HELMHOLTZ & GIBBS FREE ENERGIES (1).pptx

It should be useful to you for understanding free energy( zHelmholt and Gibbs free energy). It is given by my lecturer.

1. HELMHOLTZ & GIBBS FREE ENERGIES: HELMHOLTZ & GIBBS FREE ENERGIES generally describe the Energy available to do work. In other words they measure the amount of energy in a system that can be converted into work such as, Mechanical work( e.g moving an object) Electrical work( e.g generating electricity) Chemical work( e.g driving a chemical reaction) They provide a measure of useful energy in a system taking into account the effects of temperature, volume and pressure. They predict, Spontaneity of process Equilibrium conditions(where the system will settle) Energy changes during a process.

2. Helmholtz free energy-work function The Helmholtz Free energy “A” is defined mathematically as, A = E-TS Where E is internal energy of the system. ‘T’ is its absolute temperature and ‘S’ is its entropy. Since, E, T and S are state functions. So, A should also be a state function. For a change in state at constant temperature, ∆A = ∆E - T ∆S Where ∆A is the increase in function A, ∆E is the increase in internal energy, and ∆S is the increase in entropy. Since, ∆S = q/ T, Now we have, ∆A = ∆E – q -----------eq(1 According to 1 st law of thermodynamics, ∆E = q – W -w = ∆E – q -----------eq (2) Comparing equation 1 & 2 - ∆A = W The quantity “A” is called free enrgy by Helmholtz, but now its usually called work function

3. The Gibbs free energy: Gibbs free energy , also known as the  Gibbs function, Gibbs energy, or free enthalpy , is a quantity that is used to measure the maximum amount of work done in a thermodynamic system when the temperature and pressure are kept constant. Gibbs free energy is denoted by the symbol ‘G’. Its value is usually expressed in Joules or Kilojoules. Gibbs free energy can be defined as the maximum amount of work that can be extracted from a closed system. T his property was determined by American scientist Josiah Willard Gibbs in the year 1876 when he was conducting experiments to predict the behaviour of systems when combined together or whether a process could occur simultaneously and spontaneously. Gibbs free energy was also previously known as “available energy.” It can be visualised as the amount of useful energy present in a thermodynamic system that can be utilised to perform some work. Mathematically, G = H -- TS The thermodynamic parameters ‘H’ ‘T’ and ‘S’ are state functions. So, ‘G’ should also be a state function. Enthalpy changes from H1 to H2 and entropy changes from S1 to S2. so the Gibbs free energy change from G1 to G2 G1 = H1 - TS11 ------------eq (1) G2 = H2 - TS2 -------------eq (2) Subtracting the above 2 equations G2 – G1 = (H2 - H1 ) –T (S2 - S1 ) ∆G = ∆H - T ∆S --------------eq (3) Since, ∆S = q/ T → T ∆S = q

4. When the pressure is constant then ∆H = ∆E + P∆V Putting the values of T ∆S and ∆H in equation 3 ∆G = (∆E + P∆V) –q ∆G = (∆E- q) + P ∆V ------(eq4) According to 1 st law of thermodynamics q = ∆E + W max ∆E- q = - W max Putting the above value in eq 4. ∆G = - W max + P ∆V - ∆G = Wmax - P∆V

5. To predict whether a given process will be spontaneous when carried out at constant pressure and temperature, we have to calculate ∆G ∆G Change in process/ ∆G is negative (∆G < 0) spontaneous ∆G is zero No net change, system is at equilibrium ∆G is positive (∆G > 0) Non spontaneous , reverse change is spontaneous

6. Importance of Gibbs free energy in chemistry: Gibbs free energy as useful work: Gibbs free energy is defined as, G = H -- TS ∆G = ∆H - T ∆S …....equation ( 1) ∆H = ∆E + P∆V Therefore, ∆G = ∆E + P∆V - T ∆S Since, ∆A = ∆E - T ∆S And ∆A = -Work(max) ….equation (2) Now, we can rewrite eq (1) by putting ∆A instead of ∆E - T ∆S ∆G = ∆A + P∆V Now, putting the value of ∆A from eq 2 in eq 1 ∆G = - Wmax + P ∆V ∆G = Wmax - P ∆V Net work = Wmax - P ∆V

7. Free energy as criterion of spontaneity: Gibbs free energy (G) is a state function defined with regard to system quantities only and may be used to predict the spontaneity of a process . A negative value for ΔG indicates a spontaneous process; a positive ΔG indicates a nonspontaneous process; and a ΔG of zero indicates that the system is at equilibrium.