Dose, treat, protect & separate

Process & Water Chemistry

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Stoichiometry at Scale

  • L1
    Lesson 1
    Reading the label
    which 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.

  • L2
    Lesson 2
    The mole machine
    a weighed mass, converted into moles and into particles

    Chemistry reacts in whole numbers of particles.

    The formulas in this lesson
    n=mMn = \dfrac{m}{M},N=n NAN = n\,N_A
  • L3
    Lesson 3
    Across the equation
    the 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
    nB=nA ban_B = n_A\,\dfrac{b}{a},mB=mAMA⋅ba⋅MBm_B = \dfrac{m_A}{M_A} \cdot \dfrac{b}{a} \cdot M_B
  • L4
    Lesson 4
    Molarity, asked every way
    C = 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
    n=mMn = \dfrac{m}{M},C=nVC = \dfrac{n}{V}
  • L5
    Lesson 5
    The dilution line
    C₁V₁ = C₂V₂, from the stock drum to the day tank

    Adding water to a solution adds no solute.

    The formula in this lesson
    C1V1=C2V2C_1 V_1 = C_2 V_2
  • L6
    Lesson 6
    Gases in the vessel
    PV = 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
    PV=nRTPV = nRT,V=n VmV = n\,V_m,ρ=PMRT\rho = \dfrac{P M}{R T}
  • L7
    Lesson 7
    What runs out first
    the 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
    nexcess=nB−ba nAn_{\text{excess}} = n_B - \dfrac{b}{a}\,n_A
  • L8
    Lesson 8
    Yield on the batch record
    what the sheet allowed against what the drier delivered

    Two percentages share this lesson, and they answer completely different questions.

    The formulas in this lesson
    % yield=mactualmtheoretical×100%\%\,\text{yield} = \dfrac{m_{\text{actual}}}{m_{\text{theoretical}}} \times 100\%,%X=a MXMcompound×100%\%X = \dfrac{a\,M_X}{M_{\text{compound}}} \times 100\%
  • L9
    Lesson 9
    Titration morning
    the burette reading, equivalents, and the number 50

    A titration is a mole count performed with a tap.

    The formulas in this lesson
    Ca=n CbVbVaC_a = \dfrac{n\,C_b V_b}{V_a},N=M×neqN = M \times n_{\text{eq}},EW=Mz\mathrm{EW} = \dfrac{M}{z}
  • ★
    Boss lesson
    The Batch Sheet
    the 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
    n=mMn = \dfrac{m}{M}

Chlorination & Disinfection

  • L11
    Lesson 11
    Dose, demand, residual
    one 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.

  • L12
    Lesson 12
    The pounds formula
    lb/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
    lb/day=mg/L×MGD×8.34\text{lb/day} = \text{mg/L} \times \text{MGD} \times 8.34,lb=gal×SG×8.34×%100\text{lb} = \text{gal} \times \mathrm{SG} \times 8.34 \times \dfrac{\%}{100}
  • L13
    Lesson 13
    Hypochlorite arithmetic
    available 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
    mprod=mCl×100pm_{\text{prod}} = \dfrac{m_{\mathrm{Cl}} \times 100}{p},C=m pVC = \dfrac{m\,p}{V}
  • L14
    Lesson 14
    The breakpoint curve
    the 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
    R=Cl2NH3-NR = \dfrac{\mathrm{Cl_2}}{\mathrm{NH_3\text{-}N}}
  • L15
    Lesson 15
    CT credit
    residual 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
    T10=θ×BFT_{10} = \theta \times \mathrm{BF},CT=C T10\text{CT} = C \, T_{10}
  • L16
    Lesson 16
    Log kill
    what 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
    LR=log⁡10 ⁣(N0N)\mathrm{LR} = \log_{10}\!\left(\dfrac{N_0}{N}\right),P=1−10−LRP = 1 - 10^{-\mathrm{LR}},LR=k C n t\mathrm{LR} = k\,C^{\,n}\,t
  • L17
    Lesson 17
    Decay in the main
    first-order loss between the plant and the far hydrant

    The residual that leaves the plant is not the residual that arrives.

