Units, stoichiometry, and chemical equilibrium
What does 1 part per million (ppm) represent as a mass fraction, and what is its common equivalent unit in water quality analysis?
1 ppm represents a mass fraction of 10−610^{-6}10−6. In water, 1 ppm is approximately equal to 1 mg/L assuming the density of water is 1 kg/L.
What does pH represent mathematically?
pH is the negative base-10 logarithm of the hydrogen ion concentration:
pH=−log_10 [H+]
What is the value of Kw, and what equilibrium does it describe?
Kw=10^−14; it describes the dissociation of water into hydrogen and hydroxide ions.
Write the general mass balance equation.
Accumulation = Input − Output + Generation − Consumption.
What is contaminant flux, and what does it represent physically?
Flux is the amount of contaminant crossing a unit area per unit time, representing the rate and direction of transport.
What fundamental conservation principles must be satisfied when balancing a chemical reaction using stoichiometry?
All atoms must be conserved and total charge must be conserved.
Why is oxygen commonly used as a “proxy” for organic contamination in water?
Because measuring every organic compound individually is impractical, oxygen demand estimates the total potential impact of organic matter on dissolved oxygen levels.
What condition defines a neutral solution in terms of ion concentrations?
A solution is neutral when [H+]=[OH−]
What distinguishes steady-state from non-steady-state systems?
In steady state, concentrations do not change with time; in non-steady-state systems, concentrations vary with time.
Write the flux equation for advection and define each term.
J = CU where C = concentration and U = fluid velocity
What does the magnitude of an equilibrium constant K indicate about the relative amounts of reactants and products at equilibrium?
If K>1, products are favored at equilibrium; if K<1, reactants are favored; if K=1, neither is favored.
State Henry’s Law and explain what a high Henry’s Law constant indicates about a compound.
Henry’s Law states that the concentration of a dissolved gas in water is proportional to its partial pressure in the gas phase K_H = Cw/Pg.
A high Henry’s Law constant indicates higher solubility (more “water-loving”).
What is true about the relative concentrations of an acid and its conjugate base when pH = pKa?
The concentrations are equal: [HA]=[A−]
Which reactor model assumes no axial mixing and concentration changes along the flow path?
The plug flow reactor (PFR) model.
Why is molecular diffusion effective at small scales but ineffective at large spatial scales?
Diffusion relies on random molecular motion, which occurs quickly over short distances but is too slow to cause significant transport over large distances.
How is reaction order defined, and why cannot it be determined directly from the balanced chemical equation?
Reaction order describes how reaction rate depends on reactant concentrations and is determined experimentally. It cannot be determined from the balanced equation because stoichiometric coefficients do not necessarily reflect the reaction mechanism.
Why does increasing temperature generally decrease gas solubility in water? Use equilibrium concepts in your explanation.
Increasing temperature shifts equilibrium toward the gas phase (Le Chatelier’s principle), reducing gas solubility in water.
Define oxidation and reduction in terms of electron transfer.
Oxidation is the loss of electrons, and reduction is the gain of electrons.
For a first-order reaction in a batch reactor, how does concentration change with time?
C = C_0 e^-kt
What forces determine particle steady state settling velocity in a fluid?
Gravitational force and drag force.
A contaminant undergoes first-order decay in a completely mixed batch reactor with a rate constant of k = 0.2 / day.
If the initial concentration is C_0 = 10 mg/L, what will the concentration be after 7 days?
First order batch reaction:
C = C_0 e^-kt
C = 10 mg/L (e^-(0.2/day)(7 days))
C = 2.47 mg/L
Water is equilibrated with air at 25C. The Henry's law constant for oxygen is K_H = 1.29 x 10^-3 M/atm. Assume the partial pressure of oxygen in air is P_O2 = 0.21 atm.
What is the dissolved oxygen concentration in mol/L?
C = K_H (P)
C = 2.709 x 10^-4 mol/L
A city faces increasing flooding risk due to climate change. City planners propose the following actions:
Option A: Transition the city’s power supply from coal-fired electricity to renewable energy sources.
Option B: Elevate roads, expand stormwater drainage systems, and construct flood barriers.
Identify which option represents mitigation and which represents adaptation.
A = mitigation
B = adaptation
What is a Lorenz plot and what relationship does it show between fraction of global population and global energy consumption?
we are far from energy equality but have been getting closer over time.
<20% of world consumes 50% of energy
10% of world consumes 0% of energy
What key public health insight did John Snow provide during the 19th-century cholera outbreak?
He linked cholera outbreaks to contaminated drinking water, demonstrating that waterborne pathogens cause disease.