Process & Water Chemistry formula sheet — printable

Moles from Mass (n = m/M)

n = \frac{m}{M}

Molarity (C = n/V)

C = \frac{n}{V}

Mass Percent of a Solution

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

Particles from Moles (Avogadro's Number)

N = n\,N_A

Dilution Equation (C1V1 = C2V2)

C_1 V_1 = C_2 V_2

Ideal Gas Law

P V = n R T

Gas Volume at STP

V = n\,V_m

Gas Density from Molar Mass

\rho = \frac{PM}{RT}

Percent Yield

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

Percent Composition of an Element

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

Titration: Concentration of an Unknown

C_a = \frac{n\,C_b V_b}{V_a}

Normality from Molarity

N = M \times n_{\text{eq}}

Equivalent Weight from Molar Mass and Valence

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

Chlorine Dose, Demand and Residual

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

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

\dot m = C \, Q

Pounds of Active Chemical in a Tank

m = V \times \mathrm{SG} \times \rho_w \times p

Hypochlorite Product Mass from Available Chlorine

m_{\text{prod}} = \frac{m_{\mathrm{Cl}} \times 100\%}{p}

Chlorine Dose from a Weight of Product

C = \frac{m \, p}{V}

Breakpoint Chlorine-to-Ammonia Ratio

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

CT Achieved (Disinfectant Residual × Contact Time)

\text{CT} = C \, T_{10}

Effective Contact Time from Baffling Factor

T_{10} = \theta \times \mathrm{BF}

Log Inactivation from Counts

\mathrm{LR} = \log_{10}\!\left(\frac{N_0}{N}\right)

Log Reduction to Percent Kill

P = 1 - 10^{-\mathrm{LR}}

Chick–Watson Inactivation

\log_{10}\!\left(\frac{N_0}{N}\right) = k \, C^{\,n} \, t

First-Order Chlorine Decay

C = C_0 \, e^{-k t}

First-Order Integrated Rate Law

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

Total Hardness as CaCO₃

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

Ion Concentration as CaCO₃ Equivalent

C_{\mathrm{CaCO_3}} = C_{\mathrm{ion}} \times \frac{50.04}{\mathrm{EW}}

Grains per Gallon ↔ ppm Hardness

H = 17.118\,G

Total Alkalinity as CaCO₃ from Species

\mathrm{TA} = 0.8202\,\mathrm{HCO_3} + 1.6679\,\mathrm{CO_3} + 2.9425\,\mathrm{OH}

Acid Feed to Reduce Alkalinity

\dot m = \frac{\Delta \mathrm{Alk} \, Q \times \frac{\mathrm{EW}}{50.04}}{p/100\%}

TDS Estimated from Conductivity (TDS = k × EC)

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

Water Resistivity and Conductivity

\rho = \frac{1}{\sigma}

Hardness Load Removed per Regeneration

m = C \, V

Softener Resin Volume Required

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

Days Between Softener Regenerations

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

Salt Dose per Regeneration

m_{\text{salt}} = D \, V

Hardness Removal Efficiency and Leakage

R = \frac{C_{\text{in}} - C_{\text{out}}}{C_{\text{in}}}

Cycles of Concentration (COC = M/B)

\text{COC} = \frac{M}{B}

Cycles of Concentration from Conductivity

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

Cycles of Concentration from Chloride

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

Cooling Tower Evaporation Rate

E = 0.001 \, R \, \Delta T

Blowdown Rate from Cycles

B = \frac{E}{\text{COC} - 1}

Cooling Tower Makeup Water Rate

M = E + B + D

Cooling Tower Drift Loss

D = \frac{d}{100} \, R

Cooling Tower Range

\Delta T = T_h - T_c

Cooling Tower Approach

A = T_c - T_{wb}

Cooling Tower Heat Rejection

Q = 500 \, R \, \Delta T

Chemical Feed Rate from Dose

W = C \, Q \, \rho_w

Dose Achieved from Chemical Added

C = \frac{m}{V \, \rho_w}

Product Dose from Active Strength

D_p = \frac{100 \, D_a}{A}

Closed Loop Slug Dose Volume

V_p = \frac{C \, V_s \, \rho_w}{\rho_p}

Holding Time Index

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

System Volume from Turnover Time

V = R \, t

Boiler Cycles of Concentration

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

Boiler Blowdown Percent

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

Boiler Blowdown Rate from Steam Rate

B = \frac{S}{\text{COC} - 1}

Condensate Return Percentage

\%CR = \frac{S_c}{S} \times 100

Boiler Makeup from Condensate Return

M = S\left(1 - \frac{\%CR}{100}\right)

Flash Steam Percentage

\%F = \frac{h_{f1} - h_{f2}}{h_{fg2}} \times 100

Langelier Saturation Index (LSI)

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

Saturation pH (pHs) for Langelier's Index

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

Ryznar Stability Index (RSI)

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

Puckorius (Practical) Scaling Index

\mathrm{PSI} = 2\,\mathrm{pH_s} - \mathrm{pH_{eq}}, \quad \mathrm{pH_{eq}} = 1.465\,\log_{10}\mathrm{Alk} + 4.54

