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.
Variables
| Symbol | Description | Unit |
|---|---|---|
| Molarity | mol/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.
Variables
| Symbol | Description | Unit |
|---|---|---|
| Molality | mol/kg |
Normality (N)
Equivalents of solute per liter of solution. Used for acid-base titrations and redox reactions.
Variables
| Symbol | Description | Unit |
|---|---|---|
| Normality | eq/L | |
| Molarity | mol/L | |
| Number 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.
Variables
| Symbol | Description | Unit |
|---|---|---|
| Parts per million | ppm |
Solution Stoichiometry and Chemical Analysis (Titration)
Stoichiometry in Solutions
Chemical analysis of solutions often relies on stoichiometry. When working with solutions, molarity () and volume () are used to calculate the moles of solute involved in a reaction ().
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.
Variables
| Symbol | Description | Unit |
|---|---|---|
| Molarity of the acid | mol/L | |
| Volume of the acid | L | |
| Molarity of the base | mol/L | |
| Volume of the base | L |
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.
Always Soluble:
- Alkali metal ions (, , , ...) and Ammonium ().
- Nitrates (), Acetates (), Chlorates (), Perchlorates ().
Usually Soluble:
- Chlorides (), Bromides (), Iodides () — Except with , , .
- Sulfates () — Except with , , , .
Usually Insoluble:
- Carbonates (), Phosphates (), Sulfides () — Except with Alkali metals or .
- Hydroxides () — Except with Alkali metals, , , .
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.
Variables
| Symbol | Description | Unit |
|---|---|---|
| Vapor pressure of the solution | - | |
| Mole fraction of the solvent | - | |
| Vapor pressure of the pure solvent | - |
Boiling Point Elevation
The boiling point of a solvent increases when a solute is added.
Variables
| Symbol | Description | Unit |
|---|---|---|
| Boiling point elevation | ||
| Van 't Hoff factor (particles per formula unit) | - | |
| Molal boiling-point elevation constant | ||
| Molality of the solution | mol/kg |
Freezing Point Depression
The freezing point of a solvent decreases when a solute is added. This is the basis for salting roads.
Variables
| Symbol | Description | Unit |
|---|---|---|
| Freezing point depression | ||
| Van 't Hoff factor | - | |
| Molal freezing-point depression constant | ||
| Molality of the solution | mol/kg |
Osmotic Pressure
Pressure required to stop osmosis. Important in reverse osmosis water treatment.
Variables
| Symbol | Description | Unit |
|---|---|---|
| Osmotic pressure | atm | |
| Van 't Hoff factor | - | |
| Molarity of the solution | mol/L | |
| Ideal gas constant | ||
| Absolute temperature | K |
Van 't Hoff Factor ($i$)
The Van 't Hoff factor () represents the number of particles per formula unit of solute. For example, (), (), and glucose (non-electrolyte) (). Constants for water are and .
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.
Variables
| Symbol | Description | Unit |
|---|---|---|
| Concentration of the dissolved gas | mol/L | |
| Henry's Law constant | - | |
| Partial pressure of the gas above the liquid | - |
- 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 (). Ionic compounds () have a greater effect than molecular compounds ().
- 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.