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Chemistry formula solvers

Density

ρ=mV\rho = \tfrac{m}{V}

PhysicsChemistryWater TreatmentMass per unit volume.

Specific Gravity

SG=ρρwaterSG = \frac{\rho}{\rho_{water}}

Fluid MechanicsWater TreatmentChemistryDensity expressed as a multiple of water's 1000 kg/m³.

Sensible Heat (Q = mcΔT)

Q=mcΔTQ = m c \Delta T

ThermodynamicsPhysicsChemistryHeat needed to change a mass's temperature: mass times specific heat times the temperature change.

Boyle's Law

P1V1=P2V2P_1 V_1 = P_2 V_2

ThermodynamicsChemistryPhysicsAt constant temperature, pressure times volume stays constant for a fixed amount of gas.

Charles's Law

V1T1=V2T2\frac{V_1}{T_1} = \frac{V_2}{T_2}

ThermodynamicsChemistryPhysicsAt constant pressure, gas volume is directly proportional to absolute temperature.

Gay-Lussac's Law

P1T1=P2T2\frac{P_1}{T_1} = \frac{P_2}{T_2}

ThermodynamicsChemistryPhysicsAt constant volume, gas pressure is directly proportional to absolute temperature.

Combined Gas Law

P1V1T1=P2V2T2\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}

ThermodynamicsChemistryPhysicsFor a fixed amount of gas, pressure times volume over absolute temperature stays constant between any two states.

Radioactive Activity (A = λN)

A=λNA = \lambda N

Modern PhysicsChemistryPhysicsDecays per second: the decay constant times the number of undecayed nuclei.

Bohr Model Energy Levels

En=−13.606 eVn2E_n = -\frac{13.606\ \mathrm{eV}}{n^{2}}

Modern PhysicsChemistryPhysicsEnergy of the hydrogen atom's nth level: −13.606 eV divided by n².

Ideal Gas Law

PV=nRTP V = n R T

ChemistryPhysicsRelates pressure, volume, amount, and temperature of a gas. R = 8.314 J/(mol·K).

Moles from Mass (n = m/M)

n=mMn = \frac{m}{M}

ChemistryConverts a measured mass into an amount of substance by dividing by the molar mass.

Molarity (C = n/V)

C=nVC = \frac{n}{V}

ChemistryDefines molar concentration as moles of solute per volume of solution.

Percent Yield

% yield=mactualmtheoretical×100%\%\,\text{yield} = \frac{m_{\text{actual}}}{m_{\text{theoretical}}} \times 100\%

ChemistryCompares the mass actually isolated from a reaction to the maximum mass stoichiometry predicts.

Percent Composition of an Element

%X=a MXMcompound×100%\%X = \frac{a\,M_X}{M_{\text{compound}}} \times 100\%

ChemistryGives the mass percent an element contributes to a compound from the formula subscript and molar masses.

Gas Density from Molar Mass

ρ=PMRT\rho = \frac{PM}{RT}

ChemistryThermodynamicsPhysicsGives an ideal gas's density from its molar mass, pressure, and absolute temperature using R = 8.314462618 J/(mol·K).

Graham's Law of Effusion

r1r2=M2M1\frac{r_1}{r_2} = \sqrt{\frac{M_2}{M_1}}

ChemistryPhysicsRelates the effusion rates of two gases to the inverse square root of their molar masses.

Half-Life Decay

N=N0(12)t/t1/2N = N_0 \left(\frac{1}{2}\right)^{t/t_{1/2}}

ChemistryPhysicsGives the quantity remaining after repeated halvings over an elapsed time measured in half-lives.

Half-Life and Decay Constant

t1/2=ln⁡2λt_{1/2} = \frac{\ln 2}{\lambda}

ChemistryPhysicsConverts between a half-life and the exponential decay constant via the factor ln 2 = 0.6931471806.

