How to Calculate Enthalpy Change
What Is Enthalpy?
Enthalpy (H) is a thermodynamic quantity representing the total heat content of a system at constant pressure. The enthalpy change of a reaction (ΔH) is the heat absorbed or released when the reaction proceeds at constant pressure. A negative ΔH indicates an exothermic reaction (heat released to surroundings), while a positive ΔH indicates an endothermic reaction (heat absorbed from surroundings). Enthalpy is measured in joules (J) or kilojoules (kJ).
Using Standard Enthalpies of Formation
The standard enthalpy of formation (ΔHf°) is the enthalpy change when one mole of a compound is formed from its elements in their standard states at 298 K and 1 bar. The standard enthalpy of any element in its most stable form is defined as zero. The standard enthalpy of reaction is calculated as: ΔH°rxn = Σ ΔHf°(products) - Σ ΔHf°(reactants), where each term is multiplied by the stoichiometric coefficient from the balanced equation.
Step-by-Step Example: Combustion of Methane
For CH4(g) + 2 O2(g) → CO2(g) + 2 H2O(l), the standard enthalpies of formation are: CH4(g) = -74.8 kJ/mol, O2(g) = 0 kJ/mol, CO2(g) = -393.5 kJ/mol, H2O(l) = -285.8 kJ/mol. ΔH°rxn = [1(-393.5) + 2(-285.8)] - [1(-74.8) + 2(0)] = [-393.5 - 571.6] - [-74.8] = -965.1 - (-74.8) = -890.3 kJ/mol. The reaction releases 890.3 kJ per mole of methane burned.
Hess's Law
Hess's Law states that the total enthalpy change for a reaction is the same regardless of whether the reaction occurs in one step or multiple steps, because enthalpy is a state function. To apply Hess's Law, arrange known reactions (and their ΔH values) algebraically so they sum to the target reaction. If a reaction is reversed, the sign of ΔH changes; if a reaction is multiplied by a factor, ΔH is multiplied by the same factor.
Hess's Law Example
To find ΔH for C(s) + 2 H2(g) → CH4(g), use: (1) C(s) + O2(g) → CO2(g), ΔH1 = -393.5 kJ; (2) H2(g) + 1/2 O2(g) → H2O(l), ΔH2 = -285.8 kJ; (3) CH4(g) + 2 O2(g) → CO2(g) + 2 H2O(l), ΔH3 = -890.3 kJ. Take (1) + 2x(2) - (3): C + O2 + 2 H2 + O2 - CH4 - 2 O2 → CO2 + 2 H2O - CO2 - 2 H2O, simplifying to C + 2 H2 → CH4. ΔH = -393.5 + 2(-285.8) - (-890.3) = -74.8 kJ/mol.
Calorimetry: Measuring Enthalpy Experimentally
In a coffee-cup calorimeter (constant pressure), the heat of reaction is measured using q = mcΔT, where m is the mass of the solution, c is the specific heat capacity (4.184 J/g·°C for dilute aqueous solutions), and ΔT is the temperature change. The enthalpy change per mole is then ΔH = -q / n, where n is moles of the limiting reagent and the negative sign reflects the sign convention (heat released by reaction = heat absorbed by solution). Bomb calorimeters measure heat at constant volume (ΔU) rather than constant pressure (ΔH).
Bond Enthalpy Method
Enthalpy change can be estimated using average bond enthalpies: ΔH ≈ Σ (bonds broken) - Σ (bonds formed). Energy is required to break bonds (endothermic) and released when bonds form (exothermic). For H2 + Cl2 → 2 HCl: bonds broken = H-H (436 kJ/mol) + Cl-Cl (243 kJ/mol) = 679 kJ. Bonds formed = 2 x H-Cl (432 kJ/mol) = 864 kJ. ΔH ≈ 679 - 864 = -185 kJ. This method gives an estimate; actual values from formation enthalpies are more accurate.