# How would you define the concept of equilibrium in terms of free energy and entropy?

##### 2 Answers

#### Answer:

At equilibrium:

#### Explanation:

Consider the following equilibrium:

Initially we have

The total free energy of the system

As **equilibrium** , **minimum free energy**.

Regarding entropy

where

For much more details on this topic, watch this video on:

**Thermodynamics | Free Energy, Pressure & Equilibrium.**

At a general equilibrium,

An example of an equilibrium is a **phase transition**, such as vaporization, freezing, etc. Let's say we looked at **vaporization**, the liquid-vapor dynamic equilibrium at a boiling point.

That would be looking at the **enthalpy change** (e.g. **constant temperature**---the temperature stays the same until the substance fully vaporizes.

**ENTHALPY VS. TEMPERATURE, ENTROPY, PRESSURE, AND VOLUME**

From this equation we can derive the relationship between enthalpy change, *temperature*, *entropy*, *pressure*, and *volume* (*Physical Chemistry: A Molecular Approach, McQuarrie*):

#H = U + PV#

#\mathbf(dH = dU + d(PV))#

#= delq_"rev" + delw_"rev" + PdV + VdP#

Since

#= TdS - cancel(PdV + PdV) + VdP#

#color(blue)(dH = TdS + VdP)# or

#color(blue)(DeltaH = TDeltaS + VDeltaP)#

**ACHIEVING "THE" THERMODYNAMICS RELATIONSHIP**

Now, it would be nice to know how to rewrite

Therefore, an expression for Gibbs' free energy is a way to do it. We could start at the Maxwell relation, which is:

#\mathbf(dG = -SdT + VdP)#

At a constant temperature, the partial derivative of the Gibbs' free energy with respect to pressure is the volume (

#((delG)/(delP))_T = V#

Therefore, we can substitute to get:

#dH = TdS + ((delG)/(delP))_TdP#

Phase changes where you watch something while it boils is at a **constant atmospheric and vapor pressure** (stuff is vaporizing while the vapor pressure is equal to the atmospheric pressure) as well as a **constant temperature**.

Since the Gibbs' free energy is *supposed* to change with respect to pressure, when pressure *doesn't* change, at least for an ideal substance,

Therefore, for something boiling:

#dG_"vap" = 0 -> color(blue)(dH_"vap" = T_"vap"dS_"vap")# or

#DeltaG_"vap" = 0 -> color(blue)(DeltaH_"vap" = T_"vap"DeltaS_"vap")#

*So when something is boiling, if you know the enthalpy and the temperature, you should able to calculate the entropy if the pressure is also constant.*