Units of Concentration
T1 – Title Page
Language is fundamental to our understanding of the world we inhabit. Consider trying to listen to a baseball game on the radio if you had no knowledge of the language, e.g.
· Justin Verlander will be on the Hill tonight for the Tigers, with Brandon Inge behind the plate.
· And it’s a 6-4-3 double play! What does that mean? It’s the players that participated in the play. Who is player #6? That’s the shortstop. No, the shortstop is Edgar Rentaria … he’s #8. No it’s by position, numbered from the pitcher to the catcher to 1st base, etc. But the shortstop is #5. They skip the shortstop and go to 3rd, then back to the shortstop. So #6 is really #8, Edgar Rentaria. I think I prefer basketball. You mean like, Pistons 66-61 and with it? With what? Oh, never mind.
T2 – Why concentration?
Concentration is the ‘language’ which we use in speaking of pollutant levels in natural and engineered systems. We are interested in concentration because it influences:
· the driving force for mass transport, i.e. diffusion;
· the driving force for chemical reaction, i.e. first order;
· the severity of toxicity effects; and
· the fertilizing effects of nutrients
The approach to expressing concentration and the attendant units varies with the medium of interest, i.e. some work best for air, some for soil, and some for water.
T3 – Metric prefixes
Fundamental to the ‘language’ of concentration are the various prefixes which quantify the amount of material present; consider the number of kilograms of cream in my coffee:
Prefix / Meaning / ExpressionKilo- / One-thousand / 103
Milli- / One-thousandth / 10-3
Micro- / One-millionth / 10-6
Nano- / One-billionth / 10-9
Pico- / One-trillionth / 10-12
Femto- / One-quadrillionth / 10-15
T4 – Yottagrams and Yoctograms
Mass Concentration Units
1. Mass per unit mass (mass/mass): defined as the number of units chemical mass per units total mass, e.g.
Mass concentration is typically represented as mass units of chemical per million units total mass or parts per million (ppmm, where the subscript 'm' indicates mass).
The conversion factors are 109 and 1012 for parts per billion (ppbm) and parts per trillion (pptm), respectively.
Examples: mercury in Onondaga Lake sediments and fish
As in the examples, this mode of expression finds common application in relation to soils and body burden.
2. Mass per unit volume (mass/volume): defined as the number of units of chemical mass per unit total volume.
In water, concentrations are typically expressed as mass of chemical per liter or per cubic meter of water, e.g. mg·L-1 or g·m-3. Other units of mass are more appropriate for some analytes, e.g. the mercury concentration in the water column of Onondaga Lake is 11x10-6 mg·L-1. What would be a more convenient expression? (11 ng·L-1)
Again, mass concentration is typically represented as mass units of chemical per million units total mass or parts per million (ppmm, where the subscript 'm' indicates mass).
What is the appropriate ‘parts per’ representation for mercury in the water column of Onondaga Lake?
Example: mercury in the water column of Onondaga Lake
Note that there is a significant difference in the mercury content of fish (5.3 ppm) and that of the water which they inhabit (11 ppt); a factor of a million! This is due to a phenomenon termed bioaccumulation.
T9 – Bioaccumulation
T10 – Mole (the animal)
T11 – Mole (the food)
T12 – Mole (in chemistry)
3. Mole per volume (mole/volume): number of moles of chemical per unit volume water, i.e. molarity, M. This approach is most often used to report concentrations of dissolved chemicals in water and is particularly useful in making calculations relating to chemical reactions where the stoichiometry is expressed in molar units. Remembering the definition of a mole (the formula weight of a substance, expressed in grams) permits conversion between mole/volume and mass/volume units.
