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Zorluk: OrtaEntropy, Free Energy and Reaction Spontaneity

A chemical reaction has a standard enthalpy change (ΔH∘\Delta H^\circ) of +75.0 kJ mol−1+75.0\text{ kJ mol}^{-1} and a standard entropy change (ΔS∘\Delta S^\circ) of +250 J K−1mol−1+250\text{ J K}^{-1}\text{mol}^{-1}. Calculate the minimum temperature in Kelvin (K\text{K}) at which this reaction becomes spontaneous.

Cevap: 300 K

Cevap

The minimum temperature at which the reaction becomes spontaneous is 300 K.
A chemical process becomes spontaneous when the Gibbs free energy change (ΔG∘\Delta G^\circ) is negative (ΔG∘<0\Delta G^\circ < 0). Setting ΔG∘=0\Delta G^\circ = 0 defines the threshold temperature for spontaneity. From ΔG∘=ΔH∘−TΔS∘\Delta G^\circ = \Delta H^\circ - T\Delta S^\circ, re-arranging gives T=ΔH∘ΔS∘T = \frac{\Delta H^\circ}{\Delta S^\circ}. Expressing ΔH∘\Delta H^\circ as 75000 J mol−175000\text{ J mol}^{-1} and ΔS∘\Delta S^\circ as 250 J K−1mol−1250\text{ J K}^{-1}\text{mol}^{-1} yields T=75000250=300 KT = \frac{75000}{250} = 300\text{ K}.

Adım Adım Çözüm

1
Convert standard enthalpy change ΔH∘\Delta H^\circ from kilojoules per mole to Joules per mole.
ΔH∘=75.0×103 J mol−1=75000 J mol−1\Delta H^\circ = 75.0 \times 10^3\text{ J mol}^{-1} = 75000\text{ J mol}^{-1}.
Units of enthalpy and entropy must be compatible (Joules) before performing calculation.
2
Apply the Gibbs free energy relationship ΔG∘=ΔH∘−TΔS∘\Delta G^\circ = \Delta H^\circ - T\Delta S^\circ at the spontaneity boundary condition ΔG∘=0\Delta G^\circ = 0.
0=ΔH∘−TΔS∘  ⟹  T=ΔH∘ΔS∘0 = \Delta H^\circ - T\Delta S^\circ \implies T = \frac{\Delta H^\circ}{\Delta S^\circ}.
A reaction is spontaneous when ΔG∘<0\Delta G^\circ < 0, making ΔG∘=0\Delta G^\circ = 0 the exact minimum temperature threshold.
3
Divide the enthalpy change in Joules per mole by the entropy change in Joules per Kelvin-mole.
T=75000 J mol−1250 J K−1mol−1=300 KT = \frac{75000\text{ J mol}^{-1}}{250\text{ J K}^{-1}\text{mol}^{-1}} = 300\text{ K}.
Dividing Joules by Joules per Kelvin yields the temperature in Kelvin.

Anahtar Kavram

Gibbs free energy and temperature dependence of reaction spontaneity
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Entropy, Free Energy and Reaction Spontaneity