Chemistry Chapter 14: Comprehensive Study Guide on Solutions and Mixtures

Overview of Mixtures and Their Classifications

Mixture Definition: A combination of two or more substances that are mixed together physically rather than chemically.
Homogenous Mixtures: These are evenly mixed at the microscopic level and are also referred to as solutions. Components cannot be easily distinguished. Examples include lemonade and milk.
Heterogeneous Mixtures: These exhibit uneven mixing where different pieces or components are easy to distinguish. Examples include salad and pizza.
Suspensions: A heterogeneous mixture containing large particles that are more or less evenly dispersed throughout a liquid or gas temporarily. * Suspensions will eventually separate over time due to gravity. * Examples include muddy water and paint.
Colloids: A specialized type of suspension where particles remain suspended indefinitely because they possess an electrical charge. * Like charges repel each other, preventing the particles from settling. * If the charge is neutralized, the particles will settle (curdle). * Example: Milk contains the protein Casein, which has a negative charge. Adding an acid neutralizes this charge, causing the milk to curdle and form cheese. * Other examples: Jello, Milk.
Brownian Motion: The random, chaotic movement of particles in a liquid, often seen in colloids when suspended particles are observed moving around.
Tyndall Effect: The scattering of light by large particles in a colloid or suspension. This allows a light beam to be clearly seen as it passes through the mixture.

Properties and Types of Solutions

Solution Definition: A mixture that is homogeneous at a microscopic level.
Components of a Solution: * Solvent: The substance, usually a liquid, in which another substance is dissolved. Examples: water, oil, gasoline. * Solute: The substance that is dissolved into the solvent. * Aqueous Solution: A solution where water is the solvent, denoted by the symbol $(aq)$ .
Liquid-Liquid Relationships: * Miscible: Two liquids that are able to mix together effectively (e.g., alcohol and water). * Immiscible: Liquids that will not stay mixed together and will separate (e.g., oil and water).
Alloys: A solid dissolved into another solid. Specific historical and functional examples include: * Brass: Composed of Copper ( $Cu$ ) and Zinc ( $Zn$ ); valued for being corrosion resistant. * Bronze: Composed of Copper ( $Cu$ ) and Tin ( $Sn$ ); strengthens copper. Developed approximately $3500\,BCE$ . * Steel: Composed of Iron ( $Fe$ ) and Carbon ( $C$ ); hardens the iron. Developed approximately $200\,BCE$ ; manufactured on an industrial scale around $1800$ .
Techniques for Separating Mixtures: Methods based on physical properties: * Chromatography: Based on differences in molecular attraction or solubility. * Distillation: Based on differences in boiling points. * Filtering: Based on differences in particle size. * Evaporation: Evaporating the solvent to leave the solute behind.

Solution Concentration and Calculations

Concentration: The ratio of solute to solvent in a solution. Common units include percent by mass, parts per million ( $ppm$ ), molarity ( $M$ ), and molality ( $m$ ).
Percent by Mass: $\text{percent by mass} = \frac{\text{mass of solute}}{\text{mass of solution}} \times 100$ * Note: The mass of the solution is the sum of the mass of the solute and the mass of the solvent.
Percent by Volume: $\text{percent by volume} = \frac{\text{volume of solute}}{\text{volume of solution}} \times 100$
Molarity ( $M$ ): Defined as the number of moles of solute dissolved per liter of solution. $M = \frac{\text{moles of solute}}{\text{Liters of solution}}$ * Example: Calculating the grams of Copper Sulfate needed for $50\,mL$ solutions of various concentrations ( $0.0005\,M$ , $0.001\,M$ , $0.005\,M$ , $0.01\,M$ , $0.05\,M$ , $0.10\,M$ , $0.20\,M$ , and $0.50\,M$ ).
Beer's Law: Relates absorbance to concentration. $A = abc$ * $A$ : Absorbance. * $a$ : Molar absorptivity or molar extinction coefficient. * $b$ : Solution path length (typically $1\,cm$ ). * $c$ : Concentration in Molarity. * Standard curve data example: Slope = $6.414$ , Intercept = $-7.799991 \times 10^{-03}$ , Correlation Coef = $0.9791$ .
Dilution Equation: Used when diluting a concentrated stock solution. $M_1V_1 = M_2V_2$ * $M$ : Molarity; $V$ : Volume.
Molality ( $m$ ): The number of moles of solute per kilogram of solvent. $m = \frac{\text{moles of solute}}{\text{kg of solvent}}$
Mole Fraction ( $X$ ): The ratio of the number of moles of a component to the total number of moles of all components. $X_a = \frac{n_a}{n_a + n_b}$ * $n$ : Number of moles.

