Enthalpy — Definition, Formula & Exothermic vs Endothermic

Enthalpy is the quantity chemists use to track energy change in many constant-pressure processes. In most introductory chemistry problems, the key shortcut is this: if pressure is constant and the only important work is pressure-volume work, then the enthalpy change equals the heat transferred to the system:

$$\Delta H = q_p$$

That gives you a quick way to read the sign. If $\Delta H < 0$, the process is exothermic and the system releases heat. If $\Delta H > 0$, the process is endothermic and the system absorbs heat.

Enthalpy definition in chemistry

Enthalpy is defined as

$$H = U + pV$$

Here, $U$ is internal energy, $p$ is pressure, and $V$ is volume. Enthalpy is a state function, which means it depends on the current state of the system, not on the path used to get there.

In practice, chemists usually care about the change in enthalpy, not the absolute value. Most questions ask what happens during a process such as a reaction, a phase change, or mixing, so $\Delta H$ is the useful quantity.

When $\Delta H = q_p$ at constant pressure

$\Delta H$ tells you the enthalpy difference between final and initial states:

$$\Delta H = H_{final} - H_{initial}$$

Under constant pressure, a negative value means heat leaves the system, and a positive value means heat enters the system. That sign convention is always from the system's point of view.

The shortcut $\Delta H = q_p$ is useful, but it comes with a condition. It applies in the standard chemistry setting of constant pressure when pressure-volume work is the only relevant work term. Outside that setting, you should not treat it as a universal heat formula.

Exothermic vs endothermic: how to read the sign

The quickest test is to look at the sign of $\Delta H$:

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

Combustion is a common exothermic process. Melting ice is a common endothermic process. The names become easier to remember if you attach them to heat flow instead of trying to memorize the words in isolation.

The sign of $\Delta H$ does not tell you whether a process is fast. Reaction rate depends on kinetics and activation energy, not just on enthalpy change.

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 about

$$\Delta H_{fus} = 6.01\ \mathrm{kJ/mol}$$

For the amount given,

$$\Delta H = n\Delta H_{fus} = (2.00\ \mathrm{mol})(6.01\ \mathrm{kJ/mol}) = 12.0\ \mathrm{kJ}$$

The result is positive, so melting is endothermic. Under these conditions, the system absorbs $12.0\ \mathrm{kJ}$ of heat from the surroundings.

This example is useful because the sign matches the physical picture. During melting at the phase-change temperature, the absorbed energy goes into changing the state rather than raising the temperature of the sample.

Common mistakes in enthalpy problems

Using $\Delta H = q_p$ without checking the condition

The shortcut $\Delta H = q_p$ is not a universal definition of heat. It is the constant-pressure relation used in standard chemistry settings.

Mixing up system and surroundings

If a reaction feels hot to you, the surroundings are gaining heat. That usually means the system is releasing heat, so $\Delta H$ for the system is negative.

Confusing enthalpy with activation energy

Enthalpy change compares initial and final states. Activation energy is the barrier that must be crossed for a reaction step to occur. They describe different parts of the energy picture.

Assuming exothermic means spontaneous

Not always. Enthalpy helps, but spontaneity at constant temperature and pressure depends on Gibbs free energy, not on $\Delta H$ alone.

Where enthalpy is used

Enthalpy shows up across thermochemistry:

• reaction heat and calorimetry
• phase changes such as melting, freezing, and vaporization
• Hess's law calculations
• energy balances in laboratory and engineering problems

If the question asks how much heat is absorbed or released at constant pressure, enthalpy is usually the first concept to check.

Try a similar thermochemistry question

Try the same calculation for freezing instead of melting. Under the same conditions, the magnitude stays the same for the reverse process, but the sign changes:

$$\Delta H_{freeze} = -\Delta H_{fus}$$

That one comparison makes exothermic and endothermic much easier to remember. For a useful next step, compare this with Hess's law to see how enthalpy changes are combined across multiple reactions.