Process & Water Chemistry
Stoichiometry at Scale
- L1Lesson 1Reading the labelwhich number is a mole, a molarity, a mass percent
Walk a treatment plant and every surface carries a number: a drum label, a scale readout, a lab sheet, a batch record. Half the errors in process chemistry are not arithmetic at all — they are one of those numbers being taken for another.
- L2Lesson 2The mole machinea weighed mass, converted into moles and into particles
Chemistry reacts in whole numbers of particles.
The formulas in this lesson, - L3Lesson 3Across the equationthe mole ratio, and a mass of one substance from a mass of another
A balanced equation is a recipe, and its quantities are the big numbers written in front of the formulas: the coefficients.
The formulas in this lesson, - L4Lesson 4Molarity, asked every wayC = n/V solved for the strength, the moles, or the volume
That last word is worth a paragraph. V is not the water you added; it is the volume of everything in the vessel once the solute is in and dissolved.
The formulas in this lesson, - L5Lesson 5The dilution lineC₁V₁ = C₂V₂, from the stock drum to the day tank
Adding water to a solution adds no solute.
The formula in this lesson - L6Lesson 6Gases in the vesselPV = nRT, and the 22.4 L shortcut at STP
PV = nRT, read aloud P V equals n R T. P is the absolute pressure in pascals — absolute, not gauge, because a gas at zero gauge still has atmosphere in it. V is the volume in cubic metres, n the amount of gas in moles, T the absolute…
The formulas in this lesson,, - L7Lesson 7What runs out firstthe limiting reagent, and what is left of the other one
A reactor is almost never charged in exact proportion. One reactant is used up while some of the other is still there, and at that moment the reaction stops.
The formula in this lesson - L8Lesson 8Yield on the batch recordwhat the sheet allowed against what the drier delivered
Two percentages share this lesson, and they answer completely different questions.
The formulas in this lesson, - L9Lesson 9Titration morningthe burette reading, equivalents, and the number 50
A titration is a mole count performed with a tap.
The formulas in this lesson,, - ★Boss lessonThe Batch Sheetthe boss · no calculator · mass to moles to volume to yield
Every molar mass tonight is pinned to a number you can divide in your head — caustic soda 40, calcium carbonate 100, salt 58.5 — and every tank volume is round.
The formula in this lesson
Chlorination & Disinfection
- L11Lesson 11Dose, demand, residualone sum rules every chlorination problem
You are solving for whichever one the paper leaves out. Note where each number comes from, because that is how you tell them apart in a sentence.
- L12Lesson 12The pounds formulalb/day = mg/L × MGD × 8.34 — the operator's daily bread
This lesson is written in mg/L, million gallons per day and pounds per day, and it is written that way on purpose: it is the convention every North American operator certification exam uses, and the constant is the point of the lesson.
The formulas in this lesson, - L13Lesson 13Hypochlorite arithmeticavailable chlorine strength scales every product weight
Chlorine gas is 100% chlorine. Nothing else on the pallet is, and forgetting that is the most expensive habit in this chapter.
The formulas in this lesson, - L14Lesson 14The breakpoint curvethe chlorine-to-ammonia ratio that clears the hump
Add chlorine to a water carrying ammonia and the residual does something no other chemistry does: it rises, then falls, then rises again.
The formula in this lesson - L15Lesson 15CT creditresidual times contact time, corrected by the baffling factor
The product CT comes out in mg·min/L, which is exactly the unit every regulator's table is printed in.
The formulas in this lesson, - L16Lesson 16Log killwhat 3-log means, and what it never means
Put it the other way and the answer arrives negative, which is the equation telling you so.
The formulas in this lesson,, - L17Lesson 17Decay in the mainfirst-order loss between the plant and the far hydrant
The residual that leaves the plant is not the residual that arrives.
- ★Boss lessonThe Compliance Morningthe boss · no calculator · dose the plant, earn the CT, log the kill
Every number this morning is chosen to fit in your head: doses land on whole milligrams, the flow is 1 or 2 MGD, and the baffling factors are tenths.