Gas Volume at STP

V=n VmV = n\,V_m

ChemistryConverts between moles of an ideal gas and its volume at STP using the molar volume Vm = 22.414 L/mol.

pH from Hydrogen Ion Concentration

pH=−log⁡10 [H+]\mathrm{pH} = -\log_{10}\,[\mathrm{H^+}]

ChemistryWater TreatmentExpresses acidity as the negative base-10 logarithm of the hydrogen ion concentration in mol/L.

pH and pOH Relation

pH+pOH=14\mathrm{pH} + \mathrm{pOH} = 14

ChemistryLinks the acidity and basicity scales of any aqueous solution at 25 °C, where pKw = 14.

Dilution Equation (C1V1 = C2V2)

C1V1=C2V2C_1 V_1 = C_2 V_2

ChemistryWater TreatmentStates that concentration times volume is conserved when a solution is diluted, since the moles of solute do not change.

Particles from Moles (Avogadro's Number)

N=n NAN = n\,N_A

ChemistryConverts an amount in moles into an actual particle count using the Avogadro constant NA = 6.02214076 × 10²³ per mole.

Heat of Reaction

q=nΔHq = n \Delta H

ChemistryThermodynamicsScales a reaction's molar enthalpy change by the amount reacted to give the total heat released or absorbed.

Molality (b = n/m)

b=nmsolventb = \frac{n}{m_{\text{solvent}}}

ChemistryDefines molality as moles of solute per kilogram of solvent.

Mole Fraction

x1=n1n1+n2x_1 = \frac{n_1}{n_1 + n_2}

ChemistryGives the fraction of all moles in a two-component mixture contributed by the solute.

Osmotic Pressure (Π = MRT)

Π=MRT\Pi = M R T

ChemistryGives the osmotic pressure of a dilute solution from its molar concentration and absolute temperature using the van 't Hoff equation.

Raoult's Law

P=x P0P = x \, P^{0}

ChemistryGives the vapor pressure of a solvent above an ideal solution as its mole fraction times the pure solvent's vapor pressure.

Boiling-Point Elevation

ΔTb=Kb b\Delta T_b = K_b \, b

ChemistryGives how far a dissolved solute raises a solvent's boiling point from the molality and the solvent's ebullioscopic constant.

Freezing-Point Depression

ΔTf=Kf b\Delta T_f = K_f \, b

ChemistryGives how far a dissolved solute lowers a solvent's freezing point from the molality and the solvent's cryoscopic constant.

Mass Percent of a Solution

c=msolutemsolution×100%c = \frac{m_{\text{solute}}}{m_{\text{solution}}} \times 100\%

ChemistryExpresses a solution's concentration as the solute's share of the total solution mass in percent.

Beer–Lambert Law (A = εbc)

A=ε b cA = \varepsilon\, b\, c

ChemistryRelates a sample's absorbance to its molar absorptivity, path length, and concentration — the working equation of UV-Vis spectrophotometry.

Absorbance and Transmittance

A=−log⁡10 ⁣(%T100)A = -\log_{10}\!\left(\frac{\%T}{100}\right)

ChemistryConverts a spectrophotometer's percent transmittance into absorbance and back, the logarithmic bridge between what a detector sees and what Beer's law needs.

Henderson–Hasselbalch Equation (Weak Acid Buffer)

pH=pKa+log⁡10 ⁣[A−][HA]\mathrm{pH} = \mathrm{p}K_a + \log_{10}\!\frac{[\mathrm{A^-}]}{[\mathrm{HA}]}

ChemistryGives the pH of a buffer from the acid's pKa and the ratio of conjugate base to undissociated acid, the master equation of buffer preparation.

