Question

Prove that DeltaG=DeltaH- -TDeltaS​

Answer 1

Explanation:

Energy

Lesson Objectives

Define Gibbs free energy, and be able to calculate the change in Gibbs free energy for a given process when provided with the appropriate data.

Use the value for Gibbs free energy to predict whether a reaction will occur spontaneously.

Lesson Vocabulary

Gibbs free energy: A thermodynamic quantity that combines enthalpy and entropy into a single value in order to predict whether or not a process is spontaneous.

Check Your Understanding

What must be true for a reaction to be considered spontaneous?

Gibbs Free Energy

We have learned that a spontaneous reaction must increase the total entropy in the universe:

ΔSuniv>0

. To analyze the entropic effects of a given process, we generally break this quantity down into two separate components. This is expressed with the following equation:

ΔSuniv=ΔSsys+ΔSsurr>0

In general, the entropy change for a chemical reaction or phase change can be easily determined from standard entropy values. Additionally, we saw in the previous lesson that the following relationship is true:

ΔSsurr=−ΔHsysT

Substituting this into the above equation, we get the following:

ΔSuniv=ΔSsys−ΔHsysT>0

This equation can then be rearranged as follows:

TΔSuniv−TΔSuniv==−ΔHsys+TΔSsys>0ΔHsys−TΔSsys<0

Now we can talk about the entropy changes in the universe simply by looking at data about the system of interest. If the results of the equation are less than zero, the reaction will be spontaneous. The American physicist Josiah Gibbs took this idea and introduced a thermodynamic quantity that combines enthalpy and entropy into a single value that has been named after him. Gibbs free energy is defined by the following equation:

ΔG=ΔHsys−TΔSsys

where

ΔG

is the change in free energy,

ΔH

is the change in enthalpy,

T

is the temperature (in Kelvin), and

ΔS

is the change in entropy. As we can see by comparing this to the derived equations above, the value of

ΔG

must be less than zero for a spontaneous process. Stated another way, systems have a natural tendency to move towards a minimum amount of free energy.