The formula in this lesson
Hardness, Alkalinity & Softening
- L19Lesson 19Everything as CaCO₃one common currency for every ion in the water
A water analysis lands on the desk: calcium 80, magnesium 25, bicarbonate 180, sulphate 60, all in milligrams per litre.
The formulas in this lesson,, - L20Lesson 20Grains per gallonthe 17.1 bridge, and what happens when it is crossed backwards
This lesson is authored in the trade's own units on purpose. Every softener controller sold in North America is programmed in grains, every resin is rated in grains, and every operator licensing exam asks in grains.
- L21Lesson 21The alkalinity ledgerthe water's buffer, and the acid feed that trims it
Alkalinity is not hardness and the two are easy to confuse because both get quoted as CaCO₃. Hardness is what scales — calcium and magnesium.
The formulas in this lesson, - L22Lesson 22Conductivity to TDSone factor, two prefixes, and the scale that runs upside down
A conductivity meter measures how easily current crosses a centimetre of water. Ions carry that current, so the reading tracks how many ions are dissolved — but the meter cannot tell one ion from another, and it has never weighed anything.
The formulas in this lesson, - L23Lesson 23Sizing the softenergrains in, grains of capacity — the bank account of ion exchange
Every softener calculation in this lesson is one idea in three costumes: the resin holds a fixed number of grains of hardness, the water spends them, and the regeneration puts them back.
The formulas in this lesson,, - L24Lesson 24Blending around the softenerthe bypass valve, and the flow-weighted hardness it sets
An ion-exchange bed does not soften water a little. It takes hardness down to a fraction of a grain, and that is usually more softening than the building wants.
The formula in this lesson - L25Lesson 25Salt and efficiencythe brine draw, and the leakage it buys
Regeneration is the reverse trade: a strong sodium chloride brine drives the calcium and magnesium back off the resin and down the drain, and sodium takes their places.
The formulas in this lesson, - L26Lesson 26Lime and soda ashprecipitation softening, with every term as CaCO₃
Ion exchange suits a building. A city softens by precipitation: add a cheap alkali, turn the dissolved hardness into a solid, and settle it out.
The formulas in this lesson, - ★Boss lessonThe Softener Commissioningthe boss · no calculator · test the water, size the bed, set the clock
Tonight the calcium factor is 2.5, the magnesium factor is 4, and the grains bridge is 17 mg/L per grain per gallon. Resin is rated at a flat 30,000 grains per cubic foot and the brine controller is set to 8 lb/ft³.
The formula in this lesson
Cooling Towers & Boilers
- L28Lesson 28Cycles of concentrationevaporation leaves the salts behind
A cooling tower works by evaporating water. Vapour leaves pure — it carries no calcium, no chloride, no silica — so every mineral that came in with the makeup stays behind in a shrinking amount of water.
The formulas in this lesson,, - L29Lesson 29Evaporation, blowdown, makeupone balance, three outfits
Water leaves a cooling tower by exactly three doors, and the makeup meter has to pay for all of them: M = E + B + D. M is the makeup, E the evaporation, B the blowdown or bleed, and D the drift.
The formulas in this lesson,,, - L30Lesson 30Range and approachtwo differences, and only one grades the tower
Three thermometers describe a cooling tower, and the two differences you can make from them mean completely different things.
The formulas in this lesson,, - L31Lesson 31Dosing the loopfrom a dose on paper to litres in a jug
A dose is written as a concentration, but nobody can pour a concentration. Getting from the specification to the jug takes up to four steps, and each has its own relation.
The formulas in this lesson,,, - L32Lesson 32The holding time indexhow long a slug survives in a bleeding system
Dose a closed loop and the chemical stays. Dose a cooling tower and it starts leaving immediately, because the tower is bleeding — and what bleeds out is treated water, at full strength.
The formulas in this lesson, - L33Lesson 33Boiler cyclesthe same arithmetic, with steam playing evaporation
Everything from the first two lessons transfers, with one substitution: steam is the boiler's evaporation.
