

In the
remainder of this unit we will talk about quantitative
analysis  or the measurement of concentration for
different compounds in the sample. By concentration we
mean the amount of some compound in a certain quantity of
sample. Usually "amount" is expressed in terms
of weight. Concentration can then be measured as weight
per volume, weight per weight, or weight in the whole
sample (e.g., weight of aspirin in an entire tablet).
Let's begin by talking about weight. In the chemical
laboratory we usually measure weight in terms of metric
units, which are based on the GRAM (abbreviated "g"). Twenty
eight grams make up about an ounce, or 450 grams add up
to about a pound. In some cases the gram is too small to
conveniently express weights we are interested in. For
example, a 200pound man weighs about 90,000 grams. Then
we can use another unit of weight that is larger than a
gram: the KILOGRAM (Kg). A kilogram equals 1000 grams, so
our 200pound man also weighs 90 kilograms. More often in
the HPLC lab we are interested in weights that are much
smaller than a gram. Then we can define a whole series of
smaller units of weight:


Gram 
1
g 
=
1 g 
=
10^{3}
mg 
=
10^{6} mg 
=
10^{9}
ng 
=
10^{12}
pg 
=
10^{15}
fg 
Milligram 
1
mg 
=
10^{3}
g 
=
1 mg 
=
10^{3} mg 
=
10^{6}
ng 
=
10^{9}
pg 
=
10^{12}
fg 
Microgram 
1
mg 
=
10^{6}
g 
=
10^{3}
mg 
=
1 mg 
=
10^{3}
ng 
=
10^{6}
pg 
=
10^{9}
fg 
Nanogram 
1
ng 
=
10^{9}
g 
=
10^{6}
mg 
=
10^{3}
mg 
=
1 ng 
=
10^{3}
pg 
=
10^{6}
fg 
Picogram 
1
pg 
=
10^{12}
g 
=
10^{9}
mg 
=
10^{6}
mg 
=
10^{3}
ng 
=
1 pg 
=
10^{3}
fg 
Femtogram 
1
fg 
=
10^{15}
g 
=
10^{12}
mg 
=
10^{9}
mg 
=
10^{6}
ng 
=
10^{3}
pg 
=
1 fg 



Usually we
work with milligrams and micrograms, but as the
sensitivity of HPLC continues to increase, more and more
work with nanograms and picograms is being carried out.


Often the
sample concentration will be reported as weight of
compound per volume of sample. So we also need a way to
measure volume. The basis of volume in the metric system
is the liter (L), which is about as large as a quart.
Often we need to measure smaller volumes as follows:


Liter 
1
L 
=
1 L 
=
10^{3}
mL 
=
10^{6} mL 
=
10^{9}
nL 
Milliliter 
1
mL 
=
10^{3}
L 
=
1 mL 
=
10^{3} mL 
=
10^{6}
nL 
Microliter 
1
mL 
=
10^{6}
L 
=
10^{3}
mL 
=
1 mL 
=
10^{3}
nL 
Nanoliter 
1
nL 
=
10^{9}
L 
=
10^{6}
mL 
=
10^{3}
mL 
=
1 nL 




Notice that
the prefixes "milli", "micro", and
"nano" mean "one thousandth", "one
millionth", and "one billionth,"
respectively.


Now that we
have units of weight and volume defined, we can talk
about "concentration". Often our sample comes
to us as a liquid or solution, and then we measure
concentration as weight per volume. For example, grams/liter
or the number of grams of the compound in one liter of
sample solution. In other cases we may start out with a
solid sample and weigh some quantity into a final volume
of solution  using a volumetric flask. For example, 1
gram of sample is weighed out and washed into a 100 mL
flask. The flask is then filled to mark with solvent to
give a concentration of 1 gram per 100 mL:
Concentration = 1 gram / (100 mL)
=
0.01 gram/mL
In this case,
we divide the numerator and denominator by 100 to get the
final concentration in gram/mL. We can also express 100
mL as 0.1 liters. Then
we have:
Concentration
= 1 gram / (0.1 L)
=
10 gram/L
Or we could
have converted grams to milligrams (1 gram = 1000 mg) and
had:
Concentration
= 1000 mg / 100 ml
=
10 mg/mL
From this
example it should be clear that there are many equivalent
ways to express concentration. That is, we can use many
different units. (This can be confusing and likely to
cause mistakes when calculating concentration.) The best
approach is to use the same units throughout a
calculation; for example, grams and liters, milligrams
and milliliters, or milligrams and liters. In a moment we
will provide some additional help in handling these
calculations and dealing with different units of weight
and volume.




Concentration
can also be measured as weight of compound per weight of
sample. For example, a kilogram of fish might be
contaminated with 10 micrograms of some pollutant  such
as polychlorobiphenyls (PCBs). The concentration of PCBs
is then:
Concentration =
10 mg / kg
= 10 x 10^{6}
g / 10^{3}
g
= 10 x 10^{9}
g/g
= 10 ppb
That is, 10 micrograms per
kilogram is 10 parts per billion.
If we assume that the
density of our sample solution is roughly about one (as
for water), we can also express volume concentrations in
terms of parts per hundred (percentage) parts per million
(ppm), parts per billion (ppb), and parts per trillion (ppt).
Dealing with different units and converting back and
forth is often required when calculating concentrations.
Until you become familiar with this process, the
following chart should prove helpful.


1
g / L 
=
1 mg / mL 
=
1 mg / mL 

1
mg / L 
=
1 mg / mL 
=
1 ng / mL 
=
1 ppm 
1
mg / L 
=
1 ng / mL 
=
1 pg / mL 
=
1 ppb 
1
ng / L 
=
1 pg / mL 
=
1 fg / mL 
=
1 ppt 




If we move from one row to
the next lower row (within a column), the value is
multiplied by 1000. For example, a concentration of 1 mg/mL
is equivalent to 1000 mg/mL




Now for a final example
before ending this section. Assume you weigh out 100 mg
of a sample and dissolve it in 50 mL of solvent (by
adding the sample to a 50 mL volumetric flask and filling
to mark with solvent). The concentration is:
Concentration =
100 mg / 50 ml
= 2 mg/mL
= 2 g/L (same
row)
= 2000 mg/L
(next lower row, same column)
= 2000 mg/mL (same row)