Factors Affecting Solvation

Solvation: The process of surrounding solute particles with solvent particles. When the solvent is water, the process is called hydration.
The Rule of "Like Dissolves Like": * Polar solvents dissolve other polar molecules (e.g., water and sugar). * Nonpolar solvents dissolve other nonpolar molecules (e.g., oil and fat).
Solvation of Ionic Compounds (e.g., NaCl in Water): * Water molecules collide with the salt crystal. * Positive Sodium ions ( $Na^+$ ) are attracted to the negative Oxygen end of water. * Negative Chlorine ions ( $Cl^-$ ) are attracted to the positive Hydrogen end of water. * Solvation occurs because the attraction between the ions and the polar water molecules is greater than the attraction between ions within the crystal. * If the crystal's internal attraction is stronger than its attraction to water, the compound is insoluble (e.g., gypsum, $CaSO_4$ ).
Solvation of Molecular Compounds (e.g., Sucrose): * Sucrose has 8 $O-H$ bonds that form hydrogen bonds with water, making it highly soluble. * Oil (nonpolar $C-H$ bonds) has little attraction to polar water and thus does not dissolve.
Vitamins and Solubility: * Water-Soluble (B, C): Highly polar molecules with multiple $(-OH)$ groups. They form hydrogen bonds with water and must be replaced daily. * B-Vitamins: Assist in energy release; deficiency leads to anemia. * Vitamin C: Used for collagen synthesis and as an antioxidant; deficiency causes scurvy. * Fat-Soluble (A, D, E): Nonpolar molecules that store in body fat; can be toxic in large doses. * Vitamin A: Essential for vision. * Vitamin D: Facilitates calcium absorption; synthesized in skin via UV light; deficiency causes rickets. * Vitamin E: Associated with skin elasticity.
Heat of Solution: The net overall change in heat during mixture. * Endothermic: Net absorption of heat. Breaking crystals and surrounding particles with solvent requires energy (e.g., Ammonium nitrate used in cold packs). * Exothermic: Net release of heat. When solute and solvent attract each other strongly (e.g., Calcium chloride used in warm packs).
Factors Increasing Rate of Solvation: * Agitation (Stirring): Increases contact between solvent and solute particles. * Surface Area: Larger surface area (granulated sugar vs. sugar cube) allows for more contact points. * Temperature: Increased temperature increases particle kinetic energy and collisions. * Exception: For gases, higher temperatures decrease solubility as gas particles gain enough energy to escape the liquid.

Solubility and Saturation States

Solubility: The ability of a substance to dissolve in another at specific temperature and pressure, often expressed as grams of solute per $100\,g$ of solvent.
Saturation Levels: * Saturated: No more solute can dissolve at that temperature. * Unsaturated: More solute can still be dissolved. * Supersaturated: A solution containing more dissolved solute than is normally possible at a given temperature. Created by cooling a saturated solution slowly. Adding a "seed crystal" causes the excess solute to precipitate (e.g., making rock candy).
Gas Solubility: Depends heavily on temperature and pressure. * Pressure: Higher pressure increases solubility. * Temperature: Lower temperature increases gas solubility.
Henry's Law: The solubility ( $S$ ) of a gas is directly proportional to the partial pressure ( $P$ ) of the gas above the liquid.

Colligative Properties of Solutions

Colligative Properties: Physical properties that depend on the concentration of solute particles, not their identity.
Particle Count (Van't Hoff Factor): * Sucrose ( $C_{12}H_{22}O_{11}$ ): Splits into 1 particle in solution (nonelectrolyte). * Sodium Chloride ( $NaCl$ ): Splits into 2 particles ( $Na^+$ and $Cl^-$ ). * Calcium Chloride ( $CaCl_2$ ): Splits into 3 particles ( $Ca^{2+_{}} + 2Cl^-$ ).
Types of Colligative Properties: 1. Vapor Pressure Lowering: Solvent particles surrounding solute particles prevent them from escaping into the gas phase, lowering the vapor pressure. 2. Boiling Point Elevation ($\Delta T_b$): Because vapor pressure is lowered, a higher temperature is required for the vapor pressure to equal atmospheric pressure. Formula: $\Delta T_b = k_b m$ . 3. Freezing Point Depression ($\Delta T_f$): Solute particles interfere with the ability of solvent particles to form a solid structure, lowering the temperature required to freeze. Formula: $\Delta T_f = k_f m$ . 4. Osmotic Pressure: Pressure required to stop osmosis.
Molal Constants ( $k_b$ and $k_f$ ) for Selected Substances: | Substance | $k_b\,(\text{°C kg/mol})$ | $k_f\,(\text{°C kg/mol})$ | | :--- | :--- | :--- | | Water ( $H_2O$ ) | $0.51$ | $1.86$ | | Benzene ( $C_6H_6$ ) | $2.64$ | $5.07$ | | Camphor ( $C_{10}H_{16}O$ ) | $5.95$ | $37.8$ | | Chloroform ( $CHCl_3$ ) | $3.63$ | $4.70$ | | Diethyl ether ( $C_4H_{10}O$ ) | $2.02$ | $1.79$ | | Ethyl alcohol ( $C_2H_6O$ ) | $1.22$ | $1.99$ |

