Getting Started in HPLC

Section 4B. Units and Concentration

   
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 200-pound 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 200-pound 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 = 103 mg = 106 mg = 109 ng = 1012 pg = 1015 fg
Milligram 1 mg = 10-3 g = 1 mg = 103 mg = 106 ng = 109 pg = 1012 fg
Microgram 1 mg = 10-6 g = 10-3 mg = 1 mg = 103 ng = 106 pg = 109 fg
Nanogram 1 ng = 10-9 g = 10-6 mg = 10-3 mg = 1 ng = 103 pg = 106 fg
Picogram 1 pg = 10-12 g = 10-9 mg = 10-6 mg = 10-3 ng = 1 pg = 103 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 = 103 mL = 106 mL = 109 nL
Milliliter 1 mL = 10-3 L = 1 mL = 103 mL = 106 nL
Microliter 1 mL = 10-6 L = 10-3 mL = 1 mL = 103 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 / 103 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)

 
   
   
 

 


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Last revised: April 06, 2001.