Example: mercury in the water column of Onondaga Lake
Example: LC50 for Ceriodaphnia
Other expressions of concentration:
1. As a common constituent: where the importance of a material is not influenced by its chemical form, it sometimes easiest to express concentration in terms of a common constituent. Examples of this include –
phosphorus: and other more complex inorganic and organic forms can be expressed as P.
organic carbon: e.g. acetic acid and glucose can be expressed as C.
hardness: this attribute of water is caused by the presence of divalent cations, most commonly Ca++ and Mg++, but also Fe++, Mn++ and Sr++. Rather than report each of these, they are converted to and expressed as a common constituent, here CaCO3. This is accomplished as follows:
The number of equivalents in bases such as these is equal to the number of moles of H+ which would react with one mole of base, e.g.
Thus there are 1, 2, and 3 equivalents per mole, respectively, involved in these reactions. The equivalent weight of each is given as the molecular weight divided by the number of equivalents per mole:
Example: hardness calculation.
2. Particle Concentrations
T16 – Solids concentration
3. Representation by Effect
T17 – Representation by effect (truck)
T18 – Representation by effect (cheesecake)
T19 – Representation by effect (sewage, as organic matter)
T20 – Representation by effect (organic matter - burger)
T21 – Representation by effect (organic matter – proteins, fats, etc.)
T22 – Representation by effect (photosynthesis and respiration)
T23 – Representation by effect (biochemical oxygen demand)
T24 – Representation by effect (sewage, as oxygen demand)
Example: units of mass per mass.
T5 – Mass per Mass (Onondaga Lake overview)
Mercury in lake sediments.
An industry in Syracuse, New York used the chlor-alkali process to produce chlorine gas (Cl2) and sodium hydroxide (NaOH) from salt (NaCl). Mercury is used in the process and is lost to the waste stream through leakage and dumping. Over the period 1946 - 1970, 75,000 kg of mercury (Hg) were discharged to Onondaga Lake.
T6 – Mass per Mass (Onondaga Lake sediments)
A one kilogram sample of lake sediment (dry weight) was found to contain 0.02 g of Hg. What is the mercury concentration in ppmm?
Consider the ‘ease of use’ of the mass fraction, 0.00002, and ppm (20).
Mercury in fish flesh.
T7 – Mass per Mass (Channel catfish)
The U.S. Food and Drug Administration issued consumption advisories for mercury in fish when concentrations equaled or exceeded 0.5 ppmm (wet fish flesh). A channel catfish from Onondaga Lake weighing 6 kilograms (wet weight) contained 32 milligrams of mercury. Determine the Hg concentration in ppmm and compare that to the standard.
Note that, in solids, mg/kg is equivalent to ppmm, g/kg is equivalent to ppbm, and ng/kg is equivalent to pptm.
Example: units of mass per volume.
Mercury in lake water – mass per volume expression.
T8 – Mass per Volume (Onondaga Lake)
Onondaga Lake water contains on the order of 11 ngHg·L-1. Express this concentration as ppmm. Is this the best ‘parts per’ expression?
Knowing that 1 L of water weighs approximately 1000 g:
Note that in aqueous systems, mg·L-1 = ppmm, g·L-1 = ppbm, and ng·L-1 = pptm.
T13 – Mole per Volume (Onondaga Lake)
Mercury in lake water – mole per volume expression.
Again, for the 11 ngHg·L-1 in Onondaga Lake water, express this as moles·L-1. Is this the best molar expression.
A mole of Hg has a formula weight of 200.6 grams.
T14 – Ceriodaphnia toxicity test
Animation – Depending on time, consider the toxicity animation
Copper toxicity in Ceriodaphnia – mole per volume expression.
The LC50 for Ceriodaphnia exposed to copper in water is 200 μgCu∙L-1. Express the LC50 as a molar concentration.
or
Example: hardness calculation
T15 – Hardness in water
Consider a water with a Ca2+ concentration of 25 mg/L and a Mg2+ concentration of 35 mg/L. Calculate the total hardness, expressed as mg/L CaCO3.
For calcium,
For magnesium,
yielding a total hardness of 208.3 mg/L CaCO3.