Student Podcast, Episode 2

Chapter 2: Environmental Measurements

An air monitor reads 100 parts per billion of sulfur dioxide. Convert that into a mass concentration and you get 260 micrograms per cubic meter. Take the same instrument, the same reading of 100 parts per billion, and move it to a hot afternoon, and the mass number comes out lower.

Nothing about the pollution changed. The air expanded, so there are fewer molecules packed into every cubic meter, and a unit built on cubic meters has to move with it. Two numbers, one pollutant, both correct. This chapter is about why that happens and how to move between the two without getting it backward.

Chapter 2 is a toolbox chapter. It is not asking you to weigh in on anything. It is asking you to get fluent in a language that every chapter after this one assumes you already speak. The book's own reason for putting it this early is that concentration is the driving force behind almost everything in the course.

Concentration controls how a chemical moves between air and water and soil. It sets the rate of chemical reactions. It determines how severe an effect turns out to be, whether that is toxicity, bioconcentration, or climate change.

Four objectives in this chapter, and I will take them in the order they are listed.

One: concentration in mass, volume, and mole units

There are four basic ways to say how much of something is in a sample, and Table 2.1 in the chapter lays all four side by side. Mass of chemical per total mass. Mass of chemical per total volume. Volume of chemical per total volume.

Moles of chemical per total volume. Everything in section 2.1 and 2.2 is one of those four.

Start with mass per mass, which is where parts per million lives. One milligram of something sitting in one kilogram of total mass is one part per million by mass. In soils and sediments that translates directly, so milligrams per kilogram is the same thing as parts per million by mass, and micrograms per kilogram is parts per billion by mass. One warning from the chapter worth carrying: when you see ppt, check what it means. Some people write it for parts per trillion and some for parts per thousand.

Water gets a shortcut that you should understand rather than memorize. One liter of pure water weighs about a thousand grams, so milligrams per liter and parts per million by mass come out as the same number. That is not a law. It is a consequence of water's density being close to one, and it holds only for dilute solutions where the dissolved material is not adding meaningfully to the total mass.

Most natural waters, wastewaters, and reclaimed waters are dilute enough. Seawater, brines, and some recycled process streams are not.

The chapter puts a number next to this that I think is the best line in the whole chapter. The drinking water standard for trichloroethylene is five micrograms per liter, which is five parts per billion. Five parts per billion sounds like nothing.

Then the book points out that there are over six billion people on Earth, so thirty people sitting in one of your classrooms are a human concentration of about five parts per billion. That is the level at which a chemical becomes a regulated hazard in your drinking water. The units in this field keep getting smaller because the substances that matter most cause trouble in genuinely tiny quantities.

Then air, where the convention shifts to volume per volume. Parts per million by volume. There is a specific reason for the switch, and the chapter gives it plainly. A gas concentration reported as a volume fraction does not change when the gas is compressed or expands. A gas concentration reported as micrograms per cubic meter does change, because the mass of pollutant stays put while the volume around it grows. So volume-based units travel well and mass-based units do not, which is exactly the problem in the opening of this episode.

Last in this group, moles per liter, which is molarity, and which you will use constantly once equilibrium chemistry arrives next chapter. The chapter is careful to separate molarity from molality, and they are easy to confuse because the words are nearly identical. Molarity is moles of solute per liter of total solution.

Molality is moles of solute added to a liter of solvent, which means the final volume is a little more than a liter. Molality exists to handle freezing points and boiling points, and the book says outright that it is rarely used in environmental situations. Know the difference, then reach for molarity.

Two: concentration as partial pressure

The second objective is partial pressure, and this one is short but it hides an idea worth slowing down for.

Whether a chemical is even in the gas phase at all depends on temperature. A substance exists as a gas if the air is warmer than the substance's boiling point, or if its concentration sits below its saturated vapor pressure at that temperature. The major and minor gases that make up the atmosphere all have boiling points far below anything the atmosphere reaches, which is why they are gases all the time. Table 2.3 in the chapter lists what the atmosphere is actually made of. Nitrogen is 78.1 percent, oxygen 20.9, argon just under one percent, and carbon dioxide 391 parts per million by volume, which is 0.039 percent.

Partial pressure is the pressure one component of a mixture would exert if every other component suddenly vanished and left it alone in the same container. Oxygen's partial pressure in the atmosphere is about 0.21 atmospheres, which should look familiar next to that 20.9 percent.

Here is the idea underneath. For gases, pressure fractions and mole fractions and volume fractions are all the same number. That comes straight out of the ideal gas law, because at fixed temperature and volume the pressure a gas exerts is proportional to how many moles of it are present.

So partial pressure is just the volume fraction multiplied by the total pressure, and it becomes a fourth way into the same conversion machinery you already have. Volume, moles, or partial pressure. Any of the three gets you to parts per million by volume.