Larson–Skold Index

\mathrm{LS} = \dfrac{\frac{\mathrm{Cl}}{35.45} + \frac{\mathrm{SO_4}}{48.03}}{\frac{\mathrm{Alk}}{50.04}}

Dissolved Oxygen Saturation with Temperature

\ln C_s = -139.34411 + \frac{1.575701 \times 10^5}{T} - \frac{6.642308 \times 10^7}{T^2} + \frac{1.243800 \times 10^{10}}{T^3} - \frac{8.621949 \times 10^{11}}{T^4}

Corrosion Rate from Coupon Weight Loss

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

Wall Penetration and Remaining Life

L = \frac{T - T_r}{P}

Penetration Rate from Corrosion Current Density

P = \frac{i \, M}{n \, F \, \rho}

Galvanic Driving Voltage

\Delta E = E_c - E_a

Sacrificial Anode Mass for a Required Life

W = \frac{I \, t}{C \, u}

Anode Current Output

I = \frac{\Delta E}{R}

Cathodic Protection Current Demand

I = A \, i \, f

Pitting Resistance Equivalent Number (PREN)

PREN = \%Cr + 3.3\,\%Mo + 16\,\%N

Hydraulic Detention Time

t = \frac{V}{Q}

Surface Overflow Rate

v_o = \frac{Q}{A}

Clarifier Solids Loading Rate

\text{SLR} = \frac{(Q + Q_r) \, X}{A}

Stokes Settling Velocity

v_s = \frac{g (\rho_s - \rho) d^2}{18 \mu}

Filtration Rate (Filter Loading Rate)

v_f = \frac{Q}{A}

Backwash Water Volume

V_{bw} = v_b \, A \, t

Percent Backwash Water

\%BW = \frac{V_{bw}}{V_f} \times 100

Jar Test Dose Scale-Up

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

Alkalinity Remaining After Alum

A_f = A_0 - 0.45 \, D

BOD Mass Loading

W = Q \, C

BOD Removal Efficiency

E = \frac{C_i - C_e}{C_i} \times 100

Population Equivalent

PE = \frac{W}{w}

Food-to-Microorganism (F/M) Ratio

\frac{F}{M} = \frac{Q \, S_0}{V \, X}

Mean Cell Residence Time (Sludge Age)

\text{SRT} = \frac{V \, X}{Q_w \, X_w}

Sludge Volume Index (SVI)

\text{SVI} = \frac{SV_{30}}{X}

Return Activated Sludge Rate

Q_r = \frac{Q \, X}{X_r - X}

Raoult's Law

P = x \, P^{0}

Henry's Law (Gas Solubility)

C = H\,P

Relative Volatility (Binary)

\alpha = \frac{y\left(1 - x\right)}{x\left(1 - y\right)}

Column Material Balance (Distillate and Bottoms Split)

D = F\,\frac{z_F - x_B}{x_D - x_B}

Reflux Ratio

R = \frac{L}{D}

Boilup Ratio

V_B = \frac{V}{B}

Fenske Equation (Minimum Stages)

N_{min} = \frac{\ln\!\left[\frac{x_D}{1 - x_D}\cdot\frac{1 - x_B}{x_B}\right]}{\ln \alpha}

Overall Column Efficiency

E_o = \frac{N_t}{N_a}

Gilliland Correlation (Actual Stages)

\frac{N - N_{min}}{N + 1} = 1 - \exp\!\left[\left(\frac{1 + 54.4X}{11 + 117.2X}\right)\!\left(\frac{X - 1}{\sqrt{X}}\right)\right],\quad X = \frac{R - R_{min}}{R + 1}

Rectifying Operating Line (McCabe–Thiele)

y = \frac{R}{R + 1}\,x + \frac{x_D}{R + 1}

Stripping Operating Line (McCabe–Thiele)

y = \frac{V_B + 1}{V_B}\,x - \frac{x_B}{V_B}

Feed Line (q-Line)

y = \frac{q}{q - 1}\,x - \frac{z_F}{q - 1}

Packed Column Height from HTU and NTU

Z = H_{OG} \, N_{OG}

Transfer Units for Dilute Absorption

N_{OG} = \frac{\ln \left[ \dfrac{y_1}{y_2} \left( 1 - \dfrac{1}{A} \right) + \dfrac{1}{A} \right]}{1 - \dfrac{1}{A}}

Absorption Factor

A = \frac{L}{m V}

Kremser Equation for Absorption Stages

N = \frac{\ln \left[ \dfrac{y_1}{y_2} \left( 1 - \dfrac{1}{A} \right) + \dfrac{1}{A} \right]}{\ln A}

D-Value (Decimal Reduction Time)

D = \frac{t}{\mathrm{LR}}

z-Value (Thermal Resistance Constant)

z = \frac{T_2 - T_1}{\log_{10} D_1 - \log_{10} D_2}

F-Value (Equivalent Time at Reference Temperature)

F = t \times 10^{\,(T - T_{ref})/z}