Free Energy And Free Energy Change
Category : JEE Main & Advanced
Gibb's free energy (G) is a state function and is a measure of maximum work done or useful work done from a reversible reaction at constant temperature and pressure.
(1) Characteristics of free energy
(i) The free energy of a system is the enthalpy of the system minus the product of absolute temperature and entropy i.e., \[G=H-TS\]
(ii) Like other state functions E, H and S, it is also expressed as \[\Delta G\]. Also \[\Delta G=\Delta H-T\Delta {{S}_{system}}\]where \[\Delta S\]is entropy change for system only. This is Gibb's Helmholtz equation.
(iii) At equilibrium \[\Delta G=0\]
(iv) For a spontaneous process decrease in free energy is noticed i.e., \[\Delta G=-ve\].
(v) At absolute zero, \[T\Delta S\]is zero. Therefore if \[\Delta G\]is – ve, \[\Delta H\]should be – ve or only exothermic reactions proceed spontaneously at absolute zero.
(vi) \[\Delta {{G}_{system}}=T\Delta {{S}_{universe}}\], where \[\Delta H=0\]
(vii) The standard free energy change,
\[\Delta {{G}^{o}}=-2.303RT{{\log }_{10}}\,K,\] where K is equilibrium constant.
(a) Thus if \[K>1,\]then \[\Delta {{G}^{o}}=-ve\]thus reactions with equilibrium constant K>1 are thermodynamically spontaneous.
(b) If K<1, then \[\Delta {{G}^{o}}=+ve\] and thus reactions with equilibrium constant K<1 are thermodynamically spontaneous in reverse direction.
(2) Criteria for spontaneity of reaction : For a spontaneous change \[\Delta G=-ve\] and therefore use of \[\Delta G=\Delta H-T\Delta S,\]provides the following conditions for a change to be spontaneous.
Criteria for spontaneity of reaction
|
\[\Delta H\] |
\[\Delta S\] |
\[\Delta G\] |
Reaction characteristics |
Example |
|
– |
+ |
Always negative |
Reaction is spontaneous at all temperatures |
\[2{{O}_{3(g)}}\to 3{{O}_{2(g)}}\] |
|
+ |
– |
Always positive |
Reaction is non spontaneous at all temperatures |
\[3{{O}_{2(g)}}\to 2{{O}_{3(g)}}\] |
|
– |
– |
Negative at low temperature but positive at high temperature |
Reaction is spontaneous at low temperature but becomes non spontaneous at high temperature |
\[Ca{{O}_{(s)}}+C{{O}_{2(g)}}\to CaC{{O}_{3(s)}}\] |
|
+ |
+ |
Positive at low temperature but negative at high temperature |
Reaction is non spontaneous at low temperature but becomes spontaneous at high temperature |
\[CaC{{O}_{3(s)}}\to Ca{{O}_{(s)}}+C{{O}_{2(g)}}\] |
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