The chapter works this on gas-phase P.C.B's measured in the air over Lake Superior at 450 picograms per cubic meter. The partial pressure comes out around three times ten to the negative fourteen atmospheres. P.C.B's are worth a second of your attention as a class of chemical. They are a family of over two hundred related compounds, they were valued industrially precisely because they were so chemically stable, and that same stability meant they did not break down, they bioaccumulated up the food chain, and manufacture was banned in the United States in 1976. The chapter also runs a version of the partial pressure calculation with humidity in it, where you have to subtract the water vapor's contribution before you work with the dry air numbers.

Three: common constituent units

The third objective is the one where units stop being pure arithmetic and start being a decision about what to report.

The problem is this. Phosphorus in a lake or an estuary exists simultaneously as orthophosphates, polyphosphates, metaphosphates, and organic phosphates, and it converts between those forms. Nitrogen does the same thing across ammonia, nitrite, and nitrate. Reporting every species separately is technically precise and practically useless to someone who has to make a decision. So you convert every form to a shared reference, add them up, and report one number.

Total phosphorus as milligrams of P per liter. Total nitrogen as milligrams of N per liter.

Run that conversion once and you learn something. The chapter takes a water with 30 milligrams per liter of ammonia and 5 milligrams per liter of nitrate. The ammonia contributes 24.7 milligrams of nitrogen. The nitrate contributes 1.1. Most of nitrate's mass is the three oxygens, not the nitrogen you actually care about. The raw numbers on a lab sheet do not tell you that. The conversion does.

Hardness works the same way, with a different reference. Hardness comes from divalent cations in the water, mostly calcium and magnesium, though iron, manganese, and strontium can contribute. Everything gets converted to milligrams per liter as calcium carbonate and summed.

And the reason hardness runs on charge rather than mass is that what makes water hard is how many units of charge are floating around, not how heavy the ions are. That is why the equivalent weight, molecular weight divided by number of equivalents, keeps showing up.

Which brings in normality, equivalents per liter, and a genuinely elegant trick. A one molar solution of hydrochloric acid is one normal, because each molecule donates one proton. A one molar solution of sulfuric acid is two normal, because each molecule donates two.

On an equivalent basis, sulfuric acid is twice as strong at the same molarity. Now, every water solution has to be electrically neutral, which means the cations and the anions have to balance on an equivalent basis. So you can audit a lab report you have never seen before.

The chapter does exactly that, and it is a good story. Professor Mihelcic, one of the authors, was in Dunedin, New Zealand, looking at yellow-eyed penguins and albatrosses, and he bought a bottle of local mineral water. He ran the label's chemical analysis through the equivalence check.

The cations came out more than three times the anions, well outside the five percent you would tolerate. Either the reported numbers are wrong, or an anion is missing from the label, and bicarbonate is the usual suspect because it is present in nearly every natural water. That is an analytical tool disguised as a vacation anecdote.

Four: using the ideal gas law to convert

The fourth objective is the conversion the whole chapter has been building toward.

Pressure times volume equals moles times the gas constant times absolute temperature. The gas constant comes in many unit flavors, and the chapter lists eight of them, so the practical advice is to pick the one whose units cancel against what you have and check that they actually do.

Two results fall out of that equation and both are worth holding. First, at one atmosphere and 273 Kelvin, one mole of any pure gas occupies 22.4 liters, and it does not matter which gas. Molecular weight and composition do not enter into it. Second, for gases, volume ratios and mole ratios are the same thing, which is why you can compute parts per million by volume from either without converting between them.

The conversion itself is three moves. Write the parts per billion as a volume ratio. Rearrange the gas law into moles per volume, which is pressure over R times temperature.

Multiply by the molecular weight to get from moles to mass. That is how 100 parts per billion of sulfur dioxide at 28 degrees Celsius becomes 260 micrograms per cubic meter. The chapter also gives you the result packaged as a single equation, but I would work it by hand at least once, because the moment the problem hands you a different combination of units the memorized formula will not save you and the logic will.

And notice where temperature sits in that expression. It is in the denominator. Warmer air means fewer moles in every cubic meter, which means the same volume-fraction reading converts to a smaller mass concentration.

The chapter's problem set has you do exactly this for ozone in Beijing on a summer day at thirty degrees Celsius. The reading is 125 parts per billion by volume. The mass concentration you calculate from it depends on the weather that day. That is not a technicality. That is the reason this chapter exists.

Two last unit types round out the chapter. Particles get measured by pulling a known volume of air through a filter and weighing what accumulates, which gives total suspended particulates. In water, solids get sorted by whether they pass through a filter, dissolved, or get caught on it, suspended, and then each of those can be burned to separate the volatile fraction from the fixed fraction.

And when a mixture is too complicated to name its components at all, which is the normal situation with sewage, you stop trying to identify chemicals and instead measure what the mixture does. How much oxygen it consumes. That is representation by effect, it is called biochemical or chemical oxygen demand, and it is a unit you will be living with from the biology chapter onward.