Ideal Gas Law

n/V = P/(R*T) n= (P*V)/(R*T)

R for P = 8.314 J mol^-1 K^-1 , R for atm = 82.05 x 10^-6 atm m³ mol^-1 K^-1 1.0 atm = 1.01325 x 10⁵ PA

Air: 8.0 x 10^-11 mol CHCl₃/mol Air = 8.0 x 10^-2 ppb_v CHCl₃

Water: 42 μg/L of something = 42 ppb and mg/L = ppm

Percent concentration of a gas in air is by pressure or moles (multiply P_T by percentage in IGL to calculate moles)

Percent concentration in water is by mass typically

Hardness = TH = 2 * [Ca²⁺] + 2 * [Mg²⁺] + N of other multivalent Cations (answers in eq/L)

Carbonate Hardness = CH = [HCO₃^-] + 2 * [CO₃^2-] up to the TH (answers in eq/L)

TDS = Σ mass concentrations of all ions (answers in mg/L)

Alkalinity = K_w/[H⁺] or [OH^-] + [HCO₃^-] + 2 * [CO₃^2-] - [H⁺]

Ionic Strength = I = 1/2 Σ c_iz_i² (molar concentration * the square of the charge for all ions)

pH = -log [H⁺], 10^-5 M of [H⁺] has a pH of 5

TS = M_B/V_A TDS = M_G/V_D SS = M_E/V_D TVS = (M_B-M_C)/V_A VSS = (M_E-M_F)/V_D

V_A w/o water = M_B which burned = M_C

V_D filtered = M_E on paper + M_G still in solution, M_E burned = M_F (for the VSS)

Turbidity

concentration = particles/cm³ surface area concentration = μm²/cm³

Volume of a sphere = 4/3πr³ Cross sectional area of a sphere = πr²

Volume of particles = density x mass total mass/mass of one particle = # of particles OR number per gram

If this is particles per L, be sure to change to particles per cm³ etc.

Total cross sectional area = cross sectional area of one particle x number of particles per cm³

Acid-Base Reactions & Acid Dissociation & Strong & Weak Acids

HA ↔ H⁺ + A^-

KA = [H⁺][A^-] pK_A = -log₁₀(K_A) pK_A = pH - log₁₀[A^-] + log₁₀[HA]

[HA]

[HCO₃^-] typically balances natural waters for electroneutrality

(pK_A) for HCO₃^- à CO₃^2- + H⁺ is 10.33, K = 10^-10.33

K = [CO₃^-][H⁺]

[HCO₃^-]

Relative Humidity = Vapor Pressure/Saturation Vapor Pressure

Kinetics Rate Law R = k [A]^a[B]^b

Y_A = 100 ppb, Y_B = 50 ppb, Y_C = 1 ppb

A + B à C, k₁ = 2 x 10^-4ppb^-1min^-1, R₁ = k₁ [A][B]; C à A + B, k₂ = 0.2 min^-1 , R₂ = -k₂ [C] Therefore dY_C/dt = k₁ [A][B] - k₂ [C]

A+ B à C & C à A + B τ = (C)/((k₁*A*B)-(k₂*C));

A + A à Products τ = A_o/(2k A_o²); A à products τ = A_o/(k₁ A_o); A à Products τ = A_o/(k_o)

Rate Law R = - 1/a (d[A]/dt) = -1/b (d[B]/dt) = 1/c (d[C]/dt) where A + B à C

dx/dt = production(x) - consumption (x) @ steady state dYx/dt = 0 = k₁ YAYB - k₂YC solve for YC

Henry's Law C_W = K_H,g P_g P_g = H_g C_W K_H,g is M/atm H_g is atm/M

C_W is the species concentration in aqueous phase (M)

P_g is the partial pressure of the gaseous species (atm)

Material Balance Cx*V_W + (Px*Va)/(R*T) = moles

Solubility Product & Solid Precipitation (solid must be present)

A_xB_y à xA + yB [A]^x * [B]^y = K_sp (T) e.g. [Ca⁺][F^-]² = 3 x 10^-11 M³ for CaF₂

Adsorption

Linear: q_e = K_ads C_e Langmuir: q_e = q_max (b C_e)/(1 + b C_e) Freundlich: q_e = K_f C_e^1/n

q_e = mass of sorbed contaminant (moles or mg per g of sorbant) C_e = concentration in fluid at equ. (moles or mg per liter)

q_max = max sorbtion K_ads & b are L/g or moles

Freundlich linearized: log q_e = 1/n log C_e + log K_f Langmuir linearized: C_e/q_e = C_e/q_max + 1/(b * q_max) [plot C_e/q_e on Y and C_e on X]

Uptake = contaminant on AC (mol or mmol)/grams AC = q; then plug in values of q to graph

Often, sorbed moles + C_t + gaseous moles = some total number of moles