Conductivity and Specialized Chemical Solutions

Electrolytes: Substances that break into ions in water and conduct electricity. * Strong Electrolytes: Many ions (e.g., strong acids, salts). * Weak Electrolytes: Few ions (e.g., baking soda). * Nonelectrolytes: Do not conduct electricity (e.g., sugar).
Acids and Hydronium Ions: When acids dissolve, $H^+$ ions combine with water to form the Hydronium ion ( $H_3O^+$ ). * Example: $HCl + H_2O \rightarrow Cl^- + H_3O^+$
Conductivity of Water: * Pure water conducts electricity very poorly due to lack of ions. * Drinking water conducts electricity because it contains dissolved ions from soil, pipes, and wells.
Osmosis: Diffusion of solvent across a semipermeable membrane to balance concentrations. * Isotonic: Equal concentration; no net movement. * Hypotonic: Lower concentration outside; water moves into the cell (turgid). * Hypertonic: Higher concentration outside; cell loses water and shrivels (plasmolyzed).
Surfactants: Compounds that concentrate at the boundary between two immiscible phases. * Detergent: A synthetic surfactant cleaner. * Soap: Salts made from long-chain fatty acids; contains a polar hydrophilic head and a nonpolar hydrophobic tail. * Emulsion: Colloid-sized droplets of one liquid suspended in another using a surfactant.
Hard Water: Contains Calcium ions ( $Ca^{2+}$ ), Magnesium, or Iron. * Calcium binds with soap to form insoluble salts (soap scum), preventing emulsion formation. * Synthetic detergents use sulfonate ions ( $-SO_3H$ ) which do not form these insoluble precipitates.

Vocabulary

Mixture: A combination of two or more substances that are mixed together physically rather than chemically.
Homogeneous Mixtures: Evenly mixed at the microscopic level; also referred to as solutions.
Heterogeneous Mixtures: Unevenly mixed where different components are easily distinguishable.
Suspensions: A heterogeneous mixture containing large particles that are temporarily suspended in a liquid or gas.
Colloids: A specialized type of suspension where particles remain suspended indefinitely due to electrical charge.
Brownian Motion: Random movement of particles in a liquid, observed in colloids.
Tyndall Effect: Scattering of light by large particles in a colloid or suspension.
Solvent: The substance in which another is dissolved (e.g., water, oil).
Solute: The substance that is dissolved in a solvent.
Aqueous Solution: A solution where water is the solvent (denoted by the symbol $(aq)$ ).
Miscible: Liquids that can mix together (e.g., alcohol and water).
Immiscible: Liquids that do not mix (e.g., oil and water).

Important Formula

$M = rac{ ext{moles of solute}}{ ext{Liters of solution}}$
Molarity ( $M$ ): Number of moles of solute per liter of solution.

Important Concept

The Rule of "Like Dissolves Like": Polar solvents dissolve polar molecules (e.g., water and sugar); nonpolar solvents dissolve nonpolar molecules (e.g., oil and fat).

Important Formula

$M = \frac{ ext{moles of solute}}{ ext{Liters of solution}}$
Molarity ( $M$ ): Number of moles of solute per liter of solution.

Types of Colligative Properties:

Vapor Pressure Lowering: Solvent particles surrounding solute particles prevent them from escaping into the gas phase, lowering the vapor pressure.
Boiling Point Elevation ( $riangle Tb$ ): Because vapor pressure is lowered, a higher temperature is required for the vapor pressure to equal atmospheric pressure. Formula: $riangle Tb = k_b m$ .
Freezing Point Depression ( $riangle Tf$ ): Solute particles interfere with the ability of solvent particles to form a solid structure, lowering the temperature required to freeze. Formula: $riangle Tf = k_f m$ .
Osmotic Pressure: Pressure required to stop osmosis.

Dilution Equation:

Used when diluting a concentrated stock solution.
$M1 V1 = M2 V2$
$M$ : Molarity; $V$ : Volume.