Thermodynamics: The First Law and Thermochemistry

Burn methane in a kitchen stove and its stored chemical energy becomes heat; burn the same methane in an engine and that energy becomes mechanical work instead; run it through a galvanic cell like a dry battery and it becomes electrical energy. The same chemical transformation, three genuinely different outcomes, and thermodynamics is the discipline that tracks exactly where energy goes regardless of which form it takes, concerned only with a system's initial and final states, never with how fast the change happens or the exact mechanism involved. This chapter answers three concrete questions any chemist eventually needs answered: how much energy does a given reaction actually involve, will a reaction happen at all, and how far will it actually proceed before stopping.

A system is whatever part of the universe is actually under observation; everything else is the surroundings, and system plus surroundings together make up the entire universe. Systems sort into three types purely by what their own boundary lets through: an open system exchanges both matter and energy with its surroundings, an open beaker of reactants being the standard example; a closed system exchanges energy but not matter, reactants sealed inside a conducting copper or steel vessel; and an isolated system exchanges neither, reactants inside a thermos flask or any well-insulated closed vessel, the boundary specifically called an adiabatic wall when it blocks heat transfer entirely. Which type of system a chemist is actually studying decides directly which equations apply, making this classification the first, essential step in any thermodynamic analysis.

A system's state is described by measurable, macroscopic properties like pressure, volume and temperature, called state variables or state functions specifically because their value depends only on the system's current state, never on the route taken to reach it, a pond's own water volume, for instance, being identical whether filled by rain, a tubewell, or both together. Internal energy, U, the total energy stored in a system, chemical, electrical, mechanical, everything combined, earns state-function status through a genuine experimental demonstration: J. P. Joule, between 1840 and 1850, showed that raising water's temperature by an identical amount using mechanical work, churning paddles, or using electrical work, an immersion coil, always changed the internal energy by exactly the same amount regardless of which method was used, meaning the adiabatic work needed to reach a given state depends only on that state, never on the specific path taken there, exactly the defining property a state function needs.

Combining heat and work into a single equation gives the First Law of Thermodynamics itself, ΔU equals q plus w, where q and w individually depend on exactly how a change is carried out, yet their sum, ΔU, depends only on the system's initial and final states, exactly the state-function behaviour already established. By IUPAC convention, both q and w carry a positive sign when energy flows into the system, heat absorbed or work done on it, and a negative sign when energy flows out; for a genuinely isolated system, with no heat or work crossing the boundary at all, ΔU is necessarily zero, giving the First Law its more familiar phrasing: the energy of an isolated system is constant, energy neither created nor destroyed, only ever moved or converted from one form into another.

For a gas compressed by a piston under constant external pressure pex, the work done on the system works out to w equals negative pex times the volume change, the negative sign ensuring compression, where volume decreases, yields a genuinely positive work value, exactly the convention already established. When compression instead happens through an infinite series of infinitesimally small steps, external pressure always just barely exceeding internal pressure at every instant, the process is called reversible, capable of reversing direction with only an infinitesimal change at any moment, the system and surroundings staying in near-continuous equilibrium throughout; any process that cannot do this is irreversible instead. A genuinely special case, free expansion into a vacuum, where external pressure is zero, does zero work under any conditions, reversible or not, since work depends directly on the external pressure being pushed against, and pushing against nothing costs nothing.

Chemical reactions overwhelmingly happen not at constant volume but in an open flask or test tube, at constant atmospheric pressure instead, and heat absorbed at constant volume, qV, equals ΔU directly, but a genuinely different state function suits constant-pressure conditions better: enthalpy, H, defined as U plus pV, chosen specifically so that qp, the heat absorbed at constant pressure, equals ΔH directly, exactly the quantity most real chemistry actually measures. Since H depends entirely on U, p and V, themselves all state functions, H is necessarily a state function too, meaning ΔH, unlike q on its own, never depends on path. For reactions involving gases specifically, ΔH and ΔU differ by ΔngRT, where Δng is the change in moles of gas between products and reactants, a correction that vanishes for reactions involving only solids and liquids, since their volumes barely shift with heating at all. Two further property types matter here: an extensive property, like mass, volume or enthalpy itself, depends directly on how much substance is present, while an intensive property, like temperature, density or pressure, does not, splitting a container of gas in half leaves its temperature unchanged even though its total volume has halved.

Heat absorbed and temperature rise are directly proportional, q equals C times ΔT, where C, the heat capacity, depends on a substance's own size, composition and nature; the molar heat capacity, heat needed to raise one mole by one degree, differs at constant volume, CV, versus constant pressure, Cp, and for one mole of an ideal gas the two are related simply, Cp minus CV equals R, derived directly from ΔH equalling ΔU plus RΔT. Calorimetry puts these relationships to direct experimental use: a bomb calorimeter, a sealed steel vessel immersed in a water bath, holds volume genuinely constant, so no pV work is ever done, meaning the temperature rise measured there converts straight to qV, and therefore ΔU, a real worked example showing 1 g of graphite combusted in oxygen raising a calorimeter's temperature by exactly 1 K, giving, once scaled to a full mole and since Δng equals zero for that specific reaction, ΔU equal to ΔH equal to negative 2.48 times ten squared kJ per mole. A second calorimeter design, open to the atmosphere, measures heat directly at constant pressure instead, giving qp, and therefore ΔH, straightaway.

Because enthalpy is a state function, the total enthalpy change for a reaction is identical whether it happens in a single step or through a whole series of intermediate ones, Hess's Law of Constant Heat Summation, and this matters enormously in practice whenever the direct reaction cannot actually be measured cleanly. Carbon burning to carbon monoxide is a genuine example: some carbon dioxide always forms alongside it, contaminating a direct measurement, but two other, cleanly measurable reactions, graphite burning fully to CO2 with a known enthalpy, and CO burning to CO2 with a known enthalpy, combine algebraically to give the answer anyway: reversing the CO-to-CO2 equation, flipping its own enthalpy sign in the process, then adding it to the graphite-to-CO2 equation, yields exactly the graphite-to-CO reaction wanted, its enthalpy simply the sum of the two known values. Enthalpy of formation reactions follow one further, useful convention: any element in its own standard reference state, hydrogen gas, graphite for carbon, is assigned exactly zero enthalpy of formation by definition, giving every other formation enthalpy a fixed, comparable baseline to be measured against.

A whole family of specifically named enthalpy changes each answer a different practical question. Standard enthalpy of combustion measures the heat released per mole when a substance burns completely; enthalpy of atomization measures the heat needed to break every bond in one mole of a substance down to separate gaseous atoms, matching a diatomic molecule's own bond dissociation enthalpy exactly, but requiring a mean bond enthalpy for a polyatomic molecule like methane instead, since each successive C-H bond broken actually costs a slightly different amount of energy, 427, 439, 452 and 347 kJ per mole in sequence, averaged to a single practical value of 416 kJ per mole. Lattice enthalpy, the energy needed to separate one mole of an ionic solid into gaseous ions, cannot be measured directly at all, so chemists build a Born-Haber cycle instead, a closed loop of measurable steps, sublimation, ionisation, bond dissociation, electron gain, and lattice formation, whose enthalpies must sum to zero around the complete cycle by Hess's Law, letting the one unmeasurable step be calculated from all the others. And enthalpy of solution, the heat change when one mole of a substance dissolves, splits cleanly into two opposing contributions, lattice enthalpy, energy needed to pull the solid apart, and hydration enthalpy, energy released as ions solvate, sodium chloride's own two values, +788 and -784 kJ per mole, so nearly cancelling that dissolving table salt barely changes a solution's temperature at all.