Enthalpy — Definition, Formula & Exothermic vs Endothermic

Should you reach for $\Delta H$ or for heat $q$ when a chemistry problem asks how much energy moved during a reaction or phase change? At constant pressure, with pressure-volume work as the only relevant work, the two coincide:

That single equality is what makes enthalpy the go-to bookkeeping quantity for constant-pressure thermochemistry, and the rest of this topic is about reading it correctly.

Enthalpy and heat side by side

                  Enthalpy H = U + pV        Heat q
What it is         a state function           energy in transit
Depends on path?   no                         yes
Sign convention    from the system's view     from the system's view
When they match    constant p, only pV work   ΔH = q_p holds
Typical use        ΔH of reactions, phase     calorimetry readings
                   changes, Hess's law

Here $U$ is internal energy, $p$ is pressure, and $V$ is volume. Because $H$ is a state function, it depends only on the current state, not on how the system got there. In practice chemists track the change $\Delta H = H_{final} - H_{initial}$ rather than the absolute value, since reactions, phase changes, and mixing are all described by a difference.

When to use $\Delta H = q_p$, and how to read its sign

The shortcut applies in the standard chemistry setting: constant pressure, with pressure-volume work as the only work term. Outside that setting it is not a universal heat formula. When it does hold, the sign tells you the direction of heat flow, always from the system's point of view:

• $\Delta H < 0$: exothermic, the system releases heat to the surroundings
• $\Delta H > 0$: endothermic, the system absorbs heat from the surroundings

Combustion is the familiar exothermic case; melting ice is the familiar endothermic one. Attaching the names to heat flow rather than memorizing them in isolation keeps them straight.

Worked example: melting ice

Suppose $2.00\ \mathrm{mol}$ of ice melts at $0^\circ \mathrm{C}$ and $1\ \mathrm{atm}$. The molar enthalpy of fusion of water is

For the amount given,

The result is positive, so melting is endothermic: the system absorbs $12.0\ \mathrm{kJ}$ from the surroundings. The sign matches the physical picture, because at the phase-change temperature the absorbed energy changes the state rather than raising the sample's temperature.

Choosing what to apply, and the traps

Picking enthalpy is usually right when the question asks how much heat is absorbed or released at constant pressure. The recurring traps are about overreaching with that choice:

• Using $\Delta H = q_p$ without checking constant pressure and pressure-volume work. It is a relation with conditions, not a definition of heat.
• Mixing up system and surroundings. If a reaction feels hot to you, the surroundings are gaining heat, so the system is releasing it and $\Delta H$ for the system is negative.
• Confusing enthalpy change with activation energy. Enthalpy compares initial and final states; activation energy is the barrier crossed during a step.
• Assuming exothermic means spontaneous. Spontaneity at constant $T$ and $p$ depends on Gibbs free energy, not on $\Delta H$ alone.

Enthalpy recurs across reaction heat and calorimetry, phase changes, Hess's law calculations, and energy balances in lab and engineering work.

One comparison that locks it in

Reverse the worked example: freeze $2.00\ \mathrm{mol}$ of water under the same conditions. The magnitude is unchanged but the sign flips,

so freezing releases the same $12.0\ \mathrm{kJ}$ that melting absorbed. Holding melting and freezing next to each other is the fastest way to keep exothermic and endothermic straight. To see how several such enthalpy changes combine across multiple reactions, compare this with Hess's law.