  • ★
    Boss lesson
    The Compliance Morning
    the 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
    D=Cdemand+CresD = C_{\text{demand}} + C_{\text{res}}

Hardness, Alkalinity & Softening

  • L19
    Lesson 19
    Everything as CaCO₃
    one 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
    EW=Mz\mathrm{EW} = \dfrac{M}{z},CCaCO3=Cion×50.04EWC_{\mathrm{CaCO_3}} = C_{\mathrm{ion}} \times \dfrac{50.04}{\mathrm{EW}},TH=2.497 Ca+4.118 Mg\mathrm{TH} = 2.497\,\mathrm{Ca} + 4.118\,\mathrm{Mg}
  • L20
    Lesson 20
    Grains per gallon
    the 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.

  • L21
    Lesson 21
    The alkalinity ledger
    the 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
    TA=0.8202 HCO3+1.6679 CO3+2.9425 OH\mathrm{TA} = 0.8202\,\mathrm{HCO_3} + 1.6679\,\mathrm{CO_3} + 2.9425\,\mathrm{OH},m˙=ΔAlk  Q  EW50.04  100p\dot m = \Delta\mathrm{Alk}\;Q\;\dfrac{\mathrm{EW}}{50.04}\;\dfrac{100}{p}
  • L22
    Lesson 22
    Conductivity to TDS
    one 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
    TDS=k EC\mathrm{TDS} = k\,\mathrm{EC},ρ=1σ\rho = \dfrac{1}{\sigma}
  • L23
    Lesson 23
    Sizing the softener
    grains 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
    m=C Vm = C\,V,V=mcapqV = \dfrac{m_{\text{cap}}}{q},t=mcapC Qt = \dfrac{m_{\text{cap}}}{C\,Q}
  • L24
    Lesson 24
    Blending around the softener
    the 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
    C=Q1C1+Q2C2Q1+Q2C = \dfrac{Q_1 C_1 + Q_2 C_2}{Q_1 + Q_2}
  • L25
    Lesson 25
    Salt and efficiency
    the 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
    msalt=D Vm_{\text{salt}} = D\,V,R=Cin−CoutCinR = \dfrac{C_{\text{in}} - C_{\text{out}}}{C_{\text{in}}}
  • L26
    Lesson 26
    Lime and soda ash
    precipitation 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
    L=CO2+Alk+Mg+ExL = \mathrm{CO_2} + \mathrm{Alk} + \mathrm{Mg} + \mathrm{Ex},S=TH−AlkS = \mathrm{TH} - \mathrm{Alk}
  • ★
    Boss lesson
    The Softener Commissioning
    the 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
    TH=2.497 Ca+4.118 Mg\mathrm{TH} = 2.497\,\mathrm{Ca} + 4.118\,\mathrm{Mg}

Cooling Towers & Boilers

  • L28
    Lesson 28
    Cycles of concentration
    evaporation 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
    COC=MB\text{COC} = \dfrac{M}{B},COC=σtσm\text{COC} = \dfrac{\sigma_t}{\sigma_m},COC=CltClm\text{COC} = \dfrac{\mathrm{Cl}_t}{\mathrm{Cl}_m}
  • L29
    Lesson 29
    Evaporation, blowdown, makeup
    one 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
    E=0.001 R ΔTE = 0.001\,R\,\Delta T,B=ECOC−1B = \dfrac{E}{\text{COC} - 1},D=d100 RD = \dfrac{d}{100}\,R,M=E+B+DM = E + B + D
  • L30
    Lesson 30
    Range and approach
    two 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
    ΔT=Th−Tc\Delta T = T_h - T_c,A=Tc−TwbA = T_c - T_{wb},Q=500 R ΔTQ = 500\,R\,\Delta T
  • L31
    Lesson 31
    Dosing the loop
    from 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
    W=C QW = C\,Q,C=1000 mVC = \dfrac{1000\,m}{V},Dp=100 DaAD_p = \dfrac{100\,D_a}{A},Vp=C Vs1000 ρpV_p = \dfrac{C\,V_s}{1000\,\rho_p}
  • L32
    Lesson 32
    The holding time index
    how 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
    V=R tV = R\,t,HTI=0.693 VB\text{HTI} = \dfrac{0.693\,V}{B}
  • L33
    Lesson 33
    Boiler cycles
    the 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
    COC=TDSbTDSfw\text{COC} = \dfrac{\text{TDS}_b}{\text{TDS}_{fw}},%B=100 TDSfwTDSb\%B = \dfrac{100\,\text{TDS}_{fw}}{\text{TDS}_b},B=SCOC−1B = \dfrac{S}{\text{COC} - 1}
  • L34
    Lesson 34
    Condensate comes home
    what 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
    %CR=100 ScS\%CR = \dfrac{100\,S_c}{S},M=S(1−%CR100)M = S\left(1 - \dfrac{\%CR}{100}\right),%F=100 (hf1−hf2)hfg2\%F = \dfrac{100\,(h_{f1} - h_{f2})}{h_{fg2}}
  • ★
    Boss lesson
    The Tower Survey
    the 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
    COC=σtσm\text{COC} = \dfrac{\sigma_t}{\sigma_m}

