Solutions

Learning Objectives

  • Understand the general properties of aqueous solutions, including electrolytes and nonelectrolytes.
  • Calculate and convert between different units of concentration (Molarity, Molality, Normality, ppm).
  • Apply solution stoichiometry principles to chemical analysis and titrations.
  • Predict solubility and precipitation reactions using general solubility rules.
  • Explain and calculate colligative properties (vapor pressure, boiling point, freezing point, osmotic pressure).
  • Apply Henry's Law to model gas solubility in liquids.

Introduction to Solutions

Solutions are homogeneous mixtures of two or more substances. In civil engineering, solutions are everywhere: from the hydration of cement to the chlorination of water supplies and the prevention of ice on roadways.

General Properties of Aqueous Solutions (Electrolytes vs. Nonelectrolytes)

Aqueous Solution Properties

Aqueous solutions, where water is the solvent, possess unique properties based on whether the dissolved solute forms ions.

Electrolyte

A substance whose aqueous solution contains ions and therefore conducts electricity. Strong electrolytes dissociate completely, while weak electrolytes dissociate only partially.

Nonelectrolyte

A substance that does not form ions in solution and therefore does not conduct electricity (e.g., molecular compounds like sucrose or ethanol).

Concentration Units

Importance of Concentration

To effectively utilize a solution in an engineering context, we must know its concentration—the exact ratio of solute (the substance being dissolved) to solvent (the dissolving medium, usually water). Different applications require different units of concentration depending on whether temperature changes are a factor.

Molarity (M)

Moles of solute per liter of solution. General lab work, stoichiometry in solution. Volume changes with temperature, so molarity is temperature-dependent.

M=moles of soluteliters of solutionM = \frac{\text{moles of solute}}{\text{liters of solution}}

Variables

SymbolDescriptionUnit
MMMolaritymol/L

Molality (m)

Moles of solute per kilogram of solvent. Used for colligative properties. Because it is based on mass, molality is completely independent of temperature.

m=moles of solutekg of solventm = \frac{\text{moles of solute}}{\text{kg of solvent}}

Variables

SymbolDescriptionUnit
mmMolalitymol/kg

Normality (N)

Equivalents of solute per liter of solution. Used for acid-base titrations and redox reactions.

N=M×nN = M \times n

Variables

SymbolDescriptionUnit
NNNormalityeq/L
MMMolaritymol/L
nnNumber of reactive protons or electrons per molecule-

Parts Per Million (ppm)

Mass of solute per million mass units of solution. Used in environmental engineering (pollutant levels). For dilute aqueous solutions, 1 ppm is approximately 1 mg/L.

ppm=mass of solutemass of solution×106\text{ppm} = \frac{\text{mass of solute}}{\text{mass of solution}} \times 10^6

Variables

SymbolDescriptionUnit
ppm\text{ppm}Parts per millionppm

Solution Stoichiometry and Chemical Analysis (Titration)

Stoichiometry in Solutions

Chemical analysis of solutions often relies on stoichiometry. When working with solutions, molarity (MM) and volume (VV) are used to calculate the moles of solute involved in a reaction (n=M×Vn = M \times V).

Titration

A technique used to determine the concentration of a solute in a solution by carefully adding a standard solution (titrant) of known concentration to a solution of unknown concentration until the reaction is complete.

Equivalence Point

The point in a titration at which stoichiometrically equivalent quantities of reactants have been brought together.

End Point

The point where an indicator changes color, signaling that the equivalence point has been reached.

Titration Relationship (1:1 Acid-Base Reaction)

For a simple 1:1 acid-base reaction (like HCl + NaOH), this formula relates the molarities and volumes of the acid and base.

MacidVacid=MbaseVbaseM_{\text{acid}} V_{\text{acid}} = M_{\text{base}} V_{\text{base}}

Variables

SymbolDescriptionUnit
MacidM_{\text{acid}}Molarity of the acidmol/L
VacidV_{\text{acid}}Volume of the acidL
MbaseM_{\text{base}}Molarity of the basemol/L
VbaseV_{\text{base}}Volume of the baseL

Solubility

Understanding Solubility

Solubility represents the maximum limit of solute that can dissolve in a specific volume of solvent at a given temperature to form a stable, saturated solution. In civil engineering, knowing the solubility rules is crucial, particularly in water and wastewater treatment, to predict when heavy metals or minerals will precipitate out as solids.

General Solubility Rules (Aqueous)

Knowing what dissolves is crucial for predicting precipitation reactions.

