Thermodynamics is the branch of science that deals with the relationship between heat, work, and energy. In chemistry, it tells us whether a reaction will occur spontaneously and how much energy is involved. The central theme is understanding energy changes in chemical and physical processes.
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Key Concepts
- Basic Terminology
- System: The part of the universe under study (e.g., the contents of a beaker).
- Surroundings: Everything outside the system.
- Open system: Exchanges both energy and matter with surroundings.
- Closed system: Exchanges energy but not matter.
- Isolated system: No exchange of either energy or matter.
- State functions: Properties that depend only on the current state, not on how that state was reached. Examples: internal energy (U), enthalpy (H), entropy (S), Gibbs free energy (G), temperature (T), pressure (P), volume (V).
- Process functions: Path-dependent quantities. Examples: heat (q) and work (w).
- Internal Energy (U)
- The total energy stored within a system (kinetic + potential energy of all particles). We can only measure changes in internal energy: deltaU = q + w (First Law of Thermodynamics).
- For exothermic reactions: deltaU < 0 (system loses energy)
- For endothermic reactions: deltaU > 0 (system gains energy)
- First Law of Thermodynamics
- Energy can neither be created nor destroyed; it can only be converted from one form to another. Mathematically: deltaU = q + w
- q: heat absorbed by system (positive if absorbed; negative if released)
- w: work done on the system. For expansion against constant pressure: w = -Pext x deltaV
Enthalpy (H)
Since most reactions occur at constant pressure, it is convenient to define enthalpy: H = U + PV
At constant pressure: deltaH = deltaU + P x deltaV = qp (heat at constant pressure)
- Relation to internal energy: deltaH = deltaU + deltang x RT, where deltang = moles of gaseous products - moles of gaseous reactants.
- Thermochemistry
- Standard enthalpy of reaction (deltaH°): Enthalpy change under standard conditions (25 degree C, 1 bar, 1 M solutions).
- Standard enthalpy of formation (deltaH°f): Enthalpy change when 1 mole of a compound is formed from its constituent elements in their standard states. By convention, deltaH°f for elements in standard state = 0.
- Hess's Law: The total enthalpy change of a reaction is the same regardless of the pathway taken. Allows calculation of deltaH using a series of known reactions.
- Bond Enthalpy: Energy required to break 1 mole of a specific bond in gaseous phase. deltaHrxn = sum(bond enthalpies of bonds broken) - sum(bond enthalpies of bonds formed).
- Entropy (S)
- A measure of the degree of disorder or randomness of a system. The universe tends towards maximum disorder.
- deltaS = qrev / T (for a reversible process)
- Entropy increases: solid → liquid → gas; dissolution; heating; mixing.
Second Law of Thermodynamics
The entropy of the universe always increases (or remains constant) for a spontaneous process:
deltaSuniverse = deltaSsystem + deltaSsurroundings ≥ 0
Gibbs Free Energy (G) and Spontaneity
George Gibbs combined enthalpy and entropy into a single criterion for spontaneity:
G = H - TS (at constant T and P)
deltaG = deltaH - T x deltaS
- deltaG < 0: Spontaneous (product-favoured)
- deltaG = 0: System at equilibrium
- deltaG > 0: Non-spontaneous (reverse reaction is spontaneous)
Conditions for Spontaneity:
| deltaH | deltaS | Spontaneous? |
|---------|---------|-------------|
| - | + | Always spontaneous |
| + | - | Never spontaneous |
| - | - | Spontaneous at low T |
| + | + | Spontaneous at high T |
Relationship between deltaG and Equilibrium Constant:
deltaG° = -RT ln Keq, where R = 8.314 J/(mol·K) and K is the equilibrium constant.
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Worked Examples
In a process, a system absorbs 500 J of heat and does 200 J of work on the surroundings. Calculate deltaU.
Using sign convention: q = +500 J (heat absorbed), w = -200 J (work done by system on surroundings).
deltaU = q + w = 500 + (-200) = +300 J
Calculate deltaH for the combustion of methane if deltaU = -885 kJ/mol. (CH4 + 2O2 → CO2 + 2H2O, all gases. T = 298 K, R = 8.314 J/mol·K)
deltang = (1 + 2) - (1 + 2) = 0. deltaH = deltaU + deltang RT = -885 + 0 = -885 kJ/mol
Using Hess's Law, find deltaH for C(s) + 1/2 O2(g) → CO(g), given:
(1) C(s) + O2(g) → CO2(g), deltaH1 = -393.5 kJ
(2) CO(g) + 1/2 O2(g) → CO2(g), deltaH2 = -283 kJ
Target = reaction (1) - reaction (2): deltaH = -393.5 - (-283) = -110.5 kJ/mol
Calculate deltaH for the formation of HCl(g) using bond enthalpies. Bond energies: H-H = 436 kJ/mol, Cl-Cl = 242 kJ/mol, H-Cl = 431 kJ/mol. H2 + Cl2 → 2HCl
Bonds broken: H-H (436) + Cl-Cl (242) = 678 kJ
Bonds formed: 2(H-Cl) = 2(431) = 862 kJ
deltaH = 678 - 862 = -184 kJ (for 2 mol HCl) or -92 kJ/mol HCl.
For a reaction, deltaH = -40 kJ/mol and deltaS = -120 J/(mol·K). At what temperature does the reaction shift from spontaneous to non-spontaneous?
At crossover, deltaG = 0: T = deltaH / deltaS = (-40,000 J) / (-120 J/K) = 333 K. Below 333 K: spontaneous; above 333 K: non-spontaneous.
A reaction has Keq = 100 at 298 K. Calculate deltaG°.
deltaG° = -RT ln K = -(8.314)(298) ln(100) = -(2477.6)(4.605) = -11,408 J/mol = -11.4 kJ/mol
Predict whether dissolving NH4Cl in water is entropy-driven or enthalpy-driven, given the process is endothermic (deltaH > 0) but spontaneous.
Since deltaH > 0 (unfavourable) and the process is still spontaneous, it must be driven by a large positive deltaS (increase in entropy upon dissolution), so T x deltaS > deltaH, making deltaG < 0.
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Common mistakes
A very common error is sign confusion: heat absorbed by the system is positive (q > 0), and work done on the system is positive (w > 0), but work done by the system is negative. Another mistake is confusing deltaH (constant pressure, most lab reactions) with deltaU (constant volume, e.g., bomb calorimeter reactions). Always check whether deltang = 0 or not before equating them.
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Summary
Thermodynamics governs energy flow in chemical reactions. The First Law gives us deltaU = q + w. Enthalpy (deltaH) accounts for work done at constant pressure. Hess's Law lets us calculate deltaH indirectly. The Second Law says entropy of the universe must increase. Gibbs free energy (deltaG = deltaH - T deltaS) is the master criterion for spontaneity: negative deltaG means a spontaneous process.