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Based on syllabus of SYBSc Sem 3 , University of Mumbai. Free energy functions- Gibbs and Helmholtz Variation of Gibbs Free energy with temperature and pressure, Gibbs- Helmholtz equation, Partial Molal Properties, Chemical potential and its variation with temperature and pressure, Gibbs Duhem equation, Concept of fugacity and activity, van't Hoff reaction isotherm , van't Hoff reaction isochore.

- 1. 22 September2023 Dr. Aqeela Sattar Qureshi, Royal College , Mira Road CHEMICAL THERMODYNAMICS Semester : III PAPER 1 , UNIT - I
- 2. Chemical Thermodynamics • Chemical Thermodynamics deals with the application of the laws of thermodynamics to chemical system • FREE ENERGY FUNCTIONS • The concept of free energy gives the amount of available energy to perform useful work • The free energy change is used – to predict the spontaneous nature of a chemical process to study physical and chemical equilibria 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road
- 3. FREE ENERGY FUNCTIONS • HELMHOLTZ FREE ENERGY (A) • Introduced by German Physicist Hermann von Helmholtz (1821-1894) to define equilibrium at constant temeperature • Symbol ‘A’ is taken from German word ‘Arbeit’ which means work • Work function is defined as A = E – T S 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road
- 4. HELMHOLTZ FREE ENERGY (A) • Work function is defined as A = E – T S • ‘A’ is an extensive property • ‘’E’ and ‘S’ are state functions, independent of history , mechanism, path etc so A is also a state function • For an isothermal change from state 1 to state 2 • A1 = E1 – T S1 and A2 = E2 – T S2 • A2 - A1 = E2 – T S2 - E1 + T S1 • Δ A = Δ E – T ΔS 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road
- 5. HELMHOLTZ FREE ENERGY (A) 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road max max rev rev rev rev rev rev W A or W A work maximum to equal is associated work , reversibly out carried is process Since W A (3) and (2) equation Comparing q E W i.e W q E mics thermodyna of law first by But (2) - - - q E A (1) eqn in ng Substituti q S T T q S e temperatur constant at process reversible a For (1) - - - - S T E A ) 3 ( Thus decrease in Helmholtz free energy gives the maximum work that can be done by the system
- 6. GIBBS FREE ENERGY (G) • Introduced by American Physicist J. W. Gibbs (1839-1903) , it relates to net work done by the system • Gibbs free energy is defined as G = H– T S • ‘G’ is an extensive property • ‘G’ is also a state function • For an isothermal change from state 1 to state 2 • G1 = H1 – T S1 and G2 = H2 – T S2 • G2 - G1 = H2 – T S2 - H1 + T S1 • Δ G = Δ H – T ΔS 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road
- 7. GIBBS FREE ENERGY (G) 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road V P W G (3) and (2) equation Comparing q E W i.e W q E mics thermodyna of law first by But V P q E G q V P E G V P E H But q H G (1) eqn in ng Substituti q S T T q S e temperatur constant at process reversible a For (1) - - - - S T H G rev rev rev rev rev rev rev rev ) 3 ( ) 2 (
- 8. GIBBS FREE ENERGY (G) 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road net exp max exp max exp max max max rev rev W W W W W G V P W by given is pressure constant against gas of expansion to due done work But V P W G - OR V P W G W W work maximum to equal is associated work , reversibly out carried is process Since V P W G ) ( Thus decrease in Gibbs free energy gives the net work that can be done by the system
- 9. Relation between Gibb’s free energy and Helmholtz free energy • Gibbs free energy change ∆G is given by, ∆G = ∆H – T∆S -- (1) • Helmholtz free energy is given by , ∆A =∆E – T∆S -- (2) • But enthalpy change for a chemical reaction at constant pressure is given by, ∆H = ∆E + P∆V --(3) • Substituting (3) in equation (1) we get, • ∆G = ∆E + P∆V – T∆S ie. ∆G = ∆E – T∆S + P∆V • Since , ∆A = ∆E – T∆S • from equation (2), we get ∆G = ∆A + P∆V 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road
