Thermochemistry, Gases, Liquids, Solutions, Kinetics, and Equilibrium: Mini-Study Guide

Thermochemistry

First Law of Thermodynamics

The First Law of Thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. In chemical systems, this law governs the flow of energy as heat and work.

• Statement: The total energy of the universe is constant; energy can be transferred between the system and surroundings.

• Equation: $\Delta E = q + w$

• System vs. Surroundings: Energy flows as heat (q) or work (w) between the system (the part under study) and the surroundings (everything else).

• Sign Conventions:

  • q > 0: Heat absorbed by system (endothermic)

  • q < 0: Heat released by system (exothermic)

  • w > 0: Work done on system

  • w < 0: Work done by system

Heat Flow and Specific Heat Capacity

Heat flow is related to the mass, specific heat capacity, and temperature change of a substance.

• Equation: $q = m c \Delta T$

• Direction of Heat Flow: Heat flows from higher to lower temperature.

• System and Surroundings: $q_{system} = -q_{surroundings}$

Exothermic and Endothermic Processes

Exothermic reactions release heat; endothermic reactions absorb heat.

• Exothermic: $\Delta H < 0$ (e.g., freezing, combustion)

• Endothermic: $\Delta H > 0$ (e.g., melting, evaporation)

• Determining Heat: Use $\Delta H_{rxn}$ to calculate heat for a given amount of reactant or product.

Calorimetry and Reaction Enthalpies

Calorimetry measures heat changes at constant pressure.

• Constant Pressure Calorimetry: $q = m c \Delta T$

• Manipulating Equations:

  • Multiply equation: $\Delta H$ scales by same factor

  • Reverse equation: $\Delta H$ changes sign

  • Sum equations: $\Delta H$ values add

• Hess's Law: $\Delta H_{rxn}$ is the sum of enthalpy changes for individual steps.

• Bond Enthalpies: $\Delta H_{rxn} = \sum \text{(bond energies broken)} - \sum \text{(bond energies formed)}$

• Standard Molar Enthalpy of Formation ($\Delta H^\circ_f$): Enthalpy change for forming 1 mole of compound from elements in their standard states.

• Calculating $\Delta H^\circ_{rxn}$: $\Delta H^\circ_{rxn} = \sum \Delta H^\circ_f \text{(products)} - \sum \Delta H^\circ_f \text{(reactants)}$

Gases

Pressure and Gas Laws

Pressure is the force exerted per unit area by gas molecules.

• Definition: $P = \frac{F}{A}$

• Units: atm, torr, mmHg (1 atm = 760 mmHg = 760 torr)

Kinetic Molecular Theory

This theory explains gas behavior based on molecular motion.

• Assumptions: Gas particles are in constant, random motion; collisions are elastic; volume of particles is negligible; no intermolecular forces.

• Relationships: Higher temperature increases kinetic energy and molecular speed; lighter molecules move faster.

• Root Mean Square Speed: $u_{rms} = \sqrt{\frac{3RT}{M}}$

Gas Laws

• Boyle's Law: $P \propto \frac{1}{V}$ at constant T and n ($PV = \text{constant}$)

• Charles's Law: $V \propto T$ at constant P and n ($\frac{V}{T} = \text{constant}$)

• Avogadro's Law: $V \propto n$ at constant P and T ($\frac{V}{n} = \text{constant}$)

• Ideal Gas Law: $PV = nRT$

• STP: Standard Temperature and Pressure (0°C, 1 atm)

• Standard Molar Volume: 22.4 L at STP for 1 mole of gas

• Density: $d = \frac{PM}{RT}$

• Molar Mass: $M = \frac{dRT}{P}$

• Dalton's Law of Partial Pressures: $P_{total} = \sum P_i$

• Partial Pressure: Pressure exerted by each gas in a mixture

Real vs. Ideal Gases

• Ideal Gas: Follows all gas laws perfectly; assumptions hold at low pressure and high temperature.

• Van der Waals Equation: Corrects for intermolecular forces (a) and molecular volume (b): $\left(P + \frac{a n^2}{V^2}\right)(V - nb) = nRT$

• Conditions for Ideal Behavior: Low pressure, high temperature.

Liquids, Solids, and Intermolecular Forces

Molecular Level Differences

Solids, liquids, and gases differ in molecular arrangement and movement.

• Solids: Fixed shape and volume; molecules tightly packed.

• Liquids: Fixed volume, variable shape; molecules close but can move.

• Gases: Variable shape and volume; molecules far apart and move freely.

Intermolecular Forces

Four major types of intermolecular forces determine physical properties.

• London Dispersion Forces: Present in all molecules; strength increases with molecular size.

• Dipole-Dipole Forces: Occur between polar molecules.

• Hydrogen Bonding: Strong dipole interaction; requires H bonded to O, N, or F.

• Ion-Dipole Forces: Occur between ions and polar molecules.

• Inter vs. Intra: Intermolecular forces are between molecules; intramolecular forces are within molecules.

Effects of Intermolecular Forces

• Surface Tension: Stronger forces increase surface tension.

• Viscosity: Stronger forces increase viscosity.

• Boiling Point: Stronger forces increase boiling point.

• Vapor Pressure: Stronger forces decrease vapor pressure.

Boiling Point and Vapor Pressure

• Vapor Pressure: Pressure exerted by vapor above a liquid.

• Temperature Effect: Higher temperature increases vapor pressure.

• Boiling Point: Temperature at which vapor pressure equals external pressure.

