Tuesday, March 01, 2005

One hundred parts per billion

Let's try to make the quantity 100 ppb concrete.

Assume you have one grain of salt, a little cube about 3/10 of a millimeter long (I'm estimating, but this whole exercise is about estimation). If that is so, we have a cube of 0.03 centimeters on a side, with a volume of (0.03cm)^3= 0.000027 cubic centimeters. The density of salt is 2.165 grams per cubic centimeter, so a grain of salt is about 0.0000585 grams (almost 60 micrograms).

Now, to get a solution that is 100 parts per billion by weight salt, we need to understand what is meant by parts per billion. Percent, which is more familiar, is basically parts per hundred. If I want a 10% solution, I want a 10 parts per hundred solution.

So lets do it for 100 ppb. To get 1 part per billion, I need a billion times more mass of liquid than salt, less the mass of the salt, which will be neglible, so let's ignore it. So 0.0000585 grams x 1,000,000,000= 58,500 grams of water. 100 ppb is 100 times more concentrated than 1 ppb, so we can divide the mass of solvent by 100 to get 585 grams of water. One gram of water is 1 milliliter, and 500mL is about a pint, so we are talking about dissolving a grain of salt or two in a bit over a pint of water to get a salt concentration of 100 ppb.

Applying this to earlier posts, this is about the concentration of perchlorates being discussed. With respect to the methylmercury post, this is 1000 times bigger. The projected reduction in methylmercury content in seafood would be akin to one-onethousandth of a grain of salt in a pint of water.