Henderson–Hasselbalch Equation (Weak Base Buffer)

pOH=pKb+log⁡10 ⁣[BH+][B]\mathrm{pOH} = \mathrm{p}K_b + \log_{10}\!\frac{[\mathrm{BH^+}]}{[\mathrm{B}]}

ChemistryGives the pOH of a weak base buffer from the base's pKb and the ratio of conjugate acid to free base, the mirror image of the acid form.

pKa from Acid Dissociation Constant

pKa=−log⁡10Ka\mathrm{p}K_a = -\log_{10} K_a

ChemistryConverts an acid dissociation constant into its logarithmic pKa form and back, compressing a huge range of acid strengths onto one readable scale.

pKb from Base Dissociation Constant

pKb=−log⁡10Kb\mathrm{p}K_b = -\log_{10} K_b

ChemistryConverts a base dissociation constant into its logarithmic pKb form and back, the basic-side counterpart of the pKa scale.

Ka and Kb Relation through Kw

Ka Kb=KwK_a \, K_b = K_w

ChemistryLinks a weak acid's dissociation constant to that of its conjugate base through the ion product of water, Kw = 1.0 × 10⁻¹⁴ at 25 °C.

pH of a Weak Acid from Ka

pH=−log⁡10Ka C\mathrm{pH} = -\log_{10}\sqrt{K_a\,C}

ChemistryEstimates the pH of a weak monoprotic acid solution from its dissociation constant and formal concentration using the standard x-is-small approximation.

Percent Ionization of a Weak Acid

% ion=[H+]C×100%\%\,\text{ion} = \frac{[\mathrm{H^+}]}{C} \times 100\%

ChemistryExpresses what fraction of a weak acid has actually donated its proton, comparing the equilibrium hydrogen ion concentration to the formal concentration.

Solubility Product of a 1:1 Salt

Ksp=s2K_{sp} = s^{2}

ChemistryLinks the solubility product of an AB salt such as AgCl or BaSO4 to its molar solubility, since each formula unit releases one cation and one anion.

Solubility Product of an AB₂ Salt

Ksp=4s3K_{sp} = 4s^{3}

ChemistryLinks the solubility product of an AB2 or A2B salt such as CaF2 or Mg(OH)2 to its molar solubility, with the factor 4 from the doubled ion.

Kp from Kc (Kp = Kc(RT)^Δn)

Kp=Kc(RT)ΔnK_p = K_c (RT)^{\Delta n}

ChemistryThermodynamicsConverts a gas-phase equilibrium constant between pressure and concentration bases using the change in moles of gas, with R = 0.08206 L·atm/(mol·K).

Equilibrium Constant Kc (A + B ⇌ C + D)

Kc=[C][D][A][B]K_c = \frac{[\mathrm{C}][\mathrm{D}]}{[\mathrm{A}][\mathrm{B}]}

ChemistryComputes the equilibrium constant or reaction quotient for a one-to-one reaction from the four species concentrations, the law of mass action in its simplest form.

Nernst Equation

E=E∘−RTnFln⁡QE = E^{\circ} - \frac{RT}{nF}\ln Q

ChemistryCorrects a cell's standard potential for non-standard concentrations, the equation behind every pH meter, ion-selective probe, and battery voltage curve.

Standard Cell Potential from Half-Cells

Ecell∘=Ecathode∘−Eanode∘E^{\circ}_{\text{cell}} = E^{\circ}_{\text{cathode}} - E^{\circ}_{\text{anode}}

ChemistryBuilds a galvanic cell's standard voltage by subtracting the anode's standard reduction potential from the cathode's, using tabulated half-cell values.

Gibbs Free Energy Change (ΔG = ΔH − TΔS)

ΔG=ΔH−T ΔS\Delta G = \Delta H - T\,\Delta S

ChemistryThermodynamicsCombines a reaction's enthalpy and entropy changes at a given temperature to decide whether it can happen spontaneously.

Gibbs Free Energy and the Equilibrium Constant

ΔG∘=−RTln⁡K\Delta G^{\circ} = -RT\ln K

ChemistryThermodynamicsConverts between a reaction's standard free energy change and its equilibrium constant, the bridge joining thermodynamics to equilibrium tables.

Arrhenius Equation

k=A e−Ea/RTk = A\,e^{-E_a/RT}

ChemistryGives a reaction's rate constant from its activation energy, pre-exponential factor, and absolute temperature — the core law of chemical kinetics.

