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
KiloMilliMicroNanoPicoFemtoT4 – Yottagrams and Yoctograms
Meaning
One-thousand
One-thousandth
One-millionth
One-billionth
One-trillionth
One-quadrillionth
Expression
103
10-3
10-6
10-9
10-12
10-15
Mass Concentration Units
1. Mass per unit mass (mass/mass): defined as the number of units chemical mass per
units total mass, e.g.
mi
mass fraction 
m total
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).
ppmm  mass fraction 106
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).
ppmm  mass fraction 106
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: H 3 PO4 , H 2 PO4 , HPO42 , PO43 and other more complex inorganic and
organic forms can be expressed as P.
organic carbon: e.g. acetic acid C2 H 4O2 and glucose C6 H 6O6 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:
mgM 2 eqv wt CaCO3 mg


as CaCO3
L
eqv wt M 2
L
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.
NaOH  Na   OH   1H   H 2O
CaCO3  Ca 2  CO32  2 H   H 2CO3
FePO4  Fe3  PO43  3H   H 3 PO4
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:
NaOH :  40  1  40
CaCO3  100  2  50
FePO4  150  3  50
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?
mass fraction 
mi
0.02gHg kgSed 0.00002 g Hg



m total
kgSed 103 gSed
gSed
ppmm  mass fraction 106  0.00002 106  20 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.
mass fraction 
mi
32 mg Hg kg fish
0.0000053 mg Hg

 6

mtotal 6 kg fish 10 mg fish
mg fish
ppmm  mass fraction 106  0.0000053 106  5.3 ppmm
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:
mass fraction 
mi 11 ngHg
L water
gHg
11x1012 gHg


 9

mtotal L water 1000 g water 10 ngHg
g water
ppmm  mass fraction 106  11x1012 106  11x106 ppmm
ppt m  mass fraction 1012  11x1012 1012  11 ppt m
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.
11 ng Hg
g Hg
mole Hg
5.48x1011 moles Hg
 9


L
10 ng Hg 200.6 g Hg
L
5.48 x1011 moles Hg 1012 picomoles
picomoles

 54.8
L
mole
L
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.
200
 gCu
L

gCu
mole Cu
moles

 3.15 x106
10  gCu 63.55 gCu
L
6
or
3.15
 moles
L
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,
25
mgCa 2 50
mg

 62.5
as CaCO3
L
40  2
L
For magnesium,
35
mgMg 2 50
mg

 145.8
as CaCO3
L
24  2
L
yielding a total hardness of 208.3 mg/L CaCO3.