5mm diameter in size which can penetrate deep
  into human lung.

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Particle Concentrations

• In aquatic systems and determination of metal,
  o.45mm particles size diameter, determines the
  cutoff between dissolved and particulate
  metal.
• In areas of drinking water, wastewater and
  leachate, solids are first divided into
  dissolved and suspended fraction.
• Each of the dissolved and suspended fraction
  is further divided into fixed and volatile
  fraction

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Particle Concentrations in Wastewater
Sample volume, x ml
Place sample in crucible and dry at 103oC
Dry filter at 103oC and then place filter in
furnace and ignite at 550oC
Place filtrate in crucible and dry at 103oC
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Particle Concentrations in Wastewater

• TS, TDS and TSS can be further broken down into
  into fixed and volatile fractions.
• The volatile portion of TSS is called volatile SS
  (VSS) and the fixed portion is called fixed SS
  (FSS).
• VSS is obtained from the weight loss of the
  sample (TSS) ignited in a furnace at 500oC.

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Example 15

• An air-sampling program sampled 100,000 L of air
  for particles. The following mass of particles
  were collected for particular size fractions 12
  mg retained with particle size gt 2.5 mm and 6 mg
  retained with particle size lt 2.5 mm.
• What are the PM2.5 and total suspended
  particulate (TSP) concentration of this air
  sample?

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Example 16

• A laboratory provides the following analysis
  obtained from a 50 mL sample of wastewater.
  Total solids 200 mg/L, total suspended solids
  160 mg/L, fixed suspended solids 40mg/L, and
  volatile suspended solids 120mg/L
• (a) What is the concentration of total dissolved
  solids of this sample?
• (b) If this sample was filtered through a
  glass-fiber filter, then the filter was placed in
  a muffle furnace at 550 oC overnight, what would
  be the weight of the solids (in mg) remaining on
  the filter after the night in the furnace?
• (c) Is this water sample turbid, and
  approximately what of the solids are composed
  of organic matter?
• (Answer 36.5 g/eqv 49 g/eqv 40 g/eqv 50 g/eqv)

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Representation by Effect

• The strength of a solution is defined by some
  common factor on which all the chemicals in the
  mixture depend on and not by measuring
  concentration of a specific chemicals but the
  effect that they have on wastewater.
• For many organic wastes, biological and chemical
  degradation of these wastes result in oxygen
  depletion and is harmful to the ecosystem.
• The effect of oxygen depletion is measured as the
  mg of O2 that can be consumed per liter of water
  in oxidizing organic matter, or known as
  biochemical oxygen demand (BOD)

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Common Concentration of Pollutants in Surface and
Groundwater

• Range of Concentrations Encountered in Natural
  Waters

36
Common Concentration of Pollutants in Surface and
Groundwater

• Arsenic Concentration in Southern California's
  Central and West Basin Groundwater Supplies

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Common Concentration of Pollutants in Municipal
Wastewater and Landfill Leachate
Dry Weather Leachate Concentration from the Goff
Mountain Landfill, West Virginia
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Common Concentration of Pollutants in Municipal
Wastewater and Landfill Leachate
Composition of the Atmosphere
39
Class Assignment

• Problem 1 (2.9)
• Concentrations of nitrate exceeding 44.3 mg
  NO3-/L are a concern in drinking water due to the
  infant disease, methemoglobinemia. Nitrate levels
  can be enhanced by improper use synthetic and
  natural fertilizers, irrigation practices,
  livestock-handling operations, and
  industrial-waste handling. Due to the
  presence/absence of animal wastes, fertilizer
  application, and groundwater recharge patterns,
  nitrate concentrations near three rural wells
  were reported as 0.01 mg NO3- N/L, and 20 NO3-
  N/L. Do any of these three wells exceed the 44.3
  ppm level?

40
Class Assignment

• Problem 2 (2.24)
• Carbon monoxide (CO) affects the oxygen carrying
  capacity of your lungs. CO competes with oxygen
  for one of the four iron sites of your bloods
  hemoglobin molecules. In fact, CO has about a
  210-times stronger affinity for these sites than
  oxygen. Exposure to 50 ppm CO for 90 min has been
  found to impair ones ability to time/interval
  discriminate thus, motorist in heavily polluted
  areas may be more prone to accidents. Are
  motorist at a greater risk to accidents if the CO
  concentration is 65 mg/m3? Assume a temperature
  of 298 K.

41
Class Assignment

• Problem 3 (2.26)
• Polycyclic aromatic hydrocarbons (PAHs) are a
  class of organic chemicals that consist of two or
  more fused benzene rings placed in a linear,
  angular, fuels and some are considered
  carcinogenic or mutanogenic. Undeveloped areas
  may have total PAH concentrations in the soil of
  5 mg /kg, while urban areas may have soil
  concentrations that range from 600 mg/kg to 3000
  mg/kg. What is the concentration of PAHs in
  undeveloped areas in units of ppm.

42
Class Assignment

• Problem 4 (2.30)
• A laboratory provides the following solid
  analysis for a wastewater sample TS 200 mg/L
  TDS 30 mg/L FSS 30 mg/L. (a) What is the
  TSS of this sample? (b) Does this sample have
  appreciable organic matter? (why or why not?)