Arrhenius Two-Temperature Form

ln⁡k2k1=EaR(1T1−1T2)\ln\frac{k_2}{k_1} = \frac{E_a}{R}\left(\frac{1}{T_1} - \frac{1}{T_2}\right)

ChemistryExtracts an activation energy from two rate constants measured at two temperatures, eliminating the pre-exponential factor entirely.

Activation Energy from an Arrhenius Plot

Ea=−R×slopeE_a = -R \times \text{slope}

ChemistryConverts the slope of a ln k versus 1/T Arrhenius plot into an activation energy, the standard graphical method for kinetics data.

Zero-Order Integrated Rate Law

[A]=[A]0−kt[\mathrm{A}] = [\mathrm{A}]_0 - kt

ChemistryGives the concentration remaining in a zero-order reaction, where the rate is constant and concentration falls in a straight line with time.

First-Order Integrated Rate Law

[A]=[A]0 e−kt[\mathrm{A}] = [\mathrm{A}]_0\,e^{-kt}

ChemistryGives the concentration remaining in a first-order reaction, the exponential decay that governs radioactive decay and most drug clearance.

Second-Order Integrated Rate Law

1[A]=1[A]0+kt\frac{1}{[\mathrm{A}]} = \frac{1}{[\mathrm{A}]_0} + kt

ChemistryGives the concentration remaining in a second-order reaction, where the reciprocal of concentration rises linearly with time.

Half-Life of a Second-Order Reaction

t1/2=1k [A]0t_{1/2} = \frac{1}{k\,[\mathrm{A}]_0}

ChemistryGives the half-life of a second-order reaction, which unlike a first-order half-life depends on the starting concentration.

Titration: Concentration of an Unknown

Ca=n CbVbVaC_a = \frac{n\,C_b V_b}{V_a}

ChemistryFinds an analyte's concentration from the titre volume, titrant concentration, and the reaction's mole ratio at the equivalence point.

Normality from Molarity

N=M×neqN = M \times n_{\text{eq}}

ChemistryConverts molarity into normality by multiplying by the number of reactive equivalents each mole of solute supplies.

Partial Pressure from Mole Fraction

Pi=xi PtotalP_i = x_i \, P_{\text{total}}

ChemistryThermodynamicsGives a gas component's partial pressure as its mole fraction times the total pressure, the practical form of Dalton's law of partial pressures.

Hess's Law (Three-Step Sum)

ΔHrxn=ΔH1+ΔH2+ΔH3\Delta H_{\text{rxn}} = \Delta H_1 + \Delta H_2 + \Delta H_3

ChemistryThermodynamicsHess's law: the enthalpy change of a target reaction is the sum of the enthalpy changes of the steps you route it through.

Standard Enthalpy of Reaction from Formation Enthalpies

ΔHrxn∘=∑ΔHf,prod∘−∑ΔHf,react∘\Delta H^{\circ}_{\text{rxn}} = \sum \Delta H^{\circ}_{f,\text{prod}} - \sum \Delta H^{\circ}_{f,\text{react}}

ChemistryThermodynamicsThe tabulated form of Hess's law: standard enthalpy of reaction equals the summed formation enthalpies of the products minus those of the reactants.

Reaction Quotient Q (aA + bB ⇌ cC)

Q=[C]c[A]a [B]bQ = \frac{[\mathrm{C}]^{c}}{[\mathrm{A}]^{a}\,[\mathrm{B}]^{b}}

ChemistryReaction quotient Q from any concentrations, raised to stoichiometric powers — the number you compare with K to predict which way a mixture shifts.

Faraday's Law of Electrolysis (m = QM/nF)

m=QMnFm = \frac{Q M}{n F}

ChemistryFaraday's law of electrolysis: the mass plated out at an electrode from the charge passed, the molar mass, and the electrons transferred per ion.