Phase Changes and Diagrams

• Phase Changes: Melting, freezing, vaporization, condensation, sublimation, deposition.

• Phase Diagram: Shows regions of solid, liquid, gas; significant points include triple point and critical point.

• Heating Curve: Shows temperature changes and phase transitions as heat is added.

• Energy Calculations:

  • Heat of vaporization ($\Delta H_{vap}$): Energy to convert liquid to gas.

  • Heat of fusion ($\Delta H_{fus}$): Energy to convert solid to liquid.

  • $\Delta H_{vap} > \Delta H_{fus}$

Solutions

Solution Formation

Solutions form when solute particles disperse uniformly in solvent.

• Saturated: Maximum solute dissolved; equilibrium exists.

• Unsaturated: Less than maximum solute dissolved.

• Supersaturated: More than maximum solute dissolved; unstable.

• Determining Saturation: Add more solute; if it dissolves, solution is unsaturated.

Concentration Units

• Molarity (M): $M = \frac{\text{moles of solute}}{\text{liters of solution}}$

• Other Units: molality, mass percent, mole fraction.

Solubility Factors

• Pressure: Higher pressure increases solubility of gases.

• Temperature: Higher temperature usually increases solubility of solids, decreases solubility of gases.

Colligative Properties

Properties that depend on the number of solute particles, not their identity.

• Raoult's Law: $P_{solution} = X_{solvent} P^\circ_{solvent}$

• Van't Hoff Factor (i): Number of particles produced per formula unit.

• Osmosis: Movement of solvent through a semipermeable membrane toward higher solute concentration.

• Effects: Solutions have lower vapor pressure, lower freezing point, higher boiling point than pure solvent.

• Calculations:

  • Boiling Point Elevation: $\Delta T_b = i K_b m$

  • Freezing Point Depression: $\Delta T_f = i K_f m$

  • Osmotic Pressure: $\Pi = i M R T$

• Molar Mass Determination: Use colligative property equations to find unknown molar mass.

Chemical Kinetics

Rate of Reaction

The rate of reaction measures how quickly reactants are converted to products.

• Collision Theory: Reactions occur when particles collide with sufficient energy and proper orientation.

• Factors Affecting Rate: Concentration, temperature, structure, and orientation.

• Potential Energy Diagram: Shows energy changes during reaction; includes reactants, transition state, products.

Rate Laws and Reaction Order

• Rate Law: $\text{Rate} = k [A]^m [B]^n$

• Order: Exponents m and n indicate order with respect to each reactant; sum is overall order.

• Determining Rate Law: Use initial rate data or concentration-time data.

• Units of k: Depend on reaction order (e.g., s-1 for first order).

• Integrated Rate Laws:

  • Zero Order: $[A]_t = [A]_0 - k t$

  • First Order: $[A]_t = [A]_0 e^{-k t}$

  • Second Order: $\frac{1}{[A]_t} = \frac{1}{[A]_0} + k t$

• Half-life ($t_{1/2}$): Relationship with k varies by order.

Activation Energy and Arrhenius Equation

• Activation Energy (Ea): Minimum energy required for reaction.

• Arrhenius Equation: $k = A e^{-E_a/(RT)}$

• Temperature Effect: Higher temperature increases rate.

Reaction Mechanisms and Catalysts

• Mechanism: Sequence of steps describing how reaction occurs.

• Plausibility: Mechanism must match observed rate law.

• Rate-Determining Step: Slowest step controls overall rate.

• Catalyst: Increases rate by lowering activation energy; does not affect equilibrium.

• Energy Profile: Catalyst lowers transition state energy.

Chemical Equilibrium

Nature of Equilibrium

At equilibrium, the rates of forward and reverse reactions are equal; concentrations remain constant.

• Dynamic Equilibrium: Both reactions occur; no net change.

• Static Equilibrium: No movement; rare in chemistry.

• No Memory: Equilibrium does not depend on how it was reached.

Equilibrium Constants

• Kforward and Kreverse: $K_{reverse} = \frac{1}{K_{forward}}$

• Magnitude of K: Large K: products favored; small K: reactants favored.

• Mathematical Relationships: $K$ changes with equation manipulation (multiplying, reversing, adding).

• Kc and Kp: $K_p = K_c (RT)^{\Delta n}$

• Writing K Expressions: Use concentrations (Kc) or partial pressures (Kp); omit pure solids/liquids.

ICE Tables and Calculations

• ICE Table: Tracks Initial, Change, and Equilibrium concentrations.

• Calculating K: Use equilibrium concentrations.

• Finding Equilibrium Concentrations: Use K and initial values; solve for unknowns.

Le Châtelier’s Principle

• Statement: If a system at equilibrium is disturbed, it shifts to counteract the disturbance.

• Predicting Effects: Changes in concentration, pressure, or temperature shift equilibrium position.

• Temperature Effect: For exothermic reactions, increasing T decreases K; for endothermic, increasing T increases K.

Reaction Quotient (Q) vs. Equilibrium Constant (K)

• Q: Calculated like K, but with current concentrations.

• Use: Compare Q to K to predict direction of reaction:

  • Q < K: Forward reaction favored

  • Q > K: Reverse reaction favored

  • Q = K: System at equilibrium

Example ICE Table

Step	[A]	[B]	[C]
Initial	1.0	1.0	0
Change	-x	-x	+x
Equilibrium	1.0-x	1.0-x	x

Additional info: This guide expands on brief points with academic context, definitions, and formulas to ensure completeness and clarity for exam preparation.