Entropy and Enthalpy in Non-equilibrium Systems

• Enthalpy (H) is the heat content of a system.
• Entropy (S) is a measure of the distribution of available energy, but is also a measure of disorder.
• These determine whether a reaction is:
  • Spontaneous – Proceeds without needing a continual input of energy from an external source.
  • Non-spontaneous – Requires a continual input of energy from an external source.

The Gibbs free energy formula predicts the spontaneity of a reaction.

\Delta G\degree = \Delta H\degree - T\Delta S\degree

• If [katex]\Delta G\degree > 0[/katex], reaction is non-spontaneous.
• If [katex]\Delta G\degree = 0[/katex], system is at equilibrium.
• If [katex]\Delta G\degree < 0[/katex], reaction is spontaneous.

Combustion

Consider the complete combustion of octane.

C_8H_{18 (l)} + \frac{25}2 O_{2 (g)} \rightarrow 8CO_{2 (g)} + 9H_2O_{(l)}

• Combustion is exothermic as it always releases heat, i.e. [katex]\Delta H\degree < 0[/katex]
• Entropy can either be positive or negative, depending on the number of moles of gas on each side of the reaction
• For octane, entropy decreases as there are fewer moles of gas resulting from the reaction, i.e. [katex]\Delta S \degree < 0[/katex]

However, [katex]\Delta G\degree < 0[/katex] for all combustion reactions, regardless of temperature of molar ratios, as enthalpy is always extremely negative. Therefore, combustion is a spontaneous reaction.

Photosynthesis

6CO_{2 (g)} + 6H_2O_{(l)} \rightarrow C_6H_{12}O_{6 (aq)} + 6O_{2 (g)}

• Photosynthesis is endothermic, absorbing energy from the sun, i.e. [katex]\Delta H\degree > 0[/katex]
• Entropy decreases as there are 6 moles of gas on each side but more overall particles on the reactants size, i.e. [katex]\Delta S\degree < 0[/katex]

For photosynthesis, [katex]\Delta G\degree > 0[/katex] so it is a non-spontaneous reaction which requires a constant input of energy to proceed.