ChemistryPredicting Spontaneity from Enthalpy and Entropy
Atlas stands at a lab bench scattered with ice cubes melting in warm water, a glowing hand warmer packet, and a whiteboard showing the equation ΔG = ΔH − TΔS, gesturing toward a large thermometer as he explains why some reactions run on their own while others never do.
- Explain what it means for a chemical reaction to be spontaneous in thermodynamic terms.
- Identify how the signs of ΔH and ΔS each influence whether a reaction is spontaneous.
- Calculate Gibbs free energy change using ΔG = ΔH − TΔS and interpret the result.
- Predict how changing temperature shifts the spontaneity of reactions where ΔH and ΔS have the same sign.
- Compare the four enthalpy-entropy sign combinations and state the spontaneity outcome for each.
Key terms
- Spontaneous reaction
- A reaction that can proceed on its own without continuous outside energy input.
- Enthalpy change
- The heat flow of a reaction at constant pressure, symbolized delta H.
- Entropy change
- The change in a system's disorder or number of accessible arrangements, symbolized delta S.
- Gibbs free energy
- The quantity delta G equals delta H minus T delta S that predicts spontaneity.
- Crossover temperature
- The temperature where delta G equals zero, found from T equals delta H over delta S.
Spontaneity and the competing factors
A reaction is spontaneous when it can proceed without a continuous external push, though spontaneous says nothing about speed; diamond turning to graphite is spontaneous yet takes ages. Two factors compete to decide direction. Enthalpy change, delta H, tracks heat flow, and a negative value, meaning the reaction is exothermic, tends to favor spontaneity. Entropy change, delta S, tracks disorder, and a positive value, meaning more accessible arrangements, is favored by nature. These two influences do not always agree, so chemists need a single quantity that combines them and accounts for temperature.
Gibbs free energy and the four cases
Gibbs unified the factors as delta G equals delta H minus T delta S, where T is the absolute temperature. A negative delta G means spontaneous, positive means non-spontaneous, and zero means equilibrium. Four sign combinations follow. When delta H is negative and delta S is positive, the reaction is spontaneous at all temperatures. When delta H is positive and delta S is negative, it is never spontaneous. When both are negative it is spontaneous only at low temperature, and when both are positive only at high temperature. For the temperature-dependent cases, the spontaneity flips at the crossover temperature T equals delta H over delta S.
Worked examples
Find the temperature where delta G equals zero for delta H = +120 kJ/mol and delta S = +400 J/(mol K).
- Set delta G to zero so that delta H equals T delta S.
- Solve T equals delta H over delta S, converting delta H to joules: 120000 J.
- Divide: 120000 J divided by 400 J per K equals 300.
Answer: T = 300 K, the crossover from non-spontaneous below to spontaneous above.
For N2 + 3 H2 to 2 NH3 with delta H = -92 kJ and delta S = -198 J/K, describe spontaneity.
- Both delta H and delta S are negative, so delta G equals negative minus T times negative.
- At low T the negative delta H dominates and delta G is negative, so the reaction is spontaneous.
- At high T the positive T delta S term wins and delta G turns positive, crossing over near 92000 divided by 198.
Answer: Spontaneous at low temperatures, non-spontaneous above about 465 K.
Activity
Drag each reaction card into the correct spontaneity bin based on its ΔH and ΔS signs and the given temperature condition.
Practice
For delta H = -40 kJ and delta S = -130 J/K at 250 K, compute delta G and state whether the reaction is spontaneous.
Predict at which temperatures a reaction with positive delta H and positive delta S becomes spontaneous and explain.
Common mistakes to avoid
- Every exothermic reaction is spontaneousA negative delta H favors spontaneity but a sufficiently negative delta S can make delta G positive, especially at high temperature.
- Spontaneous means the reaction is fastSpontaneity describes thermodynamic feasibility, not rate, so a spontaneous reaction can still be extremely slow.
Check your understanding
A reaction has ΔH = +120 kJ/mol and ΔS = +400 J/(mol·K). At what temperature does ΔG = 0 for this reaction?
A student claims that any exothermic reaction (ΔH < 0) must be spontaneous. Which scenario proves this claim wrong?
For the reaction N₂(g) + 3 H₂(g) → 2 NH₃(g): ΔH = −92 kJ and ΔS = −198 J/K. Which statement best describes spontaneity?
Recap
A spontaneous reaction proceeds without continuous outside energy, though it may be slow. Enthalpy and entropy compete, and Gibbs free energy delta G equals delta H minus T delta S decides the outcome: negative is spontaneous, positive is not, zero is equilibrium. The signs of delta H and delta S define four cases, and temperature-dependent ones flip at T equals delta H over delta S.
Reflect
Why is it useful to know that a reaction can be thermodynamically spontaneous yet practically too slow to observe?