- 10. Significance of Gibb’s Free Energy 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road • The sign of ∆G helps to decide the nature of process ∆G < 0 process is spontaneous ∆G > 0 process is non-spontaneous ∆G = 0 process has reached equilibrium
- 11. Variation of Gibb’s free energy with Temperature and Pressure 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road • Gibb’s free energy is defined as G = H – TS - - (1) • By definition H = E + PV • Therefore G = E + PV – TS •For infinitesimal change, equation (1) can be written as, dG = dE + PdV + VdP – SdT - TdS -- (2) • From the first law of thermodynamics, dE = dq + dW • If work is of expansion type, then dw = - PdV • . . . dE = dq - PdV or dq= dE + PdV ---- (3)
- 12. Variation of Gibb’s Free Energy with Temperature and Pressure 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road • According to definition of entropy • dS= dqrev / T or dqrev = T.dS where, dS is infinitesimal entropy change for a reversible process substituting (3) • TdS = dE + PdV --- (4) • Substituting in eqn (2) • dG = dE + PdV + VdP – SdT - TdS -- (2) • dG = TdS + VdP – SdT - TdS dG = VdP – S.dT ----- (5)
- 13. Variation of Gibb’s Free Energy with Temperature and Pressure 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road The rate of change of Gibb’s free energy with temperature at constant pressure is equal to decrease in entropy of the system. The rate of change of Gibb’s free energy with respect to pressure at constant temperature is equal to increase in volume occupied by the system. V dP dG i.e VdP dG 0 dT , e temperatur constant At S dT dG i.e SdT - dG 0 dP , pressure constant At SdT VdP dG T P
- 14. GIBB’S HELMHOLTZ EQUATION 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road dT S S S S dT G d(G dT) (-S - dT -S dG dG dT S - dG and dT S - dG dT amount small by changed is e temperatur when energy free in changes the be dG and dG Let SdT - dG 0 dP , pressure constant At SdT VdP dG as be written can pressure and e temperatur h energy wit free s Gibb’ of Variation 1 2 2 1 1 2 1 2 1 2 2 2 1 1 2 1 ) ( ) ( )
- 15. GIBB’S HELMHOLTZ EQUATION 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road (1) - - - S dT G d dT S - G d dT S S S S dT G d(G 1 2 2 1 1 2 ) ( ) ( )
- 16. GIBB’S HELMHOLTZ EQUATION 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road change. energy free of t coefficien e Temperatur as knwon is dT G d term The equation Helmholtz Gibbs as known is equation Above dT G d T H G (1) equation in S - of value ng Substituti S) T(- H G i.e S T - H G by given is energy free in change e temperatur cosnstant At P P
- 17. GIBB’S HELMHOLTZ EQUATION 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road (1) - - - dT G d T 1 T G T G dT d dT G d T 1 T G T G dT d dT G d T 1 T 1 dT d G T G dT d pressure. constant at e temperatur to respect with T G ating differenti by obtained is equation Helmholtz Gibbs of form Another P P P 2 2 1
- 18. GIBB’S HELMHOLTZ EQUATION 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road ) 2 ( 2 2 P 2 2 P 2 2 P dT G d T 1 T H T G dT G d T T T H T G T by equation above Dividing dT G d T H G is equation Helmholtz Gibbs
- 19. PARTIAL MOLAL QUANTITY 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road equation Helmholtz Gibbs of form another is equation above The T H T G dT d T H T G T G T G dT d (2) and (1) equation Comparing 2 2 2 2
- 20. 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road ) .... , i n ...... , 3 n , 2 n , 1 n , P , T ( f X t. constituen various of amount and pressure e, temperatur on depend will x' ' then study for selected system of property extensive any is x' ' If ly. respective i .... 3 , 2 , 1 ts constituen of moles of no. the be i n 3 n , 2 n 1 n Let t constituen ith of consisting system open an Consider PARTIAL MOLAL QUANTITY
- 21. 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road i ....n n , P,n T, i 2 . ....n n , P,n T, 1 . ....n n , P,n T, i ....n n , P,n T, i 2 . ....n n , P,n T, 1 . ....n n , P,n T, . ,....n ,n T,n . ,....n ,n P,n dn n x dn n x dn n x dx Pressure, and e Temperatur constant At dn n x dn n x dn n x dP P x dT T x dx as be written can dx' ' system the in change small a For 1) - i ( 3 1 i 3 1 i 3 2 1) - i ( 3 1 i 3 1 i 3 2 i 2 1 i 2 1 i n ...... , 2 n , 1 n , P , T ( f X ....... ....... 2 1 2 1 ) PARTIAL MOLAL QUANTITY
