Enthalpy Changes (ΔH) - Chemistry

1. Fundamental Concepts

Enthalpy (H): A state function that describes the total heat content of a system at constant pressure, defined by the formula $H=U+PV$ (where $U$ = internal energy, $P$ = pressure, $V$ = volume). Its value depends only on the initial and final states of the system.

Enthalpy Change (ΔH): The heat absorbed or released by a system during a reaction/process at constant pressure, calculated as $ΔH=H_{products}-H_{reactants}$ .

Sign Conventions: ΔH > 0 for endothermic processes (the system absorbs heat from the surroundings); ΔH < 0 for exothermic processes (the system releases heat to the surroundings).

Standard State: Standard enthalpy change (ΔH°) is measured at 1 atm, 298 K (25°C), with a 1 mol/L concentration for aqueous solutions and the stable phase for pure substances.

State Function Property: ΔH is independent of the reaction pathway; it is only determined by the initial and final states of the system.

2. Key Concepts

Molar Enthalpy: The enthalpy change per mole of a substance involved in a reaction, with the unit kJ/mol – the core basis for quantitative calculations.

Standard Enthalpy of Formation ( $ΔH°_f$ ): The enthalpy change for the formation of 1 mole of a compound from its pure elements in their standard states. The standard enthalpy of formation for all pure elements in their stable standard states is 0 kJ/mol.

Standard Enthalpy of Reaction ($ΔH°_{rxn}$): The enthalpy change of a reaction under standard constant pressure conditions, calculable from the ΔH°_f values of all reactants and products.

Enthalpy of Combustion ($ΔH°_{comb}$): The enthalpy change for the complete combustion of 1 mole of a substance in oxygen; all combustion processes are exothermic (ΔH < 0), and it is a specific type of standard enthalpy change.

Phase Change Enthalpy: The enthalpy change for a substance’s phase transition at constant temperature and pressure (e.g., enthalpy of fusion $ΔH_{fus}$, enthalpy of vaporization $ΔH_{vap}$). Temperature remains constant during phase changes, and the sign of ΔH is determined by the transition direction (melting/vaporization = endothermic, ΔH > 0; freezing/condensation = exothermic, ΔH < 0).

Stoichiometry & ΔH: The ΔH of a reaction is directly proportional to the stoichiometric coefficients in the balanced chemical equation. Doubling the coefficients doubles the ΔH; reversing the reaction flips the sign of ΔH.

3. Examples

Easy

Classify the reaction as endothermic or exothermic and explain the reasoning:

$CH_4(g) + 2O_2(g) → CO_2(g) + 2H_2O(l) \ ΔH = -890.3 \ kJ/mol$

Answer: Exothermic; the ΔH value is negative, meaning the system releases heat to the surroundings during the reaction.

Medium

Given the standard enthalpies of formation: $ΔH°_f(NH₃) = -46.1 kJ/mol$, $ΔH°_f(N₂)=0 kJ/mol$, $ΔH°_f(H₂)=0 kJ/mol$, calculate $ΔH°_{rxn}$ for the reaction:

$N_2(g) + 3H_2(g) → 2NH_3(g)$

Answer: Use the formula $ΔH°_{rxn} = ΣnΔH°_f(products) - ΣmΔH°_f(reactants)$

$ΔH°_{rxn} = [2×(-46.1)] - [1×0 + 3×0] = \boldsymbol{-92.2 \ kJ/mol}$

Hard
The molar enthalpy of vaporization for liquid water is $ΔH_{vap} = +40.7 kJ/mol$ (298 K, 1 atm). Answer the following questions:

① Calculate the total enthalpy change (ΔH) when 36 g of $H_2O(l)$ is completely vaporized to $H_2O(g)$ ;

② Write the thermochemical equation for the condensation of liquid water, and label the ΔH value.

Given: Molar mass of $H_2O = 18 \ g/mol$

Answer:

① Moles of $H_2O = 36g/18g/mol = 2mol$ ; vaporization is endothermic, so

$ΔH = 2mol × 40.7 \ kJ/mol = \boldsymbol{+81.4 \ kJ}$ ;

② Condensation is the reverse of vaporization (exothermic):

$H_2O(g) → H_2O(l) \ ΔH = \boldsymbol{-40.7 \ kJ/mol}$

4. Problem-Solving Techniques

Master Sign Conventions: First judge the endothermic/exothermic direction of a process (reaction/phase change), then verify the ΔH sign; reversing a process always flips the ΔH sign – label the sign first before quantitative calculations.

$ΔH°_{rxn}$ Calculation Steps:

List the $ΔH°_f$ values for all substances in the reaction (pure elements = 0; note the physical state – ΔH°_f is phase-specific).

Calculate the total $ΔH°_f$ for products and reactants by multiplying each value by its stoichiometric coefficient ( $ΣnΔH°_f$ ).

Substitute into the formula $ΔH°_{rxn} = Σproducts - Σreactants$ , then state the result with the correct unit.

Mole Ratio & ΔH Scaling:

If mass/volume (not moles) of a substance is given, first convert it to moles.

Calculate the target enthalpy change using the direct proportionality between stoichiometric coefficients and ΔH (e.g., ΔH for n moles = n × molar enthalpy change).

Check Phase Consistency: Always confirm the physical state (s/l/g/aq) of substances when using ΔH°_f or phase change enthalpy – different phases have distinct enthalpy values (e.g., $ΔH°_f(H₂O,l) ≠ ΔH°_f(H₂O,g)$).

Write Thermochemical Equations Correctly:

Label the physical state (s/l/g/aq) for all substances.

Label the reaction’s ΔH (include value, unit, and sign) – ΔH is uniquely tied to the equation’s stoichiometric coefficients.

Use chemical formulas for pure substances; never omit state symbols.

Apply Enthalpy of Combustion: When using $ΔH°_{comb}$ for calculations, remember it is defined for 1 mole of the combustible substance – match the stoichiometric coefficients first, then sum values using the same logic as $ΔH°_f$ calculations.

Maintain Unit Uniformity: Use consistent units in calculations (prefer kJ/mol for molar enthalpy, kJ for total enthalpy); convert mass to moles before all enthalpy calculations.