Chemistry S OF THE UNIVERSE AND G OF THE SYSTEM AS CRITERIA OF SPONTANEITY

Please Wait... While Loading Full Video

S OF THE UNIVERSE AND G OF THE SYSTEM AS CRITERIA OF SPONTANEITY

`S` of the Universe and `G` of the System as Criteria for Spontaniety :

A new thermodynamic state function `G`, the Gibbs free energy is defined as :

`G = H -TS`

at constant temperature and pressure

`Delta G = Delta H - T Delta S`

If `(Delta G)_(T, P) < P` process is irreversible (spontaneous)

`(Delta G)_(T, P) = 0` process is reversible

`(Delta G)_(T, P) > 0` process is impossible (non spontaneous)

The use of Gibbs free energy has the advantage that it refers to the system only (and not surroundings).

To summaries, the spontaneity of a chemical reaction is decided by two factors taken together:

(i) the enthalpy factor and (ii) the entropy factor

The equation `Delta G = Delta H - T Delta S` takes both the factors into consideration.

See fig.

A new thermodynamic state function `G`, the Gibbs free energy is defined as :

`G = H -TS`

at constant temperature and pressure

`Delta G = Delta H - T Delta S`

If `(Delta G)_(T, P) < P` process is irreversible (spontaneous)

`(Delta G)_(T, P) = 0` process is reversible

`(Delta G)_(T, P) > 0` process is impossible (non spontaneous)

The use of Gibbs free energy has the advantage that it refers to the system only (and not surroundings).

To summaries, the spontaneity of a chemical reaction is decided by two factors taken together:

(i) the enthalpy factor and (ii) the entropy factor

The equation `Delta G = Delta H - T Delta S` takes both the factors into consideration.

See fig.

Variation of Gibb's function (`G`) with temperature and pressure :

`G = H-TS`

`= U + PV - TS`

`dG = dU + PdV - TdS +VdP - SdT`

`dG = VdP - SdT`

(A) `text(At constant temperature)` `(dT = 0)`

for every substance, `dG = VdP ` or `((delG)/(delP))_P = V`

(i) For an ideal gas, at constant temperature

`dT =0 ` and `V = (nRT)/P`

So, `dG = (nRT)/P dp = nRTln (P_2/P_1)`

(ii) For solids/liquids, at constant temperature

`dT = 0` and `V` is almost constant change in pressure

So, `dG = VdP` [`V` = constant]

`Delta G = V(P_2 - P_1)`

(B) At constant pressure, `dP = 0`

For any substance `dG = -SdT`

`((delG)/(delT))_P = -S`

If in a question, given that `S = f(T)`, by integrating `Delta G` can be calculate.

`text(Relationship between)` `Delta G` & `w_text(non- PV)`

Decrease in Gibb's function at constant temperature and pressure in a process given an estimate or measure of maximum non-`PV` work which can be obtained from system in reversible, manner. The example of non-`PV` work is electric work done by chemical battery. Expansion of soap bubble at for a closed system capable of doing non-`PV` work apart from `PV` work first law can be written as

`dU = q + w_(PV) + w_(non- PV)` for reversible process at constant `T` & `P`

`dU + PdV - TdS = w_text(non-PV)`

`dH- TdS = w_text(non-PV)`

`(dG_text(system)_(T, P) = w_text(non-PV)`

`-( dG_text(system)_(T, P) = (w_text(non-PV))_text(system)`

Non-`PV` work done by the system = decrease in gibbs free energy.

Non-`PV` work done `dU` to chemical energy transformation of due to composition change and decrease in Gibb's function in a isothermal and isobaric process provide a measure of chemical energy stored in bonds and intermolecular interaction energy of molecules.

`text(Some facts to be remembered)` :

(a) Standard condition

(i) For gases/solid /liquid : `P = 1` bar

(ii) For ion/substance in solution : concentration = `1` `M`

(b) `DeltaG_r = (DeltaG_f)_text(product) - (DeltaG_f)_text(reactant)`

`DeltaH_r = (DeltaH_f)_text(product) - (DeltaH_f)_text(reactant)`

`DeltaS_r = (DeltaS_f)_text(product) - (DeltaS_f)_text(reactant)`

`G = H-TS`

`= U + PV - TS`

`dG = dU + PdV - TdS +VdP - SdT`

`dG = VdP - SdT`

(A) `text(At constant temperature)` `(dT = 0)`

for every substance, `dG = VdP ` or `((delG)/(delP))_P = V`

(i) For an ideal gas, at constant temperature

`dT =0 ` and `V = (nRT)/P`

So, `dG = (nRT)/P dp = nRTln (P_2/P_1)`

(ii) For solids/liquids, at constant temperature

`dT = 0` and `V` is almost constant change in pressure

So, `dG = VdP` [`V` = constant]

`Delta G = V(P_2 - P_1)`

(B) At constant pressure, `dP = 0`

For any substance `dG = -SdT`

`((delG)/(delT))_P = -S`

If in a question, given that `S = f(T)`, by integrating `Delta G` can be calculate.

`text(Relationship between)` `Delta G` & `w_text(non- PV)`

Decrease in Gibb's function at constant temperature and pressure in a process given an estimate or measure of maximum non-`PV` work which can be obtained from system in reversible, manner. The example of non-`PV` work is electric work done by chemical battery. Expansion of soap bubble at for a closed system capable of doing non-`PV` work apart from `PV` work first law can be written as

`dU = q + w_(PV) + w_(non- PV)` for reversible process at constant `T` & `P`

`dU + PdV - TdS = w_text(non-PV)`

`dH- TdS = w_text(non-PV)`

`(dG_text(system)_(T, P) = w_text(non-PV)`

`-( dG_text(system)_(T, P) = (w_text(non-PV))_text(system)`

Non-`PV` work done by the system = decrease in gibbs free energy.

Non-`PV` work done `dU` to chemical energy transformation of due to composition change and decrease in Gibb's function in a isothermal and isobaric process provide a measure of chemical energy stored in bonds and intermolecular interaction energy of molecules.

`text(Some facts to be remembered)` :

(a) Standard condition

(i) For gases/solid /liquid : `P = 1` bar

(ii) For ion/substance in solution : concentration = `1` `M`

(b) `DeltaG_r = (DeltaG_f)_text(product) - (DeltaG_f)_text(reactant)`

`DeltaH_r = (DeltaH_f)_text(product) - (DeltaH_f)_text(reactant)`

`DeltaS_r = (DeltaS_f)_text(product) - (DeltaS_f)_text(reactant)`

SiteLock