 Chemistry Gibbs Energy and Spontaneity

### Topics Covered :

● Gibbs Energy and Spontaneity

### Gibbs energy and spontaneity :

=> We have seen that for a system, it is the total entropy change, color{purple}(DeltaS_text(total)) which decides the spontaneity of the process. But most of the chemical reactions fall into the category of either closed systems or open systems.

● Therefore, for most of the chemical reactions there are changes in both enthalpy and entropy.

● It is clear that neither decrease in enthalpy nor increase in entropy alone can determine the direction of spontaneous change for these systems.

● For this purpose, we define a new thermodynamic function the Gibbs energy or Gibbs function, color{purple}(G), as

color{purple}(G = H - TS) ..............(6.20)

● Gibbs function, color{purple}(G) is an extensive property and a state function.

● The change in Gibbs energy for the system color{purple}(DeltaG_text(sys)) can be written as

color{purple}(DeltaG_text(sys) = DeltaH_text(sys) - T DeltaS_text(sys) - S_text(sys) Delta T)

● At constant temperature, color{purple}(DeltaT = 0)

therefore color{purple}(DeltaG_text(sys) = DeltaH_text(sys) - T DeltaS_text(sys))

● Usually the subscript ‘system’ is dropped and we simply write this equation as color{purple}(DeltaG = DeltaH - T Delta S) .........(6.21)

● Thus, Gibbs energy change = enthalpy change – temperature × entropy change, and is referred to as the Gibbs equation, one of the most important equations in chemistry.

● Here, we have considered both terms together for spontaneity : energy (in terms of color{purple}(DeltaH)) and entropy (color{purple}(DeltaS), a measure of disorder) as indicated earlier.

● Dimensionally if we analyse, we find that color{purple}(DeltaG) has units of energy because, both color{purple}(DeltaH) and the color{purple}(TDeltaS) are energy terms, since color{purple}(TDeltaS = (K) (J//K) = J).

=> Now let us consider how color{purple}(DeltaG) is related to reaction spontaneity. We know

color{purple}(DeltaS_text(total) = DeltaS_text(sys)+DeltaS_text(surr))

● If the system is in thermal equilibrium with the surrounding, then the temperature of the surrounding is same as that of the system.

● Also, increase in enthalpy of the surrounding is equal to decrease in the enthalpy of the system.

● Therefore, entropy change of surroundings,

color{purple}(DeltaS_text(surr) = (DeltaH_text(surr))/T = - (DeltaH_text(sys))/T)

color{purple}(DeltaS_text(total) = DeltaS_text(sys) + ( -DeltaH_text(sys))/T)

Rearranging the above equation :

color{purple}(TDeltaS_text(total) = T DeltaS_text(sys) - DeltaH_text(sys))

● For spontaneous process, color{purple}(DeltaS_text(total) > 0 ), so color{purple}(T Delta S_text(sys) - DeltaH_text(sys) > 0)

=> - color{purple}(( DeltaH_text(sys) - T Delta S_text(sys) ) > 0)

● Using equation 6.21, the above equation can be written as

color{purple}(- DeltaG > 0)

color{purple}(DeltaG = DeltaH - T Delta S < 0) ...........(6.22)

=> color{purple}(DeltaH_text(sys)) is the enthalpy change of a reaction, color{purple}(TDeltaS_text(sys)) is the energy which is not available to do useful work.

=> So color{purple}(DeltaG) is the net energy available to do useful work and is thus a measure of the ‘free energy’. For this reason, it is also known as the free energy of the reaction.

=> color{purple}(DeltaG) gives a criteria for spontaneity at constant pressure and temperature.

(i) If color{purple}(DeltaG) is negative (< 0), the process is spontaneous.

(ii) If color{purple}(DeltaG) is positive (> 0), the process is non spontaneous.

color{red}("Note ") If a reaction has a positive enthalpy change and positive entropy change, it can be spontaneous when color{purple}(TDeltaS) is large enough to outweigh color{purple}(DeltaH). This can happen in two ways :

(a) The positive entropy change of the system can be ‘small’ in which case color{purple}(T) must be large.

(b) The positive entropy change of the system can be ’large’, in which case color{purple}(T) may be small.

● The former is one of the reasons why reactions are often carried out at high temperature.

● Table 6.4 summarises the effect of temperature on spontaneity of reactions. 