During the phase transition, at constant temperature, of a solid from one form to another, the change in molar volume, ΔV_m = 1.0 cm³ mol^-1 is