Enthalpy

Enthalpy is a state function that makes tracking heat flow at constant pressure simple — instead of separately measuring internal energy change and pressure-volume work, enthalpy bundles them together so that, under constant pressure, the heat measured directly is the enthalpy change. This article covers enthalpy's definition, exothermic and endothermic reactions and their energy diagrams, phase changes, heating curves, phase diagrams, Hess's Law, bond dissociation energies, and standard enthalpy of formation.

Key Takeaways

• Enthalpy (H) is a state function, H = E + PV, defined so that at constant pressure, ΔH = q_p — the heat measured directly gives the enthalpy change, no separate work term needed.

• Negative ΔH → exothermic (releases heat, reactants higher-energy than products on an energy diagram); positive ΔH → endothermic (absorbs heat, reactants lower-energy than products). The diagram's peak is the transition state, its height above reactants the activation energy.

• Phase changes are endothermic (melting, evaporation, sublimation) or exothermic (freezing, condensation, deposition) depending on whether breaking or forming intermolecular attractions dominates.

• Heating curves use q = mcΔT on sloped (single-phase, temperature-changing) segments and q = mL on flat (phase-changing, temperature-constant) segments.

• Phase diagrams plot phase as a function of temperature and pressure; the triple point is where all three phases coexist, the critical point is where the liquid/gas distinction disappears into a supercritical fluid.

• Hess's Law: total ΔH for a reaction is path-independent — it equals the sum of ΔH for any set of steps that add up to the overall reaction, whether expressed as full reaction steps or as bond dissociation energies (ΔH = Σbonds broken − Σbonds formed).

• Standard enthalpy of formation (ΔH°f) of an element in its standard state is zero; a reaction's ΔH°rxn can be calculated as ΣnΔH°f(products) − ΣnΔH°f(reactants) without running calorimetry.

What Is Enthalpy?

Under constant pressure — the condition in most open, atmosphere-exposed lab setups — the change in internal energy is:

ΔE = q_p − PΔV

where q_p is heat flow at constant pressure, P is the constant pressure, and ΔV is the volume change. Rearranged, q_p = ΔE + PΔV: heat flow at constant pressure depends on both the internal energy change and the work done against atmospheric pressure as volume changes.

Measuring that pressure-volume work directly is inconvenient, so chemists define a new state function, enthalpy (H), that folds it in automatically:

H = E + PV

Because of how enthalpy is defined, its change matches q_p exactly:

ΔH = q_p

At constant pressure, any heat measured is a direct read of the enthalpy change — no separate work term needed. This is what makes enthalpy so useful: it simplifies constant-pressure heat calculations by inherently accounting for pressure-volume work.

Exothermic vs. Endothermic Reactions

The sign of ΔH tells you the direction of heat flow:

• ΔH negative → exothermic: the process releases heat.

• ΔH positive → endothermic: the process absorbs heat.

Reaction energy diagrams plot energy against reaction progress, giving a visual picture of how energy changes from reactants to products:

• Exothermic reactions (e.g., the combustion of methane): reactants start at higher energy than products. The reaction moves "downhill," releasing the energy difference as heat.

• Endothermic reactions: reactants start at lower energy than products. The reaction moves "uphill," absorbing heat from the surroundings.

In both cases, the highest point on the diagram is the transition state — the point of maximum energy the system must pass through to get from reactants to products. Its height above the reactants is the activation energy: the lower the activation energy, the faster the reaction.

Phase Changes: Endothermic or Exothermic?

Changes of physical state are also classified as endothermic or exothermic, based on whether bond-breaking or bond-forming dominates:

The underlying reason: endothermic phase changes absorb energy because the energy needed to break the intermolecular attractions holding the more-ordered phase together exceeds the energy released forming the new, less-ordered phase's (weaker) attractions. Exothermic phase changes release energy because the reverse is true — the energy released forming stronger attractions in the more-ordered phase exceeds what's needed to break the weaker attractions of the less-ordered starting phase.

Heating Curves

A heating curve graphs a substance's temperature against heat added, and it has two kinds of segments:

• Sloped segments: temperature is rising within a single phase (solid, liquid, or gas). Use q = mcΔT, where c is that phase's specific heat capacity.

• Flat segments: a phase change is in progress, so all added heat goes into changing phase rather than raising temperature — temperature holds constant. Use q = mL, where L is the latent heat (the heat needed to change the phase of 1 gram of substance without changing its temperature). Latent heat of fusion applies to solid↔liquid transitions; latent heat of vaporization applies to liquid↔gas transitions.

For example, heating ice below its melting point follows q = mcΔT (using ice's specific heat capacity); once the ice starts melting at 0°C, the curve flattens and q = mL applies until melting is complete.

Phase Diagrams

A phase diagram charts which phase (solid, liquid, or gas) a substance occupies across combinations of temperature (x-axis) and pressure (y-axis):

• The diagram is divided into regions, one per phase.

• The boundary lines between regions mark conditions where two phases coexist in equilibrium.

• The triple point is the single temperature/pressure combination where all three phases coexist simultaneously.

• The critical point is the highest temperature and pressure at which a distinct liquid phase can exist; beyond it, liquid and gas become indistinguishable, forming a supercritical fluid.

Phase changes are reversible: condensation is the reverse of evaporation, freezing is the reverse of melting, and so on. The exact temperatures and pressures at which they occur are substance-specific.

Hess's Law

Because enthalpy is a state function, ΔH depends only on a process's initial and final states — never on the path taken to get there. Hess's Law follows directly: the total enthalpy change for a reaction is the same whether it happens in one step or several, so ΔH for an overall reaction equals the sum of the ΔH values of any set of steps that add up to it.

