MCAT topics → Thermodynamics and Kinetics → Entropy and the Second Law

Entropy and the Second Law

MCAT trap: Applies the second law to the system alone rather than to the universe. The second law requires that entropy of the universe (system + surroundings) never decreases; the system's entropy can decrease if the surroundings increase more.

Entropy and the second law sit at the intersection of chemistry and physics on the MCAT, and they're tested more deeply than most students expect. At its core, entropy (ΔS) measures the number of accessible microstates in a system — more spread-out energy and matter means higher entropy. The second law says the entropy of the universe never decreases for a spontaneous process. The exam hits this topic from multiple angles: pure definition questions, sign prediction for reactions and phase changes, passage-based Gibbs energy calculations, and the occasional third law reference that throws students off because it requires knowing that absolute entropies (unlike formation enthalpies) are never zero for elements at standard conditions.

What makes this topic dangerous is that students carry in two bad habits. The first is applying the second law only to the system — if you see ice melting or a protein folding, you might think entropy is decreasing and therefore the process violates the second law. It doesn't, because the surroundings compensate. The second habit is conflating ΔH and ΔS: exothermic does not mean entropy decreases, and endothermic does not mean entropy increases. These are independent thermodynamic quantities. The MCAT loves questions that force you to treat them separately.

The calculation side requires a specific technique: ΔS°_rxn = Σ(S° products) − Σ(S° reactants) using tabulated absolute entropies. This looks like Hess's law but is subtly different — elements in their standard state have S° values that are not zero (unlike ΔHf°). Missing that distinction will cost you points on calculation questions. Nail the conceptual framework first, then the math follows naturally.

Common misconceptions

Common mistake
Wrong: The second law requires that entropy of the system always increases.
Right: The second law requires that entropy of the universe (system + surroundings) never decreases; the system's entropy can decrease if the surroundings increase more.
The second law is a statement about the universe — system plus surroundings — not the system alone. A process where the system's entropy decreases (like water freezing or a protein folding into a compact structure) is perfectly spontaneous as long as the surroundings gain at least as much entropy. When you see a system become more ordered, immediately ask what's happening in the surroundings, not whether the process is allowed.
Common mistake
Wrong: Dissolving any substance always increases entropy because particles become more dispersed.
Right: Most dissolutions increase entropy, but highly ordered hydration shells (e.g., some ionic solutes) can decrease entropy of the solution; the sign of ΔS depends on the specific system.
Dispersing a solute into a solvent usually does increase entropy, but it's not automatic. When ions dissolve in water, they organize water molecules into tight hydration shells — this ordering of the solvent can actually decrease the net entropy of the solution. The sign of ΔS for dissolution depends on the balance between the gain in positional entropy of the solute and the ordering of solvent around it. For the MCAT, treat dissolution as usually positive ΔS but recognize that highly charged ions can be exceptions.
Common mistake
Gap: Misapplies Hess's law logic to entropy by treating elemental standard entropies as zero
ΔS°_rxn is calculated as Σ(S° products) − Σ(S° reactants) using tabulated absolute entropies, not formation values of zero for elements.
In enthalpy calculations, elements in their standard state have ΔHf° = 0 by definition, so you can treat them as a zero baseline. Entropy doesn't work that way. Every substance — including elemental oxygen, nitrogen, and carbon — has a real, nonzero absolute entropy at standard conditions, rooted in the third law. When calculating ΔS°_rxn, you must look up and include S° for every species, reactants and products alike, including pure elements.
Common mistake
Wrong: The sign of ΔS for a reaction can be predicted solely from whether the reaction is exothermic.
Right: The sign of ΔS is best predicted from changes in the number of moles of gas and phase changes, not from the sign of ΔH.
ΔH and ΔS measure completely different things — heat flow versus dispersal of energy and matter. A reaction can be exothermic and have positive ΔS, or endothermic with negative ΔS. The best predictor of ΔS sign is the change in moles of gas: more moles of gas as products → positive ΔS; fewer moles of gas → negative ΔS. Phase changes (solid to gas, etc.) are also strong signals. Train yourself to look at the balanced equation and count gas moles, not to read off the sign of ΔH.
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What the exam tests

  1. Recognizing entropy as a measure of microstates and dispersal, and applying the second law correctly — ΔS_universe ≥ 0 for any spontaneous process.
  2. Predicting whether ΔS is positive or negative for phase changes (solid → liquid → gas increases entropy), dissolution events, and reactions that produce or consume moles of gas.
  3. Understanding the third law: a perfect crystal at 0 K has zero entropy, which means absolute entropies can be tabulated and are always positive for real substances at standard conditions.
  4. Calculating ΔS°_rxn by summing the standard absolute entropies of products minus reactants (each multiplied by stoichiometric coefficients), and knowing this differs from how ΔHf° calculations treat elements.

Can you avoid these mistakes?

Liquid water freezes to ice at −10°C. Does this process violate the second law of thermodynamics? Explain your reasoning in terms of the system and the surroundings.
For the reaction N₂(g) + 3H₂(g) → 2NH₃(g), predict the sign of ΔS without doing any calculation. What is the dominant factor driving your prediction?
A table gives you S°(H₂, g) = 131 J/mol·K, S°(O₂, g) = 205 J/mol·K, and S°(H₂O, l) = 70 J/mol·K. Calculate ΔS°_rxn for 2H₂(g) + O₂(g) → 2H₂O(l). What would you have gotten wrong if you had set S°(H₂) and S°(O₂) to zero?
A student argues that dissolving NaCl in water must increase entropy because the ions are now spread throughout the solution. What's right about this reasoning and what important factor is it ignoring?

Related topics

First Law of Thermodynamics and Internal Energy Enthalpy and Hess's Law Calorimetry and Heat Capacity Gibbs Free Energy and Spontaneity

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