- 22. 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road system. of n compositio the affect not does mole added the that system of quantity large a such to added is pressure and e temperatur constant at component particular of mole one when ... system of volume , enthalpy energy, free as such property in change the gives it that is quantity molar partial of ce significan physical The dn x dn x dn x dx property. the of symbol the over bar by writing d represente is It quantity. molal partial as known is n x term The dn n x dn n x dn n x dx i i 2 1 i ....n n , P,n T, i 2 . ....n n , P,n T, 1 . ....n n , P,n T, 1) - i ( 3 1 i 3 1 i 3 2 ...... .... 2 1 2 1 PARTIAL MOLAL QUANTITY
- 23. 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road dn V ........ dn V dn V dV dn n V dn n V dn n V dV , be l volume wil in change small pressure and e temperatur constant At volume. molal partial as known is n V uantity q the then property extensive the is volume If i i 2 2 1 1 i ...n ,n n P, T, 2 2 ...n ,n n P, T, 2 1 ...n , n P, T, 1 i 3 1 i 3 1 i 2 ...... ... PARTIAL MOLAL QUANTITY
- 24. CHEMICAL POTENTIAL 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road dn ........ dn dn dG ' ' by d represente is and potential chemical as known also is t I . G) ( energy free molal partial as known is n G uantity q dn n G dn n G dn n G dG , be ll energy wi free in change small pressure and e temperatur constant At ) n ..... n , n , n , P , T ( f G e i. property extensive an is system a of energy ree F i i 2 1 i ...n ,n n P, T, 2 2 ...n ,n n P, T, 2 1 ...n , n P, T, 1 i 3 2 1 i 3 1 i 3 1 i 2 2 1 ...... ...
- 25. Gibbs Duhem Equation 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road dn ........ dn dn dG ' ' by d represente is and potential chemical as known also is t I . G) ( energy free molal partial as known is n G uantity q dn n G dn n G dn n G dG , be ll energy wi free in change small pressure and e temperatur constant At ) n ..... n , n , n , P , T ( f G e i. property extensive an is system a of energy ree F i i 2 1 i ...n ,n n P, T, 2 2 ...n ,n n P, T, 2 1 ...n , n P, T, 1 i 3 2 1 i 3 1 i 3 1 i 2 2 1 ...... ...
- 26. 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road ) ) 1 ( ) ) ( ) 2 ( 2 1 2 1 2 1 2 2 1 1 2 1 2 1 i i 2 1 i i 2 1 i i 2 1 i i i i 2 2 1 1 i i 2 1 N P, T, i i 2 1 d n .... d n d (n dG dG dG by replaced be can eqn above in bracket first the eqn From d n .... d n d (n dn .... dn dn ( dG d n dn .... d n dn d n dn dG give, will (2) eqn of ation differenti Complete n) compositio definite N n ........ n n (G) be will (1) eqn of n integratio the n compositio definite has system the If (1) - - - dn ........ dn dn dG Gibbs Duhem Equation
- 27. 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road 2 1 2 1 2 1 2 1 2 1 0 0 0 ) d n n d d n d n d n d n is equation Duhem Gibbs mixture binary a For on. distillati as such equilibria liquid - Gas of study the in useful is equation Duhem Gibbs d n as be written also can equation above The equation. Duhem Gibbs as known is equation above The d n .... d n d n d n .... d n d (n dG dG 1 2 2 1 2 1 i i i i 2 1 i i 2 1 Gibbs Duhem Equation
- 28. 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road energy. free to equal is potential chemical substance pure any of mole 1 for Thus G , 1 n when 2) eqn N (G) be will equation Duhem Gibbs then substance pure i.e t constituen 1 only of consists system a If ve d then ve d if i.e t constituen 2nd of potential chemical the affects t constituen 1st of potential chemical that indicates equation Above d n n d N P, T, 1 2 ( . 2 1 2 1 Gibbs Duhem Equation
- 29. 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road V dP dG i.e VdP dG 0 dT , e temperatur constant At S dT dG i.e SdT - dG 0 dP , pressure constant At SdT VdP dG T P Effect of Temperature and Pressure on Chemical Potential
