Enthalpy and Entropy

Enthalpy answers "does this absorb or release heat?" and entropy answers "is the final state more spread out or more constrained?" Neither one alone settles whether a process is favorable, which is exactly why chemistry tracks both. A reaction can absorb heat and still be favorable, or release heat and still not be.

Enthalpy vs. entropy at a glance

                  Enthalpy ΔH                 Entropy ΔS
Core question     heat absorbed or released   accessible arrangements
                  at constant pressure        gained or lost
Key relation      ΔH = q_p (const. p,         dS = δq_rev / T
                  pV work only)               (reversible path)
Sign > 0 means    absorbs heat (endothermic)  state more spread out
Sign < 0 means    releases heat (exothermic)  state more constrained
Combined in       ΔG = ΔH − T ΔS, which judges favorability at
                  constant T and p

What enthalpy tells you

Enthalpy is defined as

where $U$ is internal energy. The useful quantity is the change $\Delta H$, not the absolute value. For a process at constant pressure with only pressure-volume work,

so a negative $\Delta H$ means the system releases heat under those conditions and a positive $\Delta H$ means it absorbs heat. That is why reaction enthalpy is central in thermochemistry and calorimetry.

What entropy tells you

Calling entropy "disorder" is a useful first hint but not the full definition. More carefully, entropy tracks how many microscopic arrangements are consistent with the macroscopic state. If a final state can be realized in more microscopic ways than the initial state, its entropy is higher; in chemistry this happens when particles become less confined, when substances mix, or when a solid turns into a liquid or gas. For a reversible path,

with the condition that the heat term is for a reversible path, not just any real process.

When you need each: ice melting uses both

Consider ice melting to liquid water at $1\ \mathrm{atm}$. Melting requires heat input, so $\Delta H > 0$ for the system. The hydrogen-bonded crystal is more ordered than liquid water, so the liquid has more accessible arrangements and $\Delta S > 0$ as well. Both ideas are visible at once: $\Delta H > 0$ says melting costs heat, $\Delta S > 0$ says the liquid is entropically less constrained.

You can put a number on the entropy change. For a phase change at its equilibrium temperature,

With $\Delta H_{fus} \approx 6.01\ \mathrm{kJ/mol}$ and $T = 273.15\ \mathrm{K}$,

The positive result matches the picture: liquid water has more accessible arrangements than ice. At exactly $0^\circ \mathrm{C}$ and $1\ \mathrm{atm}$, ice and liquid water are in equilibrium and

is zero. Raise the temperature slightly and the $T\Delta S$ term grows, so melting becomes favorable. At constant $T$ and $p$, the sign of $\Delta G$ is what decides favorability.

When to lean on which, and the traps

If a problem asks how much heat is absorbed or released, enthalpy is usually central. If it asks whether a state is more spread out or why temperature changes the balance, entropy is. These ideas appear when interpreting calorimetry data, comparing phase changes such as melting, freezing, vaporization, and condensation, explaining why some reactions become more favorable at higher temperature, and connecting reaction heat to equilibrium and free energy. The recurring traps:

• Treating entropy as only "disorder." Think in terms of accessible arrangements and constraints instead.
• Assuming exothermic means spontaneous. A negative $\Delta H$ helps, but $\Delta G = \Delta H - T\Delta S$ decides.
• Forgetting the condition behind $\Delta H = q_p$, which is constant pressure.
• Forgetting which system you mean. The system can lose entropy even when the overall process is spontaneous, because the surroundings count too.

A four-way comparison to make it stick

Take the four phase changes of water: melting, freezing, vaporization, condensation. Predict the signs of $\Delta H$ and $\Delta S$ for each before computing anything. Lining all four up at once is what usually makes the enthalpy-versus-entropy distinction click.