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2.5.13 · D5Thermodynamics (Chemical)

Question bank — Standard entropy S° and ΔS_rxn = Σ S°(products) − Σ S°(reactants)

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Before you start, the vocabulary these questions assume (all built in the parent):

  • = standard molar entropy — entropy of 1 mole, pure, at 1 bar and (usually) 298 K, in .
  • = number of microstates (distinct microscopic arrangements) for one macroscopic state; .
  • = entropy of products minus entropy of reactants, each weighted by its coefficient .
  • — the quantity the Second Law insists is .

True or false — justify

TRUE or FALSE: Elements in their standard state have .
FALSE — that rule belongs to . Entropy is absolute (Third Law), so every real substance including () has a positive .
TRUE or FALSE: A perfect crystal at 0 K has exactly one microstate.
TRUE — every atom sits in a single fixed arrangement, so and . This is the anchor point that makes absolute.
TRUE or FALSE: If , the reaction cannot occur.
FALSE — spontaneity is judged by , not the system alone. An exothermic reaction heats the surroundings, raising enough to keep .
TRUE or FALSE: depends on the reaction pathway you choose.
FALSE — entropy is a state function, so depends only on the start and end states. That is exactly why simple subtraction of tabulated works.
TRUE or FALSE: Heavier, larger molecules generally have larger than smaller ones.
TRUE — more atoms and heavier atoms mean more vibrational and rotational modes, so more ways to distribute energy → larger → larger .
TRUE or FALSE: Two reactions with the same change in moles of gas must have identical .
FALSE — the gas-mole rule only predicts the sign and rough magnitude. The actual depends on which specific gases and condensed phases are involved.
TRUE or FALSE: can be negative for some very ordered solids.
FALSE — a real substance at K always has , so . Only the idealized 0 K perfect crystal reaches exactly zero.
TRUE or FALSE: Dissolving a solid in water always increases entropy.
MOSTLY, but not always — mixing usually raises entropy, yet highly charged ions can order water molecules so tightly ("solvation shells") that comes out negative.

Spot the error

Student writes but forgot to check units and reports it as kJ/K. Where's the trap?
The formula is fine; the error is units — tabulated is in J K⁻¹ mol⁻¹, so the answer is in J/K, not kJ/K. Convert only when combining with in .
For a student computes . What's wrong?
The stoichiometric coefficients are missing — it should be . Entropy is extensive, so 3 mol of carries the entropy.
A student says " is positive, so must be negative." What's the logic slip?
has two terms — a positive helps but and decide the outcome. A large positive can still leave at low .
Someone predicts the sign of by counting total moles (solids + liquids + gases). Why is this shaky?
Condensed phases have small, similar entropies, so counting them dilutes the signal. The dominant contributor is gas moles; count those first for a reliable sign.
A student integrates from 298 K instead of 0 K to get . What breaks?
They lose the absolute reference — the Third Law's at 0 K is the whole point. Starting at 298 K only gives a change, not the true absolute entropy.

Why questions

Why is absolute while is only relative to elements?
The Third Law provides a genuine zero ( for a perfect crystal at 0 K), so integrating heat capacity upward gives a true absolute value. Enthalpy has no such natural zero, so we define elements as the reference.
Why does making a gas from a solid usually dominate the sign of ?
A gas has vastly more microstates (molecules free to occupy huge volumes and momenta) than a rigid solid. Creating even one mole of gas floods the system with arrangements, overwhelming small changes among condensed phases.
Why multiply each by its stoichiometric coefficient ?
Entropy is an extensive property — 2 mol has twice the entropy of 1 mol. The coefficient counts how many moles of each species appear, so it scales that species' contribution.
Why can an exothermic reaction with still be spontaneous?
The heat released raises the surroundings' entropy: is positive for exothermic reactions. If outweighs the negative , then .
Why does heating limestone () make it decompose?
The reaction has , so the term grows more negative as rises. Above , this term overtakes the positive and turns negative.
Why does a higher temperature increase a substance's entropy?
More thermal energy lets molecules access more energy levels and vibrational states, so grows. By , larger means larger .

Edge cases

For an isomerization with equal gas moles on both sides, what is ?
Not necessarily zero — the mole count is unchanged so the gas rule gives no signal, but and have different values from different structures, so , usually small but nonzero.
What is for a reaction with no gases and equal total moles of similar solids?
It will be small in magnitude (condensed phases have similar ) but generally not exactly zero. You must use the tabulated numbers; the gas shortcut is silent here.
A reaction runs at 0 K (hypothetically) — what happens to the term in ?
The term vanishes (), so . At absolute zero, entropy effects disappear entirely and only enthalpy decides direction.
Does forming a liquid from two gases give positive or negative ?
Negative — moving from the highly disordered gas phase to a condensed liquid sharply reduces . Fewer microstates means the entropy of that step drops.
For a reaction where exactly, does affect spontaneity?
No — with , the term is zero at every temperature, so and the sign of alone fixes spontaneity for all .
What is for a reaction exactly at equilibrium?
Exactly zero — at equilibrium there is no net driving force, so the total entropy of the universe is momentarily stationary (, equivalently ).

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