Enthalpy

From internal energy to enthalpy

A system has internal energy U: molecular motion, electronic energy, chemical bonding and other microscopic contributions. When the system changes volume against an external pressure, part of the energy exchange appears as pressure–volume work.

The equality is a statement about the experimental conditions. At constant volume, heat instead tracks ΔU.

Reading the sign of ΔH

An exothermic process has ΔH < 0: the system transfers heat to the surroundings. Combustion is the familiar example. An endothermic process has ΔH > 0: the system absorbs heat, as in melting ice at its melting point.

“Exothermic” does not mean “fast” or “spontaneous.” A reaction can be strongly exothermic and still proceed imperceptibly slowly if its activation barrier is large.

Hess law and formation enthalpies

Because enthalpy is a state function, reaction enthalpies can be added. This is Hess law. A practical version uses standard enthalpies of formation:

The coefficients ν are stoichiometric coefficients. Standard enthalpy of formation refers to forming one mole of a substance from its elements in their standard states.

For CH₄ + 2O₂ → CO₂ + 2H₂O(l), using approximate formation enthalpies gives a large negative ΔH°: combustion is exothermic.

Calorimetry connects temperature change to ΔH

Calorimetry is never just “plug numbers into mcΔT.” The sign depends on which object is called the system, and the calorimeter itself may absorb heat.

Bond energies: useful estimate, not exact thermochemistry

Average bond energies give a fast gas-phase estimate:

ΔH ≈ energy to break bonds − energy released forming bonds.

They are averages over many molecules. A C–H bond in methane does not have exactly the same dissociation energy as a C–H bond next to an electronegative group. Formation enthalpies are usually preferable when accurate tabulated values exist.

Working with real thermochemical data

Standard state and temperature matter

A tabulated ΔH° is tied to specified reference conditions. The superscript ° does not mean “exactly 25 °C”; it refers to standard-state activities, and tables commonly quote values at 298.15 K. If temperature changes substantially, heat capacities make ΔH change too.

Kirchhoff’s law expresses that temperature dependence: the derivative of reaction enthalpy with respect to temperature is the difference in heat capacities of products and reactants. For many classroom problems the change is small enough to neglect, but industrial calculations cannot always do so.

Formation enthalpy is a reference construction

The standard enthalpy of formation of an element in its reference state is defined as zero. This does not mean the element contains no energy; it means the thermochemical scale chooses that state as a reference. Graphite, for example, is the reference form of carbon at ordinary conditions, not diamond.

That convention allows thousands of reaction enthalpies to be assembled consistently from a single table. The power comes from state-function arithmetic, not from assigning an absolute “energy content” to each compound.

From calorimeter signal to molar enthalpy

Suppose 0.0100 mol of reactant releases 2.50 kJ at constant pressure. The molar reaction enthalpy is −250 kJ mol⁻¹ for the reaction as written. If the balanced equation is later multiplied by two, ΔH also doubles because enthalpy change is extensive.

Uncertainty should follow the measurement. A temperature rise of only a few tenths of a kelvin may make heat loss and thermometer resolution important; repeating the experiment is more informative than reporting many calculator digits.

Exercises

Sign

A reaction heats the surrounding water. What is the sign of ΔH for the reacting system?

Hess law

If A→B has ΔH = +40 kJ mol⁻¹ and B→C has ΔH = −65 kJ mol⁻¹, find ΔH for A→C.

Calorimetry

100 g of water warms by 5.0 K. Using c = 4.18 J g⁻¹ K⁻¹, how much heat did the water absorb?