Corrosion & the Water Quality Indices

  • L36
    Lesson 36
    The Langelier index
    pH 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
    pHs=(9.3+A+B)−(C+D)\mathrm{pH_s} = \left(9.3 + A + B\right) - \left(C + D\right),LSI=pH−pHs\mathrm{LSI} = \mathrm{pH} - \mathrm{pH_s}
  • L37
    Lesson 37
    Ryznar and Puckorius
    two 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
    RSI=2 pHs−pH\mathrm{RSI} = 2\,\mathrm{pH_s} - \mathrm{pH},pHeq=1.465log⁡10Alk+4.54\mathrm{pH_{eq}} = 1.465\log_{10}\mathrm{Alk} + 4.54
  • L38
    Lesson 38
    The Larson–Skold ratio
    chloride 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
    LS=Cl35.45+SO448.03Alk50.04\mathrm{LS} = \dfrac{\frac{\mathrm{Cl}}{35.45} + \frac{\mathrm{SO_4}}{48.03}}{\frac{\mathrm{Alk}}{50.04}},ΔO2=Cs(T1)−Cs(T2)\Delta \mathrm{O_2} = C_s(T_1) - C_s(T_2)
  • L39
    Lesson 39
    Coupon mathematics
    weight 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
    P=534 mρ A tP = \dfrac{534\,m}{\rho\,A\,t},L=T−TrPL = \dfrac{T - T_r}{P}
  • L40
    Lesson 40
    Current into metal
    corrosion 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
    P=i Mn F ρP = \dfrac{i\,M}{n\,F\,\rho},ΔE=Ec−Ea\Delta E = E_c - E_a
  • L41
    Lesson 41
    Cathodic protection
    size 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
    I=A i fI = A\,i\,f,I=ΔERI = \dfrac{\Delta E}{R},W=I tC uW = \dfrac{I\,t}{C\,u}
  • L42
    Lesson 42
    Choosing the alloy
    PREN 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
    PREN=%Cr+3.3 %Mo+16 %N\mathrm{PREN} = \%\mathrm{Cr} + 3.3\,\%\mathrm{Mo} + 16\,\%\mathrm{N}
  • ★
    Boss lesson
    The Corrosion Survey
    the 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
    LSI=pH−pHs\mathrm{LSI} = \mathrm{pH} - \mathrm{pH_s}

Clarifiers, Filters & the Sludge Line

  • L44
    Lesson 44
    Detention time
    volume over flow — how long the water actually stays

    Every unit process in a plant is a promise about time.

    The formula in this lesson
    t=VQt = \dfrac{V}{Q}
  • L45
    Lesson 45
    Overflow and solids loading
    the 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
    vo=QAv_o = \dfrac{Q}{A},SLR=(Q+Qr) XA\text{SLR} = \dfrac{(Q + Q_r)\,X}{A}
  • L46
    Lesson 46
    Over the weir
    weir 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
    WL=QLwW_L = \dfrac{Q}{L_w}
  • L47
    Lesson 47
    Settling by Stokes
    the settling velocity a particle can actually manage

    The overflow rate says how fast a particle must fall.

    The formula in this lesson
    vs=g (ρs−ρ) d218 μv_s = \dfrac{g\,(\rho_s - \rho)\,d^{2}}{18\,\mu}
  • L48
    Lesson 48
    The filter run
    loading 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
    vf=QAv_f = \dfrac{Q}{A},Vbw=vb A tV_{bw} = v_b\,A\,t,%BW=VbwVf×100\%BW = \dfrac{V_{bw}}{V_f}\times 100
  • L49
    Lesson 49
    The jar test
    scale 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
    D=Vst CstVsD = \dfrac{V_{st}\,C_{st}}{V_s},Af=A0−0.45 DA_f = A_0 - 0.45\,D
  • L50
    Lesson 50
    BOD on the books
    mass 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
    W=Q CW = Q\,C,E=Ci−CeCi×100E = \dfrac{C_i - C_e}{C_i}\times 100,PE=WwPE = \dfrac{W}{w}
  • L51
    Lesson 51
    Feeding the bugs
    F/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
    FM=Q S0V X\dfrac{F}{M} = \dfrac{Q\,S_0}{V\,X},SRT=V XQw Xw\text{SRT} = \dfrac{V\,X}{Q_w\,X_w}
  • L52
    Lesson 52
    SVI and the return line
    sludge 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
    SVI=SV30X\text{SVI} = \dfrac{SV_{30}}{X},Qr=Q XXr−XQ_r = \dfrac{Q\,X}{X_r - X}
  • ★
    Boss lesson
    The Plant Walkdown
    the 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
    t=VQt = \dfrac{V}{Q}

