Chapter Review

Thermochemistry

Thermodynamic Terms and First Law · Exothermic/Endothermic Reactions and Hess Law

System, Surroundings, and State Functions

A system is the portion of matter under study; everything else is the surroundings, separated by a boundary. State functions (P, T, V, E, H) depend only on the current state, not the path taken.

Key Points

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    System: the defined region of study (e.g., gas in a cylinder, reacting mixture in a flask)
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    Surroundings: everything outside the system
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    Boundary: real or imaginary surface where heat and work are exchanged
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    State function: property with a definite value for any state; its change depends only on initial and final states
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    Heat and work are NOT state functions: their values depend on the path taken
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    Common state functions: P, T, V, internal energy (E), enthalpy (H)

Internal Energy and the First Law

Internal energy (E) is the sum of all kinetic and potential energies of a system's particles. The first law states that energy cannot be created or destroyed — only transferred as heat and work.

Key Points

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    Internal energy includes: translational, rotational, and vibrational KE + all bond and intermolecular PE
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    Absolute E is unmeasurable: only the change ΔE can be determined
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    Energy transfer occurs via two mechanisms only: heat (q) and work (w)
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    First law: ΔE = q + w — change in internal energy equals heat absorbed plus work done on the system
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    Positive ΔE means the system gains energy; negative means it loses energy
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    This is the law of conservation of energy applied to thermodynamic systems
Formula

Pressure-Volume Work

When a system expands or contracts against an external pressure, it does PV work. The sign convention ensures expansion gives negative work (energy leaves the system) and compression gives positive work (energy enters).

Key Points

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    PV work is the most common form of work in chemistry (e.g., gas evolution in reactions)
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    W = −PΔV: negative sign is critical and frequently tested
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    Expansion (ΔV > 0) → W is negative → system does work on surroundings
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    Compression (ΔV < 0) → W is positive → surroundings do work on system
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    At constant volume (ΔV = 0), no PV work is done (W = 0)
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    For gases, PV work can be expressed as PΔV = ΔnRT where Δn counts only gaseous species
Formula

Enthalpy and ΔH at Constant Pressure

Enthalpy (H = E + PV) is a state function. At constant pressure, the change in enthalpy equals the heat exchanged, making ΔH the most practical energy quantity since most reactions occur at atmospheric pressure.

Key Points

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    H = E + PV: combines internal energy with the pressure-volume term
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    At constant pressure: ΔH = qp (heat of reaction at constant pressure)
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    At constant volume: ΔE = qv (no PV work, all heat changes internal energy)
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    ΔH ≈ ΔE for reactions involving only solids and liquids (negligible volume change)
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    For gaseous reactions: ΔH = ΔE + ΔnRT where Δn = ngas(products) − ngas(reactants)
  • •
    When counting Δn, only gaseous species are included — ignore solids and liquids
Formula

Exothermic and Endothermic Reactions

Reactions are classified by the sign of ΔH. Exothermic reactions release heat (ΔH < 0); endothermic reactions absorb heat (ΔH > 0). The sign reflects whether products or reactants have higher enthalpy.

Key Points

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    Exothermic (ΔH < 0): Hproducts < Hreactants — energy released, surroundings warm up
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    Endothermic (ΔH > 0): Hproducts > Hreactants — energy absorbed, surroundings cool down
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    Combustion and strong acid–strong base neutralization are always exothermic
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    Thermal decomposition and dissolution of NH₄Cl are endothermic
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    Strong acid–strong base neutralization: ΔH°n ≈ −57.4 kJ mol⁻¹ (always the same net ionic equation)
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    Weak acid–weak base neutralization gives ΔH°n less negative than −57.4 kJ mol⁻¹ (energy needed to dissociate)
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    ΔH°f of all elements in their standard states is zero by definition
Formula

Types of Enthalpy Change

Several specific enthalpy quantities describe particular processes: formation, combustion, neutralization, and solution. Each is defined for 1 mole of substance under standard conditions (25°C, 1 atm).

Key Points

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    ΔH°f: heat change when 1 mole of compound forms from its elements in standard states
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    ΔH°c: heat evolved when 1 mole of substance burns completely in excess O₂ (always negative)
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    ΔH°n: heat evolved when 1 mole of H⁺ reacts with 1 mole of OH⁻ (≈ −57.4 kJ mol⁻¹ for strong acid–strong base)
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    ΔH°sol: heat absorbed or evolved when 1 mole of solute dissolves in excess solvent (can be + or −)
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    Each type specifies one mole of a particular species — watch for this in questions
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    Sign convention is consistent: negative = exothermic, positive = endothermic for all types

Heat Capacity and Calorimetry

Calorimetry measures heat changes experimentally. Glass calorimeters measure reactions in solution at constant pressure; bomb calorimeters measure combustion at constant volume. Both use temperature change to determine heat exchanged.

Key Points

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    Heat capacity (C): heat to raise system temperature by 1 K; specific heat (s): per gram
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    Glass calorimeter (open, constant pressure): q = msΔT, measured heat = ΔH
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    Bomb calorimeter (sealed, constant volume): q = cΔT, measured heat = ΔE
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    For dilute aqueous solutions, density ≈ 1 g cm⁻³ so volume in cm³ ≈ mass in grams
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    Specific heat of water = 4.2 J g⁻¹ K⁻¹
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    To get per-mole ΔH or ΔE: divide total q by moles of the limiting reagent
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    Assign negative sign to q for exothermic reactions before dividing by moles
Formula

Hess's Law

Hess's law states that the total enthalpy change for a reaction is the same regardless of the pathway, because enthalpy is a state function. This allows calculating ΔH values for reactions that cannot be measured directly.

Key Points

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    ΣΔH around a complete cycle = 0: going one way is positive, returning is negative
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    Direct route ΔH = sum of all indirect step ΔH values
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    Reversing a reaction flips the sign of ΔH
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    Multiplying coefficients by a factor multiplies ΔH by the same factor
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    Used to find ΔH°f of CO (cannot be measured directly — carbon combustion always yields CO + CO₂ mixture)
  • •
    Write the target equation first, then identify which given reactions to add, subtract, or reverse
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    Cancel intermediates that appear on both sides of the combined equations
Formula

Born-Haber Cycle

The Born-Haber cycle applies Hess's law to calculate lattice energy — the enthalpy change when gaseous ions form one mole of an ionic solid. Lattice energy cannot be measured directly and is found by subtracting all other measurable steps from ΔH°f.

Key Points

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    Lattice energy: enthalpy change when 1 mole of ionic solid forms from its gaseous ions (always exothermic, negative)
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    Steps to form gaseous ions (ΔH°x): atomize metal → ionize metal → atomize non-metal → electron affinity of non-metal
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    Formula: ΔH°Latt = ΔH°f − ΔH°x
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    Electron affinity of most non-metals is exothermic (negative, e.g., Cl: −349 kJ mol⁻¹)
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    Atomization of diatomic non-metals uses ½ mole (e.g., ½Cl₂, not Cl₂)
  • •
    Draw the energy cycle triangle: elements → gaseous ions → ionic solid, with direct route as ΔH°f
Formula

Formulas

First Law of Thermodynamics

Change in internal energy equals heat absorbed plus work done on the system. q positive = heat enters; w positive = work done on system.

Pressure-Volume Work

Work from expansion/compression against external pressure. Expansion gives negative W; compression gives positive W.

Internal Energy at Constant Volume

At constant volume (no PV work), all heat transfer changes internal energy. Used in bomb calorimetry.

Enthalpy at Constant Pressure

At constant pressure, enthalpy change equals heat exchanged. Most reactions occur at atmospheric pressure.

PV Work via Gas Moles

Converts PV work to moles of gas. Δn = moles of gaseous products − moles of gaseous reactants. R = 8.314 J K⁻¹ mol⁻¹.

Heat from Mass and Specific Heat

Glass calorimeter formula. s = 4.2 J g⁻¹ K⁻¹ for water. Also q = CΔT where C = ms.

Hess's Law Cycle Sum

Sum of all ΔH around a closed cycle is zero. Direct route ΔH equals sum of indirect step ΔH values.

Born-Haber Lattice Energy

Lattice energy = enthalpy of formation minus total energy to form gaseous ions. All values in kJ mol⁻¹.