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Difficulty: EasyEntropy, Free Energy and Reaction Spontaneity

Match each thermodynamic sign combination of enthalpy change (ΔH\Delta H) and entropy change (ΔS\Delta S) with its corresponding condition for reaction spontaneity.

  • ΔH<0\Delta H < 0 and ΔS>0\Delta S > 0Spontaneous at all temperatures (ΔG<0\Delta G < 0)
  • ΔH>0\Delta H > 0 and ΔS<0\Delta S < 0Non-spontaneous at all temperatures (ΔG>0\Delta G > 0)
  • ΔH<0\Delta H < 0 and ΔS<0\Delta S < 0Spontaneous only at low temperatures
  • ΔH>0\Delta H > 0 and ΔS>0\Delta S > 0Spontaneous only at high temperatures

Answer

The thermodynamic combinations match as follows: negative enthalpy change and positive entropy change match spontaneous at all temperatures; positive enthalpy change and negative entropy change match non-spontaneous at all temperatures; negative enthalpy change and negative entropy change match spontaneous only at low temperatures; positive enthalpy change and positive entropy change match spontaneous only at high temperatures.
A reaction is spontaneous when ΔG<0\Delta G < 0, according to the Gibbs free energy relationship ΔG=ΔH−TΔS\Delta G = \Delta H - T\Delta S. Combining a negative enthalpy change with a positive entropy change ensures ΔG\Delta G is negative at all temperatures. Combining a positive enthalpy change with a negative entropy change ensures ΔG\Delta G is positive at all temperatures. When enthalpy and entropy changes share the same sign, temperature dictates spontaneity: negative signs require low temperatures, while positive signs require high temperatures.

Step-by-Step Solution

1
Recall the Gibbs Free Energy equation
ΔG=ΔH−TΔS\Delta G = \Delta H - T\Delta S, where TT is temperature in Kelvin (T>0T > 0).
Reaction spontaneity depends on the sign of ΔG\Delta G; a process is spontaneous if ΔG<0\Delta G < 0.
2
Analyze each sign combination in the equation
1. Negative ΔH\Delta H and positive ΔS\Delta S gives ΔG=(−)−T(+)=(−)\Delta G = (-) - T(+) = (-), always spontaneous.
2. Positive ΔH\Delta H and negative ΔS\Delta S gives ΔG=(+)−T(−)=(+)\Delta G = (+) - T(-) = (+), always non-spontaneous.
3. Negative ΔH\Delta H and negative ΔS\Delta S gives ΔG=(−)+T(+)\Delta G = (-) + T(+), which is negative only at low TT.
4. Positive ΔH\Delta H and positive ΔS\Delta S gives ΔG=(+)−T(+)\Delta G = (+) - T(+), which is negative only at high TT.
Evaluating the magnitude of TΔST\Delta S relative to ΔH\Delta H determines the temperature dependency of spontaneity.

Key Concept

Gibbs Free Energy and Reaction Spontaneity
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Topics

Entropy, Free Energy and Reaction Spontaneity