Novice reporters and more experienced journalist alike should take note of the fact that mass per volume ratios do not convert directly to simple or pure ratios. In fact, the difference between, for example, one micro gram per liter and one part per billion could be one, two, three or more orders of magnitude, depending upon what the original nature and concentration of a solution is.

The easiest way to understand this is to think of a drop of two different pure liquids, one being water, the other being, say alcohol. If you dissolve one drop of pure alcohol in one-drop of water you have a 1:1 dilution; if you dissolve one drop of pure alcohol in 10 drops of water you have a 1:10 dilution; if you dissolve one drop of alcohol in one-hundred drops of water you have a ratio of 1:100, etc. That is, if you dissolve one part of alcohol in a thousand, ten-thousand, one-hundred thousand, a million or a billion parts of water you would end up with the respective dilutions as shown below beginning with one drop or part of alcohol per one part of water and extending through the sequence to one drop of alcohol per a billion parts of water:

1:1
1:10
1:100
1:1,000
1:10,000
1:100,000
1:1,000,000
1:1,000,000,000

The later amount is one part of alcohol per billion parts of water. This is NOT the same, however as one microgram of a substance per liter of water (unless the substance being diluted, or divided by 1,000, is a microgram of water, itself). This is the point where many novice reporters and science writers alike become confused. Actually the only way to go from one part per million to one part per billion is to add 1,000 times as much water or remove all but 1/1,000 gram of mass.

In the laboratory the way such dilutions are commonly made is you take a quantity of water, say a liter, and dissolve a known mass. Then to make a dilution, you pipet, say 1 milliliter of water, from this known concentration and add it to a liter of water. Thus you have made a 1:1,000 dilution. If the concentration you started with was 1 gram per liter, then the dilution will be 0.001 grams per liter. If you then take one milliliter of this solution and add it to 1 liter the dilution will be 0.000001 grams, or one microgram per liter. Then if you take this one milliliter of this dilution and add it to l liter of water the dilution will be 0.000000001 grams per liter. In other words, in making each sequential dilution you have increased the amount of water by 1,000. For some strange reason people who do not a good knowledge of the Metric System or the process of making a diluted solution often get confused here and think they can divide a microgram by 1,000 because a liter contains 1,000 milliliter of water, and that this equates to a part per billion solution. But this is NOT how such dilutions are made! You actually have to add 1,000 times as much water relative to the unit of mass to go from one part per million to one part per billion.

In scientific notation these sequential dilutions are each one order (a factor of 1 divided by 10) of magnitude in concentration below the previous concentration and are generally written:

1 / 10^-1
1 / 100^-2
1 / 1,000^-3
1 / 10,000^-4
1 / 100,000^-5
1 / 1,000,000^-6
1 / 10,000,000^-7
1 / 100,000,000^-8

Now keeping this in mind one should easily be able to understand that if a given mass of a substance is dissolved in a give volume of water and the resulting concentration diluted a billion times, this is not the same as saying one part per billion simply because the one part you are starting out with could be a gram per liter, a hundred grams per a thousand liters or more or less mass and volume.

In other words, you can not equate a mass/volume ratio to a simple or pure ratio without knowing the units of measure involved as well as the concentration of the solution being diluted; i.e., its mass/volume. You actually have to know or measure the grams per liter which you start with, or create a known standard, and then make sequential dilutions to produce a know concentration. It is by comparison or starting with a known concentration that one arrives at a known dilution. In the laboratory it is a common practice to always use a standard or control, i.e, a known concentration, which is helpful to calibrate equipment as well as to insure that when one measures an unknown solution, they are getting a correct result. It is incorrect to think that you get a one part per billion solution simply by dividing 1 ug by 1,000 milliliters of water!

For example, the single and only case where one microgram per liter or 1.0 ug/L would not result in error if conceptually converted to one part per billion is when one is talking about one microgram of water per liter of water. For then 1x10^-6/1x10⁺³ equals 1x10^-8, which in this case has no significance as pure water is pure water! But as soon as you start talking about other substances, solid or liquid, you need to realize that their mass per unit volume is going to be more or less than that of water such that you must refer to the dilution using a mass/volume ratio to convey the proper concentration; that in fact, to make a dilution you must actually add water. This is especially important when talking about concentrations of heavy metals or their organic constitutes relative to water as the mass/volume of such substances is so much greater than that of water, that one could easily make an error of several orders of magnitude leading to all sorts of wrong conclusions.

It would be incorrect to say that 1.0 ug/L of mercury is one part per billion of mercury. First mercury is a metal, Hg, and when talking about mercury as it occurs in nature one is usually referring to organic compounds of mercury, such as methylmercury Hg(CH₃)₂.

Although a gram of any substance, by definition, has the mass of a gram, certainly it is easy to understand that a gram of mercury per liter of water is not the same dilution as a gram of water per liter of water. In the later case you actually have no dilution at all, given water diluted in water is still pure water. As this is the only case when a conversion to parts per billion of 1.0 ug/L does not result in error simply because no dilution is really being made, it is quite erroneous to say 1.0 ug/L mercury would be one part per billion of mercury. This would more correctly be written 1.0 ug Hg per liter of water, but then if one is not talking metallic mercury, but methylmercury, this should be stated 1.0 ug methylmercury per liter of water, and certainly NOT one part per billion of methylmercury, but one part per MILLION of methylmercury.