Worked example — forming CO₂(g) from its elements, directly vs. via a CO(g) intermediate:

Direct reaction:
C(s, graphite) + O₂(g) → CO₂(g), ΔH = −393.5 kJ/mol

Two-step pathway:

• Step 1: C(s, graphite) + ½O₂(g) → CO(g), ΔH₁ = −110.5 kJ/mol

• Step 2: CO(g) + ½O₂(g) → CO₂(g), ΔH₂ = −283.0 kJ/mol

Summing the two steps: ΔH₁ + ΔH₂ = −110.5 kJ/mol + (−283.0 kJ/mol) = −393.5 kJ/mol — matching the direct reaction exactly, as Hess's Law predicts. This is especially useful for reactions that are hard to measure directly: break them into steps with known ΔH values, and sum.

Bond Dissociation Energies

Hess's Law can also be applied at the level of individual bonds. Bond dissociation energy (bond enthalpy) is the average energy required to break a specific type of bond between atoms in the gas phase. Since breaking bonds always requires energy (endothermic) and forming bonds always releases energy (exothermic), a reaction's ΔH can be estimated as:

ΔH = Σ(bonds broken) − Σ(bonds formed)

Summing the bond energies of every bond broken in the reactants, then subtracting the bond energies of every bond formed in the products, gives the overall enthalpy change. This is especially useful when a reaction's ΔH is hard to measure directly but the relevant bond energies are already known.

Standard Enthalpy of Formation

There's a way to determine a reaction's standard enthalpy change without running a calorimetry experiment: use previously measured standard enthalpies of formation (ΔH°f).

Standard enthalpy of formation is the enthalpy change when 1 mole of a substance forms from its constituent elements, each in their most stable standard-state form. Two rules make it usable:

• The ΔH°f of any element in its standard state is, by definition, zero.

• A reaction's standard enthalpy change can be found from the standard enthalpies of formation of its reactants and products:

ΔH°rxn = ΣnΔH°f(products) − ΣnΔH°f(reactants)

Worked example — standard enthalpy of combustion of methane, CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(l), using standard values ΔH°f[CH₄(g)] = −74.6 kJ/mol, ΔH°f[CO₂(g)] = −393.5 kJ/mol, ΔH°f[H₂O(l)] = −285.8 kJ/mol, ΔH°f[O₂(g)] = 0 kJ/mol (element in its standard state):

• Products: (−393.5) + 2(−285.8) = −393.5 − 571.6 = −965.1 kJ/mol

• Reactants: (−74.6) + 2(0) = −74.6 kJ/mol

• ΔH°rxn = −965.1 − (−74.6) = −890.5 kJ/mol

The large negative value confirms methane combustion is strongly exothermic — consistent with its well-known role as a fuel.

Common MCAT Mistakes

• Flipping the sign convention for ΔH. Negative ΔH means exothermic (heat released, products lower-energy); positive ΔH means endothermic (heat absorbed, products higher-energy) — mixing these up flips every conclusion about spontaneity and energy diagram direction.

• Assuming melting and freezing are both endothermic (or both exothermic). Melting (solid→liquid) is endothermic; freezing (liquid→solid) is exothermic. The rule of thumb: moving toward a less-ordered phase (melting, evaporation, sublimation) absorbs energy; moving toward a more-ordered phase (freezing, condensation, deposition) releases it.

• Using q = mcΔT on a heating curve's flat segment. Flat segments represent a phase change in progress, where temperature doesn't change — q = mcΔT (which requires a nonzero ΔT) doesn't apply there; q = mL is the correct formula for that segment.

• Forgetting that ΔH°f of an element in its standard state is zero. Skipping this rule leads to over-counting energy for reactants or products that are simply elements (like O₂(g) or N₂(g)) rather than compounds — those terms should drop out of the ΔH°rxn calculation entirely.

MCAT-Style Concept Check

Question: In a hypothetical reaction, breaking all the bonds in the reactants requires 500 kJ/mol, and forming all the bonds in the products releases 620 kJ/mol. What is the reaction's ΔH, and is it exothermic or endothermic?

• A) −120 kJ/mol, exothermic

• B) +120 kJ/mol, endothermic

• C) −1,120 kJ/mol, exothermic

• D) +1,120 kJ/mol, endothermic

Answer: A

Explanation: Using ΔH = Σ(bonds broken) − Σ(bonds formed): ΔH = 500 kJ/mol − 620 kJ/mol = −120 kJ/mol. The negative value means more energy is released forming the new bonds than was required to break the old ones, making the reaction exothermic.

FAQ

What's the difference between ΔH and q_p?

They're numerically identical at constant pressure — that's the whole point of defining enthalpy the way it's defined. ΔH is the formal state-function change (H = E + PV); q_p is the heat actually measured in a constant-pressure experiment, and because ΔH = q_p, measuring q_p directly gives the enthalpy change with no separate work correction needed.

Why is breaking a bond always endothermic?

Breaking a bond means pulling two atoms apart against the attractive force holding them together, which requires an energy input — by definition, that's endothermic. Forming a bond is the reverse process (atoms coming together, releasing energy as the attraction is satisfied), which is why bond formation is always exothermic.

What is Hess's Law used for?

Hess's Law lets you calculate a reaction's ΔH by summing the ΔH values of any set of steps that add up to the overall reaction — useful when the direct reaction is difficult or dangerous to run in a calorimeter, but its component steps (or its bond dissociation energies) are already known.

Why is the standard enthalpy of formation of O₂(g) equal to zero?

By definition, the standard enthalpy of formation of any element in its standard state is zero — and O₂(g) (diatomic oxygen gas) is oxygen's standard state at 298 K and 1 atm. This convention gives every ΔH°rxn calculation a consistent zero point to measure from.