Glycol Dilution

C1V1=C2V2C_1 V_1 = C_2 V_2

Water TreatmentChemistryDilution equation for mixing glycol (or any concentrate) to a target strength.

Cycles of Concentration from Conductivity

COC=σtσm\text{COC} = \frac{\sigma_t}{\sigma_m}

Water TreatmentChemistryCycles of concentration read straight off a conductivity meter: tower water conductivity divided by makeup water conductivity.

Cycles of Concentration from Chloride

COC=CltClm\text{COC} = \frac{\mathrm{Cl}_t}{\mathrm{Cl}_m}

Water TreatmentChemistryCycles of concentration from a chloride titration — the conservative tracer that neither precipitates nor gets dosed into the system.

Chemical Feed Rate from Dose

W=C Q ρwW = C \, Q \, \rho_w

Water TreatmentChemistryChemical feed rate in pounds per day from a ppm dose and a water flow, using the trade density of 8.34 lb per US gallon.

Dose Achieved from Chemical Added

C=mV ρwC = \frac{m}{V \, \rho_w}

Water TreatmentChemistryConcentration reached in a system of known volume after adding a measured mass of chemical, at 8.34 lb of water per US gallon.

Closed Loop Slug Dose Volume

Vp=C Vs ρwρpV_p = \frac{C \, V_s \, \rho_w}{\rho_p}

Water TreatmentChemistryVolume of liquid product needed for a one-shot slug dose to hit a target ppm in a closed loop of known volume and product density.

Product Dose from Active Strength

Dp=100 DaAD_p = \frac{100 \, D_a}{A}

Water TreatmentChemistryConverts a required active-ingredient dose into the as-supplied product dose when the drum is only a given percent active.

Holding Time Index

HTI=ln⁡2  VB\text{HTI} = \frac{\ln 2 \; V}{B}

Water TreatmentChemistryHolding time index: the half-life of a chemical in a bled system, the time for half the treatment to wash out at a given blowdown rate.

Boiler Cycles of Concentration

COC=TDSbTDSfw\text{COC} = \frac{\text{TDS}_b}{\text{TDS}_{fw}}

Water TreatmentChemistryCycles of concentration in a steam boiler: boiler water TDS divided by feedwater TDS, since steam leaves the dissolved solids behind.

Boiler Blowdown Percent

%B=TDSfwTDSb×100\%B = \frac{\text{TDS}_{fw}}{\text{TDS}_b} \times 100

Water TreatmentChemistryBoiler blowdown as a percentage of feedwater, set by the ratio of feedwater TDS to the maximum TDS allowed in the drum.

Corrosion Rate from Coupon Weight Loss

P=m Yρ A tP = \frac{m \, Y}{\rho \, A \, t}

Water TreatmentChemistryUniform corrosion rate as metal thickness lost per year, from a coupon's weight loss, density, exposed area and exposure time.

Chemical Mass Consumed Over a Period

m=W tm = W \, t

Water TreatmentChemistryTreatment chemical a feed rate consumes over a period — the step that turns pounds per day into the annual tonnage a contract is priced on.

Chemical-Consuming Loss Rate

L=B+DL = B + D

Water TreatmentChemistryFluid MechanicsFlow that actually carries treatment out of a cooling tower — blowdown plus drift, because evaporation leaves every molecule of inhibitor behind.

Chemical Treatment Cost

Cp=m pcC_p = m \, p_c

Water TreatmentChemistryInvoice for a treatment chemical: the mass of product consumed over a period times its unit price, the second line of a water budget.

Total Water Treatment Program Cost

C=Cw+Cp+CeC = C_w + C_p + C_e

Water TreatmentChemistryFluid MechanicsTotal operating cost of a treated cooling system: the water and sewer bill, the chemical invoice and the energy bill added together.

Langelier Saturation Index (LSI)

LSI=pH−pHs\mathrm{LSI} = \mathrm{pH} - \mathrm{pH_s}

Water TreatmentChemistryThe classic calcium-carbonate scaling index: measured pH minus the saturation pH, positive for scaling and negative for corrosive water.