- 30. 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road i T i i T i i T dn dV dn dG P d d dn dV dP dG n d d n ' w.r.t equation above ating Differenti V dP dG ' Effect of Pressure on Chemical Potential i i V P d d
- 31. 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road i P i i P i i P dn dS dn dG T d d dn dS dT dG n d d n ' w.r.t equation above ating Differenti S dT dG ' Effect of Temperature on Chemical Potential i i S T d d
- 32. 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road CONCEPT OF FUGACITY AND ACTIVITY 1 2 1 2 ln ln 2 1 P P RT G P RT G G dP P RT dG equation, above g Integratin dP P RT dG P RT V , RT PV , gas ideal an For VdP dG e temperatur constant At SdT - VdP dG by given is pressure and e temperatur h energy wit free of variation The P P P P G G 2 1 2 1
- 33. 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road (2) - - - B lnf RT G by given is fugacity and energy free between relation The ' f ' symbol the by d represente is It substance. the of tendency escaping the measure to used is fugacity term The tendency. escaping as known is property This state. another into pass to tendency has state given a in substance every that suggested He fugacity. and activity as known parameters mic thermodyna new two introduced Lewis N. G. gases real for n calculatio energy free explain to order In gases. ideal for only valid is Equation P P RT G ) 1 ( ) 1 ( ln 1 2 CONCEPT OF FUGACITY AND ACTIVITY
- 34. 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road ) 4 ( ln ln ln ln 0 0 0 0 f f RT G - G f RT f RT G - G (2) equation from (3) equation g Subtractin (3) - - - B f RT G state standard in fugacity and energy free the be f and G Let condition. standard under done was G of ts measuremen all Hence . calculated be cannot B known, not is G of value absolute Since constant a is B where (2) - - - B lnf RT G 0 0 0 0 CONCEPT OF FUGACITY AND ACTIVITY
- 35. 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road (6) - - a a RT G a RT G a RT G G G a RT G G and a RT G G be will states two the for (5) equation the then a and a are activities when energies free are G and G If G G 1, a If a RT G G state. standard the in substance same the of fugacity the a to state given the in substance the of fugacity of ratio the as defined is activity Thus a'. ' by d represente is and activity as known is f f ratio The 0 0 1 2 0 2 0 1 2 1 2 1 0 0 1 2 1 2 2 1 0 ln ) ln ( ) ln ( ln ln ) 5 ( ln CONCEPT OF FUGACITY AND ACTIVITY
- 36. 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road a RT as be written can a RT G G i.e (5) equation G and 1 n substance, of mole 1 For activity. by replaced are ion concentrat whenever obtained are result exact more Hence solvent. with solutes of reactions and attraction mutual the ion considerat into take activities the solutions of case In possible. become ns calculatio exact pressure of place in used are activities when Thus, pressure. of place the takes activity that found is it (6) and (1) equation From (6) - - a a RT G and (1) - - P P RT G 0 ln ln ln ln 0 1 2 1 2 CONCEPT OF FUGACITY AND ACTIVITY
- 37. 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road Van’t Hoff’s Reaction Isotherm substance. indicated of potential chemical are s where be reaction the in part taking substances various of energy free molal partial the Let quantity molal partial of terms in exressed be must system of property mic thermodyna change, can n compositio ose mixture wh a is ion considerat under system the Since ..... mM L l .... B b aA reaction general the Consider , M , L , B , A ' ..... .... reactants. and product of pressures partial and G , G between relation the gives isotherm reaction Hoff t Van' 0
- 38. 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road Van’t Hoff’s Reaction Isotherm state standard in substance a of potential chemical is where a RT realtion following usign activity of terms in expressed be can state any in substance a of potetntial chemical The b a m l G G G G energy free in Change b a G m l G be will reactants and product of energy Free 0 0 B A M L reactant product B A reactant M L product ) 2 ( ln ) 1 ( .....) ( .....) ( ..... .....