Separations & Absorption

  • L54
    Lesson 54
    Volatility first
    alpha 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
    C=HPC = H P,P=x P0P = x\,P^{0}
  • L55
    Lesson 55
    The column balance
    mass 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
    D=F zF−xBxD−xBD = F\,\dfrac{z_F - x_B}{x_D - x_B}
  • L56
    Lesson 56
    Reflux and boilup
    the 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
    R=LDR = \dfrac{L}{D},VB=VBV_B = \dfrac{V}{B}
  • L57
    Lesson 57
    Counting stages
    Fenske'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
    Nmin=ln⁡[xD1−xD⋅1−xBxB]ln⁡αN_{min} = \dfrac{\ln\left[\dfrac{x_D}{1 - x_D}\cdot\dfrac{1 - x_B}{x_B}\right]}{\ln \alpha},Eo=NtheorNactualE_o = \dfrac{N_{theor}}{N_{actual}},N=Nmin+Y1−YN = \dfrac{N_{min} + Y}{1 - Y}
  • L58
    Lesson 58
    Operating lines
    rectifying, 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
    y=RR+1 x+xDR+1y = \dfrac{R}{R+1}\,x + \dfrac{x_D}{R+1},y=VB+1VB x−xBVBy = \dfrac{V_B+1}{V_B}\,x - \dfrac{x_B}{V_B},y=qq−1 x−zFq−1y = \dfrac{q}{q-1}\,x - \dfrac{z_F}{q-1}
  • L59
    Lesson 59
    The packed tower
    height 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
    A=LmVA = \dfrac{L}{m V},NOG=ln⁡[y1y2(1−1A)+1A]1−1AN_{OG} = \dfrac{\ln\left[\dfrac{y_1}{y_2}\left(1 - \dfrac{1}{A}\right) + \dfrac{1}{A}\right]}{1 - \dfrac{1}{A}},Z=HOGNOGZ = H_{OG} N_{OG}
  • L60
    Lesson 60
    The Kremser count
    stages 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
    A=LmVA = \dfrac{L}{m V}
  • ★
    Boss lesson
    The Scrubber Quotation
    the boss · no calculator · quote the tower from solubility to height

    Everything is sized to fit in your head.

    The formula in this lesson
    m=HPm = \dfrac{H}{P}

Thermal Kill: D, z and F

  • L62
    Lesson 62
    The D-value
    one 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
    D=tLRD = \dfrac{t}{\mathrm{LR}}
  • L63
    Lesson 63
    Counting log cycles
    from 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
    LR=log⁡10 ⁣(N0N)\mathrm{LR} = \log_{10}\!\left(\dfrac{N_0}{N}\right),D=tLRD = \dfrac{t}{\mathrm{LR}}
  • L64
    Lesson 64
    The z-value
    the temperature rise that cuts D tenfold

    D answers one question at one temperature.

    The formula in this lesson
    z=T2−T1log⁡10 ⁣(D1/D2)z = \dfrac{T_2 - T_1}{\log_{10}\!\left(D_1 / D_2\right)}
  • L65
    Lesson 65
    The F-value
    equivalent 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
    F=t×10 (T−Tref)/zF = t \times 10^{\,(T - T_{\mathrm{ref}})/z},D=tLRD = \dfrac{t}{\mathrm{LR}}
  • L66
    Lesson 66
    Pasteurisation units
    one 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
    D=tLRD = \dfrac{t}{\mathrm{LR}}
  • L67
    Lesson 67
    Hotter or longer
    trade 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 lesson
    The Retort Run
    the 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
    LR=log⁡10 ⁣(N0N)\mathrm{LR} = \log_{10}\!\left(\dfrac{N_0}{N}\right)

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