I repeat, the correct concentration one is working with in this case is on the order of parts per million, NOT parts per billion! Remember, you actually would have to ADD 1,000 parts of water to go from a 1ug/L concentration to a 0.001 ug/L concentration or parts per billion order of magnitude.

To say one part per billion in the context of 1ug/L introduces a huge error. In regard to mercury contamination of fish to make such errors in magnitude begs the question, "part of what?" to which the answer often is not water, but human or animal tissue, which is only a given percentage of water in and of itself! When such a mistake is made, as in writing about mercury pollution in water, mercury contamination in fish and the subsequent health risks to people, then it is a serious mistake, a huge error, which could result in major consequences and damage, such as frivolous law suits based upon false claims.

Another way to think about dilution and concentration is to imagine that if you remove, as by evaporation or distillation, all the water from a give volume and are left only with solid, than what is the mass of that solid? This is, in fact, exactly what is meant by a measurement such as 1.0 ug/L of water. It means if you took a liter of solution and could boil away all the water that you would be left with 1.0 microgram of substance. Then if you analyze that substance and find out it is mercury, lead or some other toxic agent, then you can say the amount on contaminant was 1.0 ug/L of substance X.

When you say one part per million or one part per billion in context of contamination or dilution what you actually mean one unit of mass per a million or per a billion units of volume of a given substance, usually water and/or biomass. But there is a BIG difference between parts per million and parts per billion, especially when talking about mercury or some other toxic agent in fish. In such instances reporters and science writers must use extreme care to not make order of magnitude errors which might lead to wrong conclusions and alarm the public. When such errors of magnitude are made, especially by major new media, with the results being published around the world, the damage done is magnified millions and millions of times by everyone who reads a newspaper and in thereby misinformed!

Understanding concentrations and dilutions and how this relates to people, is further complicated when one begins talking toxicity, as then rate of exposure to a given concentration, or dosage must be referenced. The recommended safe dosage of a substance X (called the reference dose – RfD) is generally stated as Y grams of X/Kg of body weight per day. When Y equals 1.0 ug, this certainly does NOT mean the same a one part per billion and to think of it in this manner would be to be making an error of up to three orders of magnitude or 1 x 10^-3. As stated earlier to go from 1.0 ug/L to 0.001 ug/L or from one part per million order of magnitude to one part per billion order of magnitued you actually have to add 1,000 times as much water.

Reporters and science writers need to be very careful in their writing, especially when dealing with the metric system so as not to make errors with respect to order of magnitude; i.e., to not confuse such units as micrograms per liter with parts per million vs. parts per billion. Also care must be taken when converting between the Metric System and English units of measure and vice versa, to use the correct conversion factors. It is errors of this later type which result in multimillion dollar space crafts crashing into Mars because someone did not understand the Metric System or make a correct conversion of units from English to Metric.

When dealing with terms like the recommended safe dosage of a substance, a good way to think of this is to calculate how much of a particular food one might have to eat before they became ill, and then to consider what period of time this might take. In the case of mercury poisoning, if a food source were considered toxic when it is consumed and results in more than 5.0 ug Hg/Kg of body weight per day, then one must ask, how mush fish must a person eat to acquire this amount of mercury (or methymercury)? Very likely in most situations a calculation would probably result in such an enormous number of fish that one would have to live several life times and eat nothing but fish, day in and day out, before they would become poisoned.

The exception is cases where fish are so highly contaminated by methylmercury that eating such fish would obviously be unwise. Such would be the case where fish are found to contain ten, twenty or many more times the amount of mercury than is considered safe for daily consumption. This measure, to be most accurate, must be made by sampling fish, not people, given that one can not be sure where in the environment mercury contamination occurs that people have been exposed to over long periods of time.

What one generally finds when sampling fish is that fish such as swordfish, which are at the top of the food chain, contain higher concentrations of mercury than, say, salmon, which are lower down the food chain. So the simple solution to avoiding mercury poisoning when eating fish is not to eat too much fish in a short period of time, especially not fish at the top of the food chain like swordfish!

In conclusion, it would be wise for those writing about environmental issues such as mercury in fish, to not confuse the issue by making incorrect metric unit calculations or conversions. Rather, endeavor to state scientific units of measure accurately using the correct units of measure and educate the public in what these measures mean with respect to their own health and safety.

Finally, if an error is discovered, make a correction as soon as possible and/or write a follow-up article which corrects the mistake. Encourage others in your audience of readers to report mistakes and credit them with citing the errors. This will contribute greatly to the reporter's or journalist's credibility, for to admit one's mistakes is an element of good character and honesty which is to be much admired!

Sources

1. Crenson, Sharon L. Research of Mercury Contamination leaves huge gaps in knowledge. AP 8 Oct. 2002.