Water Quality and Basic Water Chemistry (FE Civil)

NCEES FE Civil spec: Water Resources and Environmental Engineering, I. Water quality (e.g., ground and surface, basic water chemistry). FE Reference Handbook: Environmental Engineering chapter (Fate and Transport) and Chemistry and Biology chapter.

What the FE Civil Spec Covers

Section I covers water quality in ground and surface water and basic water chemistry. On the exam this means pH, molarity and equivalents, hardness and alkalinity, dissolved oxygen, biochemical oxygen demand (BOD), first-order decay, the mass balance for mixing a discharge into a stream, and the Streeter-Phelps oxygen sag curve. Nutrients and eutrophication appear as concept questions.

Key Concepts

pH measures hydrogen ion activity. Each pH unit is a tenfold change in [H⁺].
Equivalents. Hardness and alkalinity are reported as mg/L as CaCO₃ so different ions can be added. The equivalent weight of an ion is its molecular weight divided by its charge.
Hardness is the sum of multivalent cations, mainly Ca²⁺ and Mg²⁺. Alkalinity is acid neutralizing capacity, mainly bicarbonate, carbonate and hydroxide.
Dissolved oxygen (DO). Saturation DO drops as temperature rises. The deficit D is saturation DO minus actual DO.
BOD is the oxygen used by microorganisms to break down organic matter. It follows first-order kinetics, and the rate constant increases with temperature.
Nutrients. Excess nitrogen and phosphorus cause algal blooms and eutrophication; phosphorus is usually the limiting nutrient in fresh water.

Core Formulas

pH relations at 25°C:

pH = - lo g_{10} [H^{+}] pH + pOH = 14

Conversion to mg/L as CaCO₃ (equivalent weight of CaCO₃ is 50):

C_{as CaCO_{3}} = C_{i o n} \frac{50}{E W _{i o n}} E W = \frac{M W}{∣ charge ∣}

BOD exerted by time t, and temperature correction of the rate constant (θ is often taken as 1.047):

B O D_{t} = L_{0} (1 - e^{- k t}) k_{T} = k_{20} θ^{T - 20}

First-order decay and complete mixing of two flows:

C = C_{0} e^{- k t} C_{mi x} = \frac{Q _{1} C _{1} + Q _{2} C _{2}}{Q _{1} + Q _{2}}

Streeter-Phelps DO deficit downstream of a discharge (k_d deoxygenation, k_a reaeration):

D_{t} = \frac{k _{d} L _{0}}{k _{a} - k _{d}} (e^{- k_{d} t} - e^{- k_{a} t}) + D_{0} e^{- k_{a} t}

For example, a wastewater with BOD₅ = 180 mg/L and k = 0.23 per day (base e) has an ultimate BOD of 180 / (1 minus e^-1.15) = 180 / 0.684 = 263 mg/L. Saturation DO in fresh water is about 11.3 mg/L at 10°C, 9.1 mg/L at 20°C and 7.6 mg/L at 30°C, which is why oxygen sag problems are worst in warm summer low flows. COD is always at least as large as BOD because the chemical oxidant also attacks organics that microbes break down slowly or not at all.

Critical time, where the deficit is largest:

t_{c} = \frac{1}{k _{a} - k _{d}} ln [\frac{k _{a}}{k _{d}} (1 - \frac{D _{0} ( k _{a} - k _{d} )}{k _{d} L _{0}})]

Where It Is in the FE Reference Handbook

BOD exertion, Streeter-Phelps and other kinetics are in the Environmental Engineering chapter under Fate and Transport. pH, molarity, equivalent weights and the periodic table (for atomic weights) are in the Chemistry and Biology chapter.

Worked Example: Total, Carbonate and Noncarbonate Hardness

A groundwater has 60 mg/L Ca²⁺, 18 mg/L Mg²⁺ and an alkalinity of 150 mg/L as CaCO₃. Find total, carbonate and noncarbonate hardness.

Step 1: Equivalent weights. Ca: 40.08/2 = 20.04. Mg: 24.31/2 = 12.15.

Step 2: Convert each ion.

Ca: 60 \times \frac{50}{20.04} = 149.7 Mg: 18 \times \frac{50}{12.15} = 74.1 mg/L as CaCO_{3}

Step 3: Total hardness.

T H = 149.7 + 74.1 = 223.8 \approx 224 mg/L as CaCO_{3}

Step 4: Split. Alkalinity (150) is less than total hardness, so carbonate hardness equals the alkalinity.

C H = 150 mg/L N C H = 223.8 - 150 = 73.8 \approx 74 mg/L as CaCO_{3}

At about 224 mg/L as CaCO₃, this is hard water by any common classification, so softening would be considered. Removing the 74 mg/L of noncarbonate hardness would need soda ash as well as lime.

Common Mistakes

Dividing by molecular weight instead of equivalent weight, which halves the hardness of divalent ions.
Taking carbonate hardness as the alkalinity even when alkalinity exceeds total hardness. It is the smaller of the two.
Using log base 10 in BOD or decay equations written with e.
Confusing BOD₅ with ultimate BOD L₀ in Streeter-Phelps, which needs L₀ at the mixing point.
Averaging concentrations without weighting by flow when two streams mix.

Practice Problems

Try these from the free PolyCalc FE Civil problem bank. Each one has a full worked solution.

For a dilute aqueous solution, water with pH = 6 has an approximate hydrogen-ion concentration [H⁺] of: See the worked solution or practice the Environmental & Water Quality deck
A water analysis reports calcium at 40 mg/L as Ca²⁺ and magnesium at 12 mg/L as Mg²⁺. The total hardness expressed as CaCO₃ is most nearly: See the worked solution or practice the Environmental & Water Quality deck
A water sample contains 122 mg/L of bicarbonate ion, HCO₃⁻, which has an equivalent weight of 61. Expressed as calcium carbonate, with an equivalent weight of 50, the alkalinity is most nearly: See the worked solution or practice the Environmental & Water Quality deck
A stream immediately below a discharge has an initial dissolved oxygen deficit of 2.0 mg/L and an ultimate BOD of 20 mg/L. The deoxygenation constant is 0.25 per day and the reaeration constant is 0.45 per day. Using the Streeter-Phelps equation, the deficit one day downstream is most nearly: See the worked solution or practice the Environmental & Water Quality deck
A conservative substance decays by first-order kinetics with rate constant k = 0.35 per day. Starting at 100 mg/L, the concentration remaining after 4 days is most nearly: See the worked solution or practice the Environmental & Water Quality deck
A stream of 1 m³/s at 10 mg/L mixes completely with a stream of 2 m³/s at 4 mg/L. Assuming a conservative solute and no other sources or sinks, what is the final concentration? See the worked solution or practice the Environmental & Water Quality deck

Related Calculators and Examples

Frequently Asked Questions

How do I convert an ion concentration to mg/L as CaCO3?

Multiply the ion concentration in mg/L by 50 (the equivalent weight of CaCO3) and divide by the equivalent weight of the ion, which is its molecular weight divided by its charge. For calcium that is 40.08/2 = 20.04, and for magnesium 24.31/2 = 12.15.

What is the difference between carbonate and noncarbonate hardness?

Carbonate hardness is the part of total hardness balanced by alkalinity, and equals the smaller of total hardness and alkalinity. Any hardness above the alkalinity is noncarbonate hardness, which needs soda ash to remove during lime-soda softening.

What does the ultimate BOD represent?

Ultimate BOD, L0, is the total oxygen demand of the biodegradable organics if they were allowed to decay completely. BOD5 is only the part exerted in five days; with first-order kinetics BOD5 equals L0 times one minus e to the power of minus 5k.

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