Saturation pH (pHs) for Langelier's Index

pHs=(9.3+A+B)−(C+D)\mathrm{pH_s} = (9.3 + A + B) - (C + D)

Water TreatmentChemistryComputes the pH at which water is saturated with calcium carbonate from its TDS, temperature, calcium hardness and total alkalinity as CaCO₃.

Ryznar Stability Index (RSI)

RSI=2 pHs−pH\mathrm{RSI} = 2\,\mathrm{pH_s} - \mathrm{pH}

Water TreatmentChemistryAn empirical scaling index scaled so that values below about 6 predict scale and values above about 7 predict corrosion in the same water.

Puckorius (Practical) Scaling Index

PSI=2 pHs−pHeq,pHeq=1.465 log⁡10Alk+4.54\mathrm{PSI} = 2\,\mathrm{pH_s} - \mathrm{pH_{eq}}, \quad \mathrm{pH_{eq}} = 1.465\,\log_{10}\mathrm{Alk} + 4.54

Water TreatmentChemistryA Ryznar variant that replaces measured pH with an equilibrium pH derived from alkalinity, giving a truer scaling call in poorly buffered cooling water.

Larson–Skold Index

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}}

Water TreatmentChemistryRatio of aggressive chloride and sulphate equivalents to protective bicarbonate alkalinity, predicting pitting of mild steel in distribution water.

Total Hardness as CaCO₃

TH=2.497 Ca+4.118 Mg\mathrm{TH} = 2.497\,\mathrm{Ca} + 4.118\,\mathrm{Mg}

Water TreatmentChemistryConverts a lab report's calcium and magnesium ion results into a single total hardness expressed as milligrams per litre of CaCO₃.

Grains per Gallon ↔ ppm Hardness

H=17.118 GH = 17.118\,G

Water TreatmentChemistryConverts water hardness between grains per US gallon and mg/L as CaCO₃ using the exact 17.118 mg/L per grain trade factor.

Ion Concentration as CaCO₃ Equivalent

CCaCO3=Cion×50.04EWC_{\mathrm{CaCO_3}} = C_{\mathrm{ion}} \times \frac{50.04}{\mathrm{EW}}

Water TreatmentChemistryRestates any ion's concentration in the trade's common currency of CaCO₃ by scaling with the ratio of equivalent weights, 50.04 over the ion's own.

Equivalent Weight from Molar Mass and Valence

EW=Mz\mathrm{EW} = \frac{M}{z}

Water TreatmentChemistryGives the gram-equivalent weight of an ion or compound as its molar mass divided by the number of charges or replaceable hydrogens it carries.

Total Alkalinity as CaCO₃ from Species

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}

Water TreatmentChemistrySums bicarbonate, carbonate and hydroxide reported as their own ions into one total alkalinity expressed as milligrams per litre of CaCO₃.

TDS Estimated from Conductivity (TDS = k × EC)

TDS=k×EC\mathrm{TDS} = k \times \mathrm{EC}

Water TreatmentChemistryEstimates total dissolved solids in mg/L from a conductivity reading in µS/cm using an empirical factor k, typically 0.55 to 0.70 for natural waters.

Water Resistivity and Conductivity

ρ=1σ\rho = \frac{1}{\sigma}

Water TreatmentChemistryRelates the resistivity and conductivity of ultrapure and deionized water as exact reciprocals, the pair of scales used on DI and RO polishing loops.

Hardness Load Removed per Regeneration

m=C Vm = C \, V

Water TreatmentChemistryGives the mass of hardness as CaCO₃ a softener must remove between regenerations from the raw hardness and the volume of water treated.

Days Between Softener Regenerations

t=mcapC Qt = \frac{m_{\text{cap}}}{C \, Q}

Water TreatmentChemistryGives the run time a softener achieves between regenerations from its rated hardness capacity, the raw water hardness and the average water usage rate.

