Spontaneity of reactions and free energy

In summary, there is no definitive proof that a reaction will occur at constant temperature if the change in Helmholtz free energy is negative or at constant temperature and pressure if the change in Gibbs free energy is negative. However, it is commonly accepted that the irreversibility of chemical reactions is caused by the dispersion of heat, momentum, mass, etc. at the macroscopic level, but at smaller scales, reactions can be considered reversible. This is why criteria such as \Delta H=0 and \Delta G=0 are still useful. Additionally, the energy equation and Legendre transform can also be used to determine the spontaneity of a reaction at constant temperature, pressure, and mass.
  • #1
jdstokes
523
1
Does anyone know of a clean proof that a reaction will occur at constant temperature if the change in Helmholtz free energy is negative, or at constant temperature and pressure if the change in Gibbs free energy is negative?

The only `proofs' I've found rely on the fact that the entropy change of the system is given by [itex]\Delta Q /T[/itex]. It seems to me as though this assumption is unjustified since the relation [itex]\Delta S = \Delta Q /T[/itex] holds only for reversibly exchanged heat, but chemical reactions are irreversible processes in general.
 
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  • #2
It's true that all real-life processes are irreversible. But as we narrow our focus from a laboratory to a calorimeter to a micro-scale region of gas to individual atoms, things look more and more reversible. After all, irreversibility is caused by smoothing of energy gradients over spatial regions, so let's consider only the smallest regions. Reactions are reversible at the molecular level; it's the dispersion of heat, momentum, mass, etc. to other areas that is irreversible. That's why the [itex]\Delta H=0[/itex] and [itex]\Delta G=0[/itex] criteria are still useful.

Another way of looking at it is that the energy equation [itex]dE=T\,dS-p\,dV+\sum\mu\,dN[/itex] holds for a system in equilibrium. As before, the closer we look, the more things look like they're at equilibrium. Now do a Legendre transform to get [itex]dG=-S\,dT+V\,dp+\sum\mu\,dN=0[/itex] at constant temperature, pressure, and mass, and we have your Gibbs free energy spontaneity criterion again.
 

1. What is the definition of spontaneity in chemical reactions?

Spontaneity in chemical reactions refers to the ability of a reaction to occur without any external influence or intervention. It is a measure of the natural tendency of a reaction to proceed in a certain direction.

2. How is the spontaneity of a reaction related to the concept of free energy?

The concept of free energy is closely related to spontaneity in chemical reactions. A spontaneous reaction is one that has a negative change in free energy, meaning that the products have lower energy than the reactants. This indicates that the reaction will occur without the need for an input of energy.

3. Can a non-spontaneous reaction be made spontaneous?

Yes, a non-spontaneous reaction can be made spontaneous through the use of an external energy source. This can be achieved by either increasing the temperature or by adding a catalyst to lower the activation energy of the reaction.

4. How can the spontaneity of a reaction be predicted?

The spontaneity of a reaction can be predicted by calculating the change in free energy (∆G) using the equation ∆G = ∆H - T∆S. If the value of ∆G is negative, the reaction is spontaneous, while a positive value indicates a non-spontaneous reaction.

5. What factors affect the spontaneity of a reaction?

The spontaneity of a reaction is influenced by several factors, including temperature, pressure, and concentration of reactants and products. Additionally, the presence of a catalyst or the use of a different solvent can also impact the spontaneity of a reaction.

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