Total entropy change and feasibility

Entropy of the surroundings (spec 12.6, 12.8)

ΔStotal = ΔSsystem + ΔSsurroundings

ΔSsurroundings = -ΔH / T

Convert ΔH from kJ to J first. An exothermic reaction (ΔH negative) releases heat into the surroundings, so ΔSsurroundings is positive. The effect is larger at low temperature: the same amount of heat makes more difference to cold surroundings.

Feasibility (spec 12.9, 12.10)

A reaction is thermodynamically feasible when ΔStotal > 0, even if ΔSsystem or ΔSsurroundings is negative.

• Endothermic, ΔSsystem positive: feasible only above a certain temperature, found by setting ΔStotal = 0: T = ΔH / ΔSsystem (ΔH in J).
• Exothermic, ΔSsystem negative: feasible only below a certain temperature.
• Exothermic, ΔSsystem positive: feasible at all temperatures.

You may also meet ΔG = ΔH - TΔSsystem (feasible when ΔG < 0), which is the same idea multiplied by -T. It is not required.

Thermodynamic and kinetic stability (spec 12.11)

A positive ΔStotal says a reaction can happen, not how fast. If the activation energy is high, a feasible reaction may be too slow to notice: the reactants are kinetically stable (or kinetically inert). Methane and oxygen at room temperature, or diamond turning into graphite, are feasible but do not happen at a noticeable rate. A system is thermodynamically stable only when ΔStotal for its reaction is negative.

Worked example

CaCO3(s) -> CaO(s) + CO2(g): ΔH = +178 kJ mol^-1, ΔSsystem = +160.4 J mol^-1 K^-1. Is it feasible at 298 K? Above what temperature is it feasible?

1. ΔSsurroundings = -178 000 / 298 = -597.3 J mol^-1 K^-1
2. ΔStotal = 160.4 - 597.3 = -436.9 J mol^-1 K^-1, so not feasible at 298 K
3. T = ΔH / ΔSsystem = 178 000 / 160.4

Answer: Not feasible at 298 K; feasible above about 1110 K

Check yourself

1. Calculate ΔSsurroundings at 298 K for the Haber process, ΔH = -92.0 kJ mol^-1.
   Show answer

   +309 J mol^-1 K^-1. ΔSsurr = -(-92 000) / 298 = +309 J mol^-1 K^-1.

2. For N2O4(g) -> 2NO2(g), ΔH = +57.2 kJ mol^-1 and ΔSsystem = +175.8 J mol^-1 K^-1. Calculate ΔStotal at 298 K.
   Show answer

   -16.1 J mol^-1 K^-1. ΔSsurr = -57 200 / 298 = -191.9; ΔStotal = 175.8 + (-191.9) = -16.1 J mol^-1 K^-1, so it is not feasible at 298 K.

3. A reaction has ΔH = +178 kJ mol^-1 and ΔSsystem = +160.4 J mol^-1 K^-1. Calculate the minimum temperature at which it becomes feasible.
   Show answer

   1110 K. T = 178 000 / 160.4 = 1110 K.

4. A reaction is exothermic and has a negative ΔSsystem. How does raising the temperature affect its feasibility?
   • It becomes more feasible, because ΔSsystem increases
   • It becomes less feasible, because the positive ΔSsurroundings gets smaller
   • It has no effect
   • It always becomes feasible
   Show answer

   It becomes less feasible, because the positive ΔSsurroundings gets smaller. -ΔH/T is positive but shrinks as T rises, so eventually ΔStotal becomes negative.

5. Methane and oxygen do not react at room temperature, although ΔStotal is positive. What is the best description?
   • The mixture is thermodynamically stable
   • The reaction is endothermic
   • ΔSsystem is too large
   • The mixture is kinetically stable because the activation energy is high
   Show answer

   The mixture is kinetically stable because the activation energy is high. Feasible but very slow: a spark supplies the activation energy.

6. Which combination gives a reaction that is feasible at every temperature?
   • ΔH positive and ΔSsystem negative
   • ΔH negative and ΔSsystem positive
   • ΔH positive and ΔSsystem positive
   • ΔH negative and ΔSsystem negative
   Show answer

   ΔH negative and ΔSsystem positive. Both ΔSsystem and ΔSsurroundings are positive, so ΔStotal is always positive.

7. Why must ΔH in kJ mol^-1 be multiplied by 1000 before calculating ΔSsurroundings?
   • Temperature is in kelvin
   • ΔH is always negative
   • To make the answer positive
   • Entropy values are in J mol^-1 K^-1
   Show answer

   Entropy values are in J mol^-1 K^-1. Mixing kJ and J gives an answer 1000 times too small.

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Sources

• Pearson Edexcel IAL Chemistry (2018) specification
• Pearson Edexcel IAL Chemistry (2018) scheme of work

Last updated 7 November 2026. Spotted a mistake? Tell us.