Softener Resin Volume Required

V=mcapqV = \frac{m_{\text{cap}}}{q}

Water TreatmentChemistrySizes the ion-exchange resin bed from the hardness capacity required per regeneration and the resin's rated capacity per unit volume.

Salt Dose per Regeneration

msalt=D Vm_{\text{salt}} = D \, V

Water TreatmentChemistryGives the mass of sodium chloride a softener draws each regeneration from the resin volume and the programmed salt dosage per unit volume.

Hardness Removal Efficiency and Leakage

R=Cin−CoutCinR = \frac{C_{\text{in}} - C_{\text{out}}}{C_{\text{in}}}

Water TreatmentChemistryGives the fraction of hardness a softener or membrane removes from the inlet and outlet concentrations, with the remainder being leakage to service.

Chlorine Dose, Demand and Residual

D=Cdemand+CresD = C_{\text{demand}} + C_{\text{res}}

Water TreatmentChemistryThe fundamental chlorination balance: the dose applied equals the chlorine consumed by the water's demand plus the residual left for disinfection.

Chemical Feed Rate (lb/day = mg/L × MGD × 8.34)

m˙=C Q\dot m = C \, Q

Water TreatmentChemistryConverts a target chemical dose and a plant flow into a mass feed rate, the classic pounds-per-day formula built on water weighing 8.34 lb per gallon.

Hypochlorite Product Mass from Available Chlorine

mprod=mCl×100%pm_{\text{prod}} = \frac{m_{\mathrm{Cl}} \times 100\%}{p}

Water TreatmentChemistryConverts a required mass of available chlorine into the mass of hypochlorite product to weigh out, given the product's percent available chlorine.

Chlorine Dose from a Weight of Product

C=m pVC = \frac{m \, p}{V}

Water TreatmentChemistryGives the free chlorine concentration produced by dissolving a known weight of hypochlorite product of known strength in a known volume of water.

Breakpoint Chlorine-to-Ammonia Ratio

R=Cl2NH3-NR = \frac{\mathrm{Cl_2}}{\mathrm{NH_3\text{-}N}}

Water TreatmentChemistryThe weight ratio of chlorine dose to ammonia nitrogen, which must reach about 7.6 to 1 to pass breakpoint and produce a free chlorine residual.

Pounds of Active Chemical in a Tank

m=V×SG×ρw×pm = V \times \mathrm{SG} \times \rho_w \times p

Water TreatmentChemistryGives the mass of active chemical held in a storage tank from its volume, the solution's specific gravity and the percent active ingredient.

Acid Feed to Reduce Alkalinity

m˙=ΔAlk Q×EW50.04p/100%\dot m = \frac{\Delta \mathrm{Alk} \, Q \times \frac{\mathrm{EW}}{50.04}}{p/100\%}

Water TreatmentChemistrySizes the acid feed needed to knock a target amount of alkalinity out of a stream, correcting for the acid's equivalent weight and its commercial strength.

CT Value for Disinfection Credit

CT=C t\text{CT} = C \, t

Water & WastewaterWater TreatmentChemistryDisinfection CT: residual concentration multiplied by contact time, returned in the regulatory unit of mg·min/L.

BOD Mass Loading

W=Q CW = Q \, C

Water & WastewaterWater TreatmentChemistryMass of BOD, COD or solids arriving per unit time from a flow and its concentration, on the sanitary basis of 1 mg/L = 1 g/m³.

Jar Test Dose Scale-Up

D=Vst CstVsD = \frac{V_{st} \, C_{st}}{V_{s}}

Water & WastewaterWater TreatmentChemistryConverts millilitres of stock solution added to a jar test beaker into the equivalent plant dose in mg/L of raw water.

Alkalinity Remaining After Alum

Af=A0−0.45 DA_f = A_0 - 0.45 \, D

Water & WastewaterWater TreatmentChemistryAlkalinity left after coagulation, since each mg/L of alum destroys 0.45 mg/L of alkalinity as CaCO₃ in forming aluminium hydroxide floc.