Parts Per Billion

May 19, 2008 – 12:15 am

In the "Molecules of Caffeine" post, I calculated the number of caffeine molecules in a can of Mountain Dew. This lead reader Scott to e-mail me about the concept of parts per billion. For example, the Environmental Protection Agency has set their "action level" for lead in drinking water (the level at which you need to take action to reduce the lead) at 15 parts per billion. But how much is that? Is it 15 atoms of lead for every atom of something else? Is it by weight? Is it by volume?

In a case where it's in solution (dissolved in water or another liquid), it's by weight. If you have one gram of water and 15 parts per billion of lead, that means 15 billionths of that gram's weight would be from lead.

But that still didn't do it for me. I wanted to know how many lead atoms were allowable in a liter of water. Since 15 parts per billion is the point at which you have to do something, we'll conclude that the "allowable" level of lead in drinking water is 14 parts per billion. So in a liter of water, which traditionally weighs 1 kilogram, that's 14 millionths of a gram.

Now we know that a mole of lead weighs 207.2 grams, so we divide 0.000014 by 207.2, which gives us roughly 0.000000067567568. Multiply it by 6.02214179 x 10²³ and we have a mere 40,690,147,229,729,700, or 40.7 million billion atoms of lead in each liter of water.

If we applied 14 parts per billion to the population of the world, it would represent roughly 94 people, or less than 1/12th of the number of billionaires in the world in 2008 according to Forbes (1,125 as of their March 2008 billionaires report). According to Wikipedia, the average lifespan of a human right now is 67 years (this includes developed nations and third world countries averaged together). In 67 years, 14 parts per billion is just under 30 seconds. But in a liter of water, 14 parts per billion of lead is 40.7 million billion atoms.

Of course, that got me thinking, how much lead is in a swimming pool? I already got the figure for the volume of an olympic size pool for the "Pool Full Of Pudding" post, so we know that's 2,500 cubic meters. And since a cubic meter is 1,000 liters, that pool contains 2.5 million liters. If each liter contains 14 millionths of a gram, this is a simple calculation. The millionths on the lead's weight and the million on the number of liters cancel each other out, so it's 35 grams (14 x 2.5), or roughly 1.25 ounces of lead dissolved into an olympic size swimming pool's worth of water.

If we were using a simple liquid like vodka, to get an olympic size pool's vodka level (not the alcohol level, but the vodka level) to 14 parts per billion, we'd pour in around a shot glass of vodka.

Let's look at some parts per billion ratios in some of our favorite foods.

The McDonald's nutrition information chart says that a Big Mac weighs 214 grams and contains roughly 29 grams of fat. So the fat content of a Big Mac could be expressed as 135,514,018 parts per billion, roughly 10 million times higher than the allowable level of lead in drinking water.

According to calorie-count.com, the carb level in a Ho Ho is 642,857,142 parts per billion or just short of 46 million times the allowable lead level in drinking water.

So, now that you know how to express things in parts per billion, what are some Rough Equivalents you can come up with? Post them in the comments section below.