Enthalpy and Internal Energy Explained | Thermodynamics

Calorimetry measures heat changes in chemical processes. Bomb calorimetry measures heat at constant volume using a sealed steel bomb containing combustible material under high oxygen pressure, immersed in water within an insulated container. Heat absorbed by water is Q_v = C_cal × ΔT, and since reactions occur in closed vessels, measured heat equals internal energy change (ΔU). Molar heat of combustion is calculated using substance mass and molecular weight. Coffee cup calorimetry measures heat at constant pressure using an open polystyrene cup. Heat flow is Q_p = m × c × ΔT, where m is water mass and c = 4.184 J/g·K. Since reactions occur at atmospheric pressure, measured heat equals enthalpy change (ΔH). Exothermic reactions show negative ΔH; endothermic show positive ΔH.

Calorimetry is the experimental method used to measure heat changes in chemical reactions. A calorimeter is a device that measures the heat absorbed or released during a reaction. The heat measured is equal to the negative of the enthalpy change (q = -ΔH).

Calorimetry measures heat changes in chemical reactions using a calorimeter (polystyrene cup). Temperature changes are measured before and after reactions. Heat change is calculated using Q = mcΔT, where m is mass, c is specific heat capacity (4.2 J/g°C for water), and ΔT is temperature change. Three assumptions are made: solution density equals water (1 g/cm³), specific heat capacity equals water, and no heat is lost to surroundings. Exothermic reactions release heat (products lower energy), while endothermic reactions absorb heat (products higher energy).

Calorimetry is the science of measuring heat changes in chemical reactions using an insulated container called a calorimeter, which tracks temperature changes to calculate enthalpy change (ΔH) through the formula q = mcΔT, where m is mass, c is specific heat capacity, and ΔT is temperature change; this experimental approach complements Hess's Law for determining reaction enthalpies, though practical limitations like imperfect insulation and heat absorption by the calorimeter itself introduce measurement errors.

Calorimetry measures heat changes in chemical reactions using a calorimeter. The device consists of an inner chamber containing the reaction mixture surrounded by water. When a reaction occurs, the temperature change of the water indicates the heat absorbed or released. The heat absorbed by water is calculated using Q = m × c × ΔT, where m is water mass, c is specific heat of water (4.2 J/g·°C), and ΔT is temperature change. Since the reaction and water are in thermal contact, the heat released by the reaction equals the heat absorbed by water (with opposite sign). This principle allows determination of reaction enthalpies experimentally.

Entropy is a measure of disorder or randomness in a system. A system in an ordered state (such as separated blue spheres on one side and red spheres on another) has lower entropy, while a mixed state has higher entropy. The Second Law states that systems will spontaneously evolve toward states of higher disorder. With a large number of particles, the probability of returning to an ordered state becomes vanishingly small, making spontaneous order-to-disorder transitions statistically impossible to observe.

Entropy is a measure of the disorder or randomness of a system. Systems naturally tend toward states of higher entropy. The second law of thermodynamics states that the total entropy of an isolated system always increases over time. Gases have higher entropy than liquids, which have higher entropy than solids, because gas molecules have more freedom of motion. When heat is added to a system, its entropy increases according to ΔS = Q/T.

Entropy is a measure of disorder or randomness in a system. The second law of thermodynamics states that entropy increases as time progresses. This concept is fundamental to understanding why certain processes occur naturally while their reverse processes do not, despite both being consistent with the underlying physical laws.

Entropy is a measure of disorder or randomness in a system. The essential idea of the Second Law of Thermodynamics is that entropy always increases over time in an isolated system, meaning that systems naturally progress toward greater disorder and randomness.

Entropy measures disorder or chaos in a system. The Second Law states the universe's entropy always increases. There is no true 'order' - only more or less disorder. Positive ΔS (increased disorder) is favorable, while negative ΔS (decreased disorder) is unfavorable. Entropy relates to molecular motion and states of matter, with gases representing maximum disorder.

Gibbs Free Energy: ΔG = ΔH - TΔS. Case 1: ΔH < 0, ΔS > 0 → always spontaneous. Case 2: ΔH > 0, ΔS < 0 → never spontaneous. Case 3: ΔH < 0, ΔS < 0 → spontaneous at low temperatures. Case 4: ΔH > 0, ΔS > 0 → spontaneous at high temperatures. This combines enthalpy and entropy to predict spontaneity.

Gibbs free energy combines enthalpy and entropy to predict spontaneity: ΔG = ΔH - TΔS. When ΔG < 0, processes are spontaneous; when ΔG > 0, they are non-spontaneous; at ΔG = 0, equilibrium exists. This equation shows both energy content (enthalpy) and disorder (entropy) contribute to reaction direction. Temperature dependence means some reactions are spontaneous only above or below certain thresholds, explaining why reactions behave differently under varying conditions.