  1. Always Soluble:

    • Alkali metal ions (Li+Li^+, Na+Na^+, K+K^+, ...) and Ammonium (NH4+NH_4^+).
    • Nitrates (NO3NO_3^-), Acetates (CH3COOCH_3COO^-), Chlorates (ClO3ClO_3^-), Perchlorates (ClO4ClO_4^-).
  2. Usually Soluble:

    • Chlorides (ClCl^-), Bromides (BrBr^-), Iodides (II^-) — Except with Ag+Ag^+, Pb2+Pb^{2+}, Hg22+Hg_2^{2+}.
    • Sulfates (SO42SO_4^{2-}) — Except with Ca2+Ca^{2+}, Sr2+Sr^{2+}, Ba2+Ba^{2+}, Pb2+Pb^{2+}.
  3. Usually Insoluble:

    • Carbonates (CO32CO_3^{2-}), Phosphates (PO43PO_4^{3-}), Sulfides (S2S^{2-}) — Except with Alkali metals or NH4+NH_4^+.
    • Hydroxides (OHOH^-) — Except with Alkali metals, Ca2+Ca^{2+}, Sr2+Sr^{2+}, Ba2+Ba^{2+}.

Colligative Properties

Nature of Colligative Properties

Colligative properties are unique because they depend purely on the number (concentration) of solute particles in a solution, rather than the chemical identity or mass of those particles. This principle governs critical engineering applications, such as adjusting the freezing point of water on road surfaces.

Vapor Pressure Lowering (Raoult's Law)

Adding a non-volatile solute reduces the vapor pressure of the solvent.

Psoln=XsolventPsolventP_{\text{soln}} = X_{\text{solvent}} P^\circ_{\text{solvent}}

Variables

SymbolDescriptionUnit
PsolnP_{\text{soln}}Vapor pressure of the solution-
XsolventX_{\text{solvent}}Mole fraction of the solvent-
PsolventP^\circ_{\text{solvent}}Vapor pressure of the pure solvent-

Boiling Point Elevation

The boiling point of a solvent increases when a solute is added.

ΔTb=iKbm\Delta T_b = i K_b m

Variables

SymbolDescriptionUnit
ΔTb\Delta T_bBoiling point elevationC^\circ\text{C}
iiVan 't Hoff factor (particles per formula unit)-
KbK_bMolal boiling-point elevation constantC/m^\circ\text{C}/m
mmMolality of the solutionmol/kg

Freezing Point Depression

The freezing point of a solvent decreases when a solute is added. This is the basis for salting roads.

ΔTf=iKfm\Delta T_f = i K_f m

Variables

SymbolDescriptionUnit
ΔTf\Delta T_fFreezing point depressionC^\circ\text{C}
iiVan 't Hoff factor-
KfK_fMolal freezing-point depression constantC/m^\circ\text{C}/m
mmMolality of the solutionmol/kg

Osmotic Pressure

Pressure required to stop osmosis. Important in reverse osmosis water treatment.

Π=iMRT\Pi = iMRT

Variables

SymbolDescriptionUnit
Π\PiOsmotic pressureatm
iiVan 't Hoff factor-
MMMolarity of the solutionmol/L
RRIdeal gas constant0.0821Latm/(molK)0.0821 \, \text{L}\cdot\text{atm}/(\text{mol}\cdot\text{K})
TTAbsolute temperatureK

Van 't Hoff Factor ($i$)

The Van 't Hoff factor (ii) represents the number of particles per formula unit of solute. For example, NaClNa++ClNaCl \rightarrow Na^+ + Cl^- (i=2i=2), CaCl2Ca2++2ClCaCl_2 \rightarrow Ca^{2+} + 2Cl^- (i=3i=3), and glucose (non-electrolyte) (i=1i=1). Constants for water are Kb=0.512K_b=0.512 and Kf=1.86C/mK_f=1.86 \, ^\circ\text{C}/m.

Henry's Law

Gas Solubility in Liquids

Henry's law relates the solubility of a gas in a liquid to the partial pressure of that gas above the liquid. In environmental engineering, it is used to model the dissolution of oxygen in rivers and wastewater treatment aeration tanks.

Henry's Law

The concentration of a dissolved gas is directly proportional to the partial pressure of that gas.

C=kHPC = k_H P

Variables

SymbolDescriptionUnit
CCConcentration of the dissolved gasmol/L
kHk_HHenry's Law constant-
PPPartial pressure of the gas above the liquid-
Key Takeaways
  • Molarity is volume-dependent (changes with Temp), Molality is mass-dependent (Temp independent).
  • Solubility Rules predict precipitate formation, essential for water treatment and concrete formulation.
  • Colligative Properties depend on the number of particles (ii). Ionic compounds (i>1i>1) have a greater effect than molecular compounds (i=1i=1).
  • Freezing Point Depression is the mathematical principle behind using salts for de-icing infrastructure.
  • Henry's Law is critical for calculating dissolved oxygen in aquatic environments.