- 39. 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road Van’t Hoff’s Reaction Isotherm state. standard their in are reaction the in involved substances the all n change whe energy free is G where a a a a RT G G a a a a RT b a m l G a RT b a RT a a RT m a RT l G be l energy wil free in change then (2) equation from derived expression ing correspond by replaced are (1) equation in of values the If 0 b B a A m M l L 0 b B a A m M l L B A M L B B A A M M L L M L B A ) 3 ( .... .... ln .... .... ln ..)] ( ..) [( .....] ) ln ( ) ln ( [ ...] ) ln ( ) ln ( [ .. , , , 0 0 0 0 0 0 0 0
- 40. 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road Van’t Hoff’s Reaction Isotherm state. standard for equation Hoff t Van' is (5) Equation (5) - - - Kp RT G G m equilibriu at process chemical a For isotherm. rxn Hoff t Van' as knwon are (4) and (3) Equation (4) - - - Kp RT G G Kp a a a a system gaseous of case in and constant m equilibriu as known is reactants & product of activities of ratio involving term The - - - a a a a RT G G 0 0 b B a A m M l L b B a A m M l L 0 ln 0 ln .... .... ) 3 ( .... .... ln
- 41. 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road Van’t Hoff’s Reaction Isochore T Kp T R T G T Kp RT T G pressure constant at e temperatur w.r.t (1) eqn ating Differenti (1) - - - Kp RT G is state standard for isotherm Hoff t Van' - - - a a a a RT G G P 0 P 0 0 b B a A m M l L 0 . ln ) ln ( ln ) 3 ( .... .... ln equation. Helmholtz Gibbs and isotherm Hoff t van' using obtained be can relation The e. temperatur and constant m equilibriu between relation the gives equation Hoff t Van'
- 42. 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road Van’t Hoff’s Reaction Isochore Kp RT T Kp RT T G T T by equation above g Multiplyin Kp R T Kp RT T G Kp T Kp T R T G T T Kp T Kp T R T G T Kp T R T G P 0 P 0 P 0 P 0 P 0 ln ln ln ln . ln ln . ln ln . ln 2
- 43. 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road Van’t Hoff’s Reaction Isochore ) 3 ( ) 2 ( ln ln ln ln 2 2 0 0 P 0 P 0 0 0 0 P 0 0 P 0 H G T G T T G T H G is state standard for equation Helmholtz Gibbs G T Kp RT T G T Kp RT G (1) equation From Kp RT T Kp RT T G T
- 44. 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road Van’t Hoff’s Reaction Isochore (5) - - RT H T Kp T Kp RT H hence negligible is H and H between difference reaction chemical a For state. std their in are substances the all hen pressure w constant at reaction of enthalpy is H equation above n I T Kp RT H G T Kp RT H G (3) and (2) equation Equating 0 0 0 0 0 0 2 2 2 2 ln ln ) 4 ( ln ln
- 45. 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road Van’t Hoff’s Reaction Isochore 2 1 1 2 1 2 2 1 1 2 2 2 303 . 2 ln 1 1 ln ln 1 ln . 1 ln ln 2 1 2 2 1 2 T T T T R H Kp Kp T T R H Kp Kp T R H Kp T T R H Kp : equation Hoff t Van' of n Integratio equation. Hoff t Van' as known is eqn Above (5) - - RT H T Kp T T Kp Kp T T Kp Kp 1 1
- 46. 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road Van’t Hoff’s Reaction Isochore T lnRT n T Kc T Kp e temperatur w.r.t eqution above ating Differenti lnRT n lnKc lnKp equation above of log Taking .(RT) Kc Kp equation following using by obtained be can volume constant at reaction of heat involving (5) eqn of form other The (5) - - RT H T Kp n ln ln ln 2
- 47. 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road Van’t Hoff’s Reaction Isochore ) 7 ( ln ln ln ln ) 6 ( ln ln ln ln 2 2 2 2 RT nRT - H T Kc T n RT H T Kc RT H T n T Kc (5) - - RT H T Kp (5) eqn and (6) equation Equating T n T Kc T Kp T lnRT n T Kc T Kp
- 48. 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road Van’t Hoff’s Reaction Isochore Isochore Hoff t Van' or equation Hoff t Van' as known is equation above The RT E T Kc (7) equation in ng Substituti E nRT - H nRT E H equation following the by volume constant at reaction of heat to related is pressure constant at reaction of heat The RT nRT - H T Kc 2 2 ln ) 7 ( ln
- 49. Reference Books : • Advanced Physical chemistry – Gurdeep Raj • Thermodynamics – A core course – 2nd edn by R.C. Srivastava • An introduction to chemical thermodynamics – 6th edn Rastogi & Misra • Advanced physical chemistry - D. N. Bajpai (S. Chand ) 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road Recommended Reading :
- 50. 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road