Gibbs free energy change (ΔG) determines reaction spontaneity using the formula: ΔG = ΔH - TΔS. When ΔH and ΔS are given, convert temperature to Kelvin (T°C + 273) and entropy from J/K·mol to kJ/K·mol by dividing by 1000. The sign of ΔG determines spontaneity: negative ΔG indicates a spontaneous reaction, while positive ΔG indicates a non-spontaneous reaction. This principle is fundamental for predicting reaction feasibility in thermochemistry problems.

Spontaneous processes occur naturally without external intervention. Entropy (S) measures disorder - higher entropy means more disorder. Second Law: for spontaneous processes, total entropy change (ΔS_total) > 0. Gibbs energy (G = H - TS) combines enthalpy and entropy. ΔG = ΔH - TΔS. Spontaneity conditions: ΔG < 0 (spontaneous), ΔG > 0 (non-spontaneous), ΔG = 0 (equilibrium). At equilibrium, ΔG = 0, so ΔH = TΔS.

To calculate the enthalpy of formation of a compound from bond dissociation energies: (1) Write the formation reaction using standard forms of elements; (2) Apply the formula: ΔH_reaction = Σ(bond energies of reactants) - Σ(bond energies of products). For HCl formation: ½H₂ + ½Cl₂ → HCl, so ΔH_f = ½(110) + ½(52) - 103 = 55 + 26 - 103 = -22 kJ/mol. The negative sign indicates the formation is exothermic.

The standard enthalpy of formation (ΔH°f) is the heat change when one mole of a compound forms from elements in their standard states at 25°C and 1 atm. Elements in their standard states have ΔH°f = 0. The standard state is the most stable form at these conditions (e.g., O2(g), C(graphite), H2(g)). ΔH°rxn equals ΔH°f when the reaction produces one mole of a single compound from elements in their standard states. Formation equations must produce exactly one mole of compound from elements in standard states. Combustion reactions involve substances reacting with oxygen to release energy. The standard enthalpy of combustion (ΔH°c) is the heat released when one mole burns completely in oxygen under standard conditions. ΔH°c is always negative (exothermic). Conditions include one mole of substance, sufficient oxygen for complete combustion, and standard temperature and pressure. ΔH°rxn equals ΔH°c when these conditions are met. Combustion of elements produces oxides: C + O2 → CO2, H2 + 1/2O2 → H2O, S + O2 → SO2. Combustion of hydrocarbons produces CO2 and H2O. To balance: balance carbon, then hydrogen, then oxygen by adjusting O2 coefficient. Combustion of metals produces metal oxides: Fe + O2 → Fe2O3 (balanced as 2Fe + 3/2O2 → Fe2O3). ΔH°c can be calculated from ΔH°f using the formula: ΔH°c = ΣΔH°f(products) - ΣΔH°f(reactants). When one mole of substance burns, ΔH°rxn = ΔH°c. Decomposition reactions are the reverse of formation reactions. ΔH°decomp = -ΔH°f. These relationships allow calculation of formation enthalpies from decomposition data and vice versa.

The standard enthalpy of formation (ΔH°f) is the enthalpy change when one mole of a compound forms from its elements in their standard states at SATP (1 atm, 25°C); elements in their standard states have ΔH°f = 0, and the standard enthalpy of reaction can be calculated using ΔH°rxn = Σ[nΔH°f(products)] - Σ[mΔH°f(reactants)], while bond dissociation energy estimates reaction enthalpy by summing bond energies of bonds broken minus bonds formed (ΔH°rxn = Σ(bond energies broken) - Σ(bond energies formed)).

Standard enthalpy of formation requires reactants in elemental form and standard states, with one mole of product formed. Hess's Law states enthalpy change is path-independent: ΔH_total = ΣΔH_steps. Standard enthalpy of combustion requires one mole of reactant burning completely with products in standard states. Bond energy is energy to break one mole of bonds into gaseous atoms. Reaction enthalpy: ΔH_rxn = Σ(bond energies of reactants) - Σ(bond energies of products).

Enthalpy of reaction can be calculated from formation enthalpies: ΔH_rxn = Σν_pΔH_f(products) - Σν_rΔH_f(reactants). Elements in standard state have ΔH_f = 0. From combustion enthalpies: ΔH_rxn = Σν_rΔH_c(reactants) - Σν_pΔH_c(products). From bond dissociation energies: ΔH_rxn = ΣBE(reactants) - ΣBE(products). For example, in 2H2 + O2 → 2H2O, given ΔH = -571 kJ/mol, BE(H-H) = 435 kJ/mol, BE(O=O) = 498 kJ/mol, solving gives BE(OH) = 484.75 kJ/mol.