\Delta G is net energy available to do useful work and is thus a measure of “free energy”. Show mathematically that \Delta G is a measure of free energy. Find the unit of \Delta G. If a reaction has positive enthalpy change and positive entropy change, under what condition will the reaction be spontaneous?

Answers (1)

We are aware of the equation that,

\Delta S_{tot}=\Delta S_{sys}+\Delta S_{surr}

The temperature of the system and surroundings will be equal if both are in equilibrium. Also, the enthalpy changes are inversely proportional in both of them.

We can represent the entropy changes in the surroundings as:

\Delta S_{Surr}=\Delta H_{surr}/T=-(\Delta H_{sys}/T)

\Delta S_{tot}=\Delta S_{sys}-(\Delta H_{sys}/T)

Hence, we can rewrite this as:

T\Delta S_{tot}=T\Delta S_{sys}- \Delta H_{sys}

In case of a spontaneous process:

-(\Delta H_{sys}-T\Delta S_{sys})>0,since \Delta S _{tot}>0

We can write the above equation as:

-\Delta G > 0

\Delta G = \Delta H - T \Delta S > 0

ΔG is the measure of free energy as it is the net available energy for performing some useful work.

Criteria for spontaneity:

\Delta G < 0: spontaneous process

\Delta G > 0: non-spontaneous process

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