One in a million
An analogy is often useful for making a concept understandable. But sometimes an analogy is faulty, and only adds to the confusion. For example in a presentation called Environmental Truths and Environmental Myths by Stephen B. Lovejoy of Purdue University included this slide:
Not only does this example contain two rather vague amounts (an olympic size pool and a grain of salt) it is off by a factor larger than the example it is trying to explain! Most people tend to underestimate how much an amount of water weighs, but I would think that most people would still guess that a large pool would contain at least 100,000 lbs of water, and so would require at least 0.1 lbs of salt to produce one part per million (ppm). The actual mass of water (calculations shown below) in a large pool would be about four million pounds, and so it would require four pounds of salt to produce a concentration of one part per million.
I doubt if people who do not routinely weigh small amounts of material would be able to estimate how much one grain of salt weighs. Some measurements with an analytic balance show that the average grain of salt (in this case reagent grade sodium chloride) weighs less than 0.1 mg (45 grains of salt weighed 3.7 mg). Producing a one part per million solution would require dissolving the grain of salt in less than 100 ml. Rather than drinking a whole swimming pool to get one grain of salt, you would get about 4 grains in a twelve ounce (355 ml) soda. Further calculations (shown below) show that one grain of salt in a large pool produces a concentration of about one part per 10 trillion, and that the author was off by a factor of about 10 million.
It is easy to come up with analogies that are unambiguous and accurate. Examples:
One second is on millionth of just over 11 and 1/2 days.
A 100 kg (220 lb) person who takes two extra strength (500 mg each) acetaminophen (Tylenol) tablets would be 10 ppm acetaminophen.
NEW More examples from Water on the Web
A modern olympic size pool is 50 meters long, but I am not sure if there are any official requirements for the other dimensions. In addition, there may be side areas such as a diving area or children's area. In an case, the example is so far off that even an estimate will show that it is wrong. I will use a pool 50 meters long, 25 meters wide, and with an average depth of 1.5 meters.
Metric: 50*25*1.5=1875 cubic meters of water. weighing 1,875,000 kilograms. This would require 1.875 kilograms of salt to produce 1 ppm
US 50*25*1.5 (1.09*3)3 * 7.48 gallons/cubic foot * 8.34 lbs/gallon = about 4.1 million lbs, would require about 4.1 lbs of salt.
If each grain of salt weighed 0.1 mg (measurements show that they average less than that) it would take 18.75 trillion (US) to produce a 1 ppm solution. Lovejoy was off by a factor of over ten million. which is more than the amount he was trying to explain.
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Written by Jim Norton
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