The formulas in this lesson,, - L34Lesson 34Condensate comes homewhat the returns save, and what the trap throws away
Condensate is distilled water at a couple of hundred degrees that you have already bought, already treated and already heated.
The formulas in this lesson,, - ★Boss lessonThe Tower Surveythe boss · no calculator · read the meters, close the balance
Every number tonight divides in your head: the range is 10 °F, so evaporation is simply the recirculation with the decimal point moved two places; the cycles come out whole; the drift is 0.01 % and lands on a clean two figures.
The formula in this lesson
Corrosion & the Water Quality Indices
- L36Lesson 36The Langelier indexpH minus pHs — will this water scale or bite
Water either wants to put calcium carbonate down or wants to take it up, and which of those it wants decides a great deal about the inside of a pipe.
The formulas in this lesson, - L37Lesson 37Ryznar and Puckoriustwo practical rewrites of the same saturation question
Langelier tells you which side of saturation a water sits on. Operators wanted something that also graded how far, on a scale that never went negative and that could be indexed straight into a dosing table.
The formulas in this lesson, - L38Lesson 38The Larson–Skold ratiochloride and sulphate against alkalinity — the mild-steel verdict
Langelier and Ryznar both ask one question: can this water lay down calcium carbonate.
The formulas in this lesson, - L39Lesson 39Coupon mathematicsweight loss to mils per year, and the wall life it predicts
Everything so far has been a prediction from water chemistry. A coupon is different: a flat piece of the actual alloy, weighed, hung in the actual stream, pulled, cleaned to a written procedure and weighed again.
The formulas in this lesson, - L40Lesson 40Current into metalcorrosion current as a penetration rate, and the galvanic push behind it
A corroding metal is a short-circuited battery. Iron dissolves at the anodic sites, giving up electrons; oxygen takes them at the cathodic sites a few micrometres away.
The formulas in this lesson, - L41Lesson 41Cathodic protectionsize the anode mass and current for the life the tank needs
Cathodic protection makes the whole of a structure a cathode by supplying it with electrons from somewhere else — a metal that is willing to corrode instead.
The formulas in this lesson,, - L42Lesson 42Choosing the alloyPREN from the mill certificate — will this stainless pit
Stainless steel does not resist corrosion by being thick; it resists by carrying a chromium oxide film two or three nanometres deep.
The formula in this lesson - ★Boss lessonThe Corrosion Surveythe boss · no calculator · index the water, weigh the coupon, call the remaining life
Tonight the coupon's area, density and hours have already been collapsed into one number: mils per year is the milligrams lost divided by 120.
The formula in this lesson
Clarifiers, Filters & the Sludge Line
- L44Lesson 44Detention timevolume over flow — how long the water actually stays
Every unit process in a plant is a promise about time.
The formula in this lesson - L45Lesson 45Overflow and solids loadingthe two rates that size every clarifier
A clarifier is not sized by its volume. It is sized by its surface, and there is a piece of physics behind that worth understanding once and never forgetting.
The formulas in this lesson, - L46Lesson 46Over the weirweir loading rate, the third number quoted for every basin
Three numbers are quoted for every settling basin, and you now have two of them. Detention time uses the tank's volume and says how long the water stays.
The formula in this lesson - L47Lesson 47Settling by Stokesthe settling velocity a particle can actually manage
The overflow rate says how fast a particle must fall.
The formula in this lesson - L48Lesson 48The filter runloading rate, backwash volume, and the percent the wash costs
A rapid gravity filter is measured by three numbers, and they are all the same arithmetic wearing different hats.
The formulas in this lesson,, - L49Lesson 49The jar testscale the winning jar up to the full plant flow
Coagulant dose is not calculated from first principles — it is found, on a bench, in six beakers, and then scaled.
The formulas in this lesson, - L50Lesson 50BOD on the booksmass loading, removal efficiency, and the town in population equivalents
This lesson is authored in North American operator units — million gallons per day, milligrams per litre, pounds per day — because the constant at its centre is a convention of that system and does not survive translation.
The formulas in this lesson,, - L51Lesson 51Feeding the bugsF/M and sludge age — the two dials of activated sludge
Activated sludge is farming. There is a crop of bacteria in the basin, sewage is the feed, and the operator's job is to keep the herd the right size for the meal.
The formulas in this lesson, - L52Lesson 52SVI and the return linesludge volume index, and the RAS rate that keeps the blanket down
Half an hour, a litre of mixed liquor and a graduated cylinder will tell you more about a secondary plant than a day of paperwork.
The formulas in this lesson, - ★Boss lessonThe Plant Walkdownthe boss · no calculator · headworks to aeration in one pass
Every flow, volume, area and concentration tonight has been chosen so the divisions fall out in your head, and the sanitary identity 1 mg/L = 1 g/m³ does all the unit work there is.
The formula in this lesson
Separations & Absorption
- L54Lesson 54Volatility firstalpha above 1, or no column at all
Every separation in this chapter rests on one fact: put a liquid mixture in a warm vessel and the vapour standing over it is not the same mixture.
The formulas in this lesson, - L55Lesson 55The column balancemass in equals mass out, and the split is fixed before anything else
Before a single tray is counted, the split is already decided.
The formula in this lesson - L56Lesson 56Reflux and boilupthe two ratios that set how hard the column works
The balance decided what leaves. These two ratios decide what circulates, and circulation is where the energy bill lives.
The formulas in this lesson, - L57Lesson 57Counting stagesFenske's floor, Gilliland's bridge, and the efficiency that buys real trays
Sizing a column by hand has been done the same way since the 1930s, and every step is a named paper. It works by bracketing the answer between two extremes that are cheap to compute and impossible to build.
The formulas in this lesson,, - L58Lesson 58Operating linesrectifying, stripping, and the q-line that joins them
McCabe and Thiele's construction is the only version of this problem you can see. Draw the equilibrium curve on a plot of vapour y against liquid x, add the 45° diagonal, then add three straight lines.
The formulas in this lesson,, - L59Lesson 59The packed towerheight equals HTU times NTU, and where each number comes from
An absorber is a different animal from a still. Nothing is boiling; a solute is being washed out of a gas by a liquid that will dissolve it.
The formulas in this lesson,, - L60Lesson 60The Kremser countstages for an absorber, straight from the absorption factor
Put trays in the absorber instead of packing and the question changes from how many metres to how many stages.
The formula in this lesson - ★Boss lessonThe Scrubber Quotationthe boss · no calculator · quote the tower from solubility to height
Everything is sized to fit in your head.
The formula in this lesson
Thermal Kill: D, z and F
- L62Lesson 62The D-valueone decimal reduction — the time to kill ninety percent
Heat does not kill a population all at once. Hold a spore suspension at a fixed temperature and plot the survivors on semi-log paper, and what you get is a straight line going down.
The formula in this lesson - L63Lesson 63Counting log cyclesfrom a million spores to one — how many D-values is that
The trade counts kill in logs, and the public reads it in percents.
The formulas in this lesson, - L64Lesson 64The z-valuethe temperature rise that cuts D tenfold
D answers one question at one temperature.
The formula in this lesson - L65Lesson 65The F-valueequivalent minutes at the reference temperature
A real cook is never one temperature. The vessel comes up, holds, and cools, and every minute of that history kills something — just at wildly different rates.
The formulas in this lesson, - L66Lesson 66Pasteurisation unitsone minute at 60 °C, and the F-value wearing brewing's constants
That scale was built for bacterial spores in low-acid canned food. Beer is a different product with a different enemy. It is acidic, alcoholic, hopped and carbonated, and the organisms that spoil it are feeble against heat.
The formula in this lesson - L67Lesson 67Hotter or longertrade temperature against time and keep the same kill
Everything so far has been definitions. This lesson is the payoff, and it is the reason UHT milk exists. The rule, first, in one line: ten degrees hotter, one tenth the time — for an organism whose z is 10 C°.
- ★Boss lessonThe Retort Runthe boss · no calculator · D to z to F, one canning cook end to end
So every multiplier in the run is a single power of ten, and every line is a shift of the decimal point.
The formula in this lesson
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