Thermodynamics: Unit Review

Introduction

Thermodynamics organizes chemical change through carefully defined states, boundaries and constraints. The first law accounts for energy entering and leaving; enthalpy and Hess's law simplify reaction-energy comparisons; entropy and Gibbs energy address direction. The most reliable solutions begin with a precise process description before choosing an equation.

Core explanation

Choose the system first. For a closed system in the chemistry convention, ΔU = q + w, with heat or work entering positive. Expansion against external pressure gives negative work, and compression gives positive work. At constant external pressure, P–V work is −P extΔV. For an ideal gas expanding reversibly and isothermally, w = −nRT ln(V f/V i); in insulated free expansion into a vacuum, P–V work is zero. These different work values for the same volume endpoints demonstrate path dependence.

U is a state function. An ideal gas of fixed composition has U dependent only on T, so isothermal ΔU = 0 even if q and w are nonzero. Enthalpy H = U + PV is another state function. At constant pressure with only P–V work, q p = ΔH; in a rigid vessel with no other work, q V = ΔU. For ideal-gas reactions at one temperature, ΔH − ΔU ≈ Δn gRT after counting only gaseous stoichiometric coefficients. These equalities have conditions and are not interchangeable labels for “heat.”

Calorimetry converts a measured temperature change to heat through q = CΔT, mcΔT or nC mΔT. The reaction and the calorimeter have opposite heat signs in a well-insulated assembly. A coffee-cup setup often estimates constant-pressure ΔH; a rigid bomb gives a value related to ΔU. Molar reporting requires actual reaction extent, not merely a thermometer reading.

Hess's law says ΔH between matched states is independent of route. Reverse an equation and reverse ΔH's sign; scale an equation and scale ΔH; add equations and enthalpies only after matching phases and coefficients. Standard formation enthalpies yield Δ rH° = ΣνΔ fH°(products) − ΣνΔ fH°(reactants). Born–Haber cycles extend this to ionic solids using atomization, ionization, electron gain and lattice formation. A positive lattice-dissociation convention becomes negative when reversed for crystal formation.

Entropy S reflects accessible microscopic arrangements and is a state function. A system may lose entropy while surroundings gain more. For an isolated total, spontaneous irreversible change has ΔS total > 0. At constant T and P under suitable conditions, ΔG = ΔH − TΔS and negative actual ΔG favors the forward direction. Standard Δ rG° is a reference quantity; actual Δ rG = Δ rG° + RT ln Q changes with composition and becomes zero at Q = K. Δ rG° = −RT ln K, so it need not vanish at equilibrium.

Thermodynamics does not specify speed. A favorable reaction may require ignition or a catalyst to overcome a barrier. A catalyst changes a path and rate, not the endpoint ΔH or ΔG for the same states. A positive ΔG step can occur when physically coupled to a more negative step, but a negative arithmetic sum alone does not supply a coupling mechanism.

Every number needs units and state labels. Enthalpy is often kJ mol⁻¹, entropy J mol⁻¹ K⁻¹ and temperature kelvin. Product phases matter; water liquid and vapor differ. Current IUPAC standard pressure is 1 bar, while temperature is separately stated. Distinguishing these conventions prevents errors that no amount of algebra can repair afterward.

Step-by-step reasoning

1. Define system, surroundings, initial and final states with phases. 2. Identify path constraints and whether the task asks for transfer, state change or direction. 3. Select first-law, calorimetric, Hess or Gibbs relations accordingly. 4. Balance reactions and convert units and extents. 5. Interpret signs and check assumptions and plausible magnitude.

Visual explanation

Draw four connected boxes: boundary and first law; state functions and Hess cycle; system-plus-surroundings entropy; Gibbs and equilibrium. Arrows from a central balanced reaction point to the boxes. Label the first two “energy account” and the latter two “direction,” with a separate kinetic hill outside the network.

Real-world analogy

Planning a trip needs an account of fuel, a map of alternative routes, a destination preference and travel-time information. Thermodynamics provides energy accounting and favored endpoints; kinetics supplies speed and barriers. Mixing these questions makes a plan unreliable.

Real-world example

Methane combustion in a bomb warms a bath. The bath's ΔT yields heat, the rigid constraint links reaction heat to ΔU, and a gas-mole correction helps compare with a constant-pressure combustion ΔH. The reaction is exothermic, yet its rate still depends on ignition and oxygen mixing. One example uses several unit ideas without treating them as synonyms.

Why?

Why do state functions make indirect calculations possible? Their differences depend only on specified endpoints. Measured steps along an alternative route can therefore be added to obtain a difficult direct reaction change.

Common misconception

“A negative ΔH, ΔG and fast rate all mean the same thing.” ΔH describes enthalpy difference, actual ΔG describes direction at stated T, P and composition, and rate depends on kinetic barriers. Their signs and magnitudes answer different questions.

Worked example

A reaction in a near-constant-pressure cup warms a calorimeter of total C = 500 J K⁻¹ by 2.0 K while 0.020 mol of reaction occurs. The cup gains +1000 J, so q rxn ≈ −1000 J and Δ rH ≈ −50.0 kJ mol⁻¹. Suppose its reaction entropy is −100 J mol⁻¹ K⁻¹ at 300 K. Convert to −0.100 kJ mol⁻¹ K⁻¹: Δ rG ≈ −50.0 − 300(−0.100) = −20.0 kJ mol⁻¹ for the stated state approximation. The forward direction is favored, but no rate follows. This combines measurement, molar scaling, unit conversion and Gibbs interpretation.

Quick check

1. At equilibrium, which is zero: actual Δ rG or necessarily Δ rG°? Answer: Actual Δ rG is zero; Δ rG° is generally −RT ln K and need not be zero.

Exam focus

Write the governing equation with assumptions, then substitute signed quantities. Show balanced reactions, physical states and molar scale. For direction, use actual Gibbs energy at stated composition rather than heat sign alone.

Advanced insight

The different thermodynamic potentials arise from choosing natural constraints. U is central to energy conservation; H is convenient for pressure-held processes; G is convenient for temperature- and pressure-held chemical equilibrium. Recognizing constraints explains the formulas more deeply than memorizing them as unrelated rules.

Summary

First-law bookkeeping, enthalpy and Hess cycles quantify energy changes. Entropy and Gibbs energy describe favored direction under defined constraints. Heat and work depend on path; U, H, S and G depend on states. Kinetics and physical coupling remain separate from thermodynamic feasibility.

Practice questions

1. An ideal gas expands isothermally and does 200 J of work on surroundings. What are ΔU and q? Answer: ΔU = 0 and q = +200 J, since w = −200 J and q + w = 0. 2. If a reaction is reversed, what happens to its ΔH and ΔG between the same states? Answer: Both signs reverse for the reversed reaction at matching conditions. 3. A reaction has ΔG < 0 but proceeds slowly. Is that inconsistent? Answer: No. Thermodynamics favors the direction, while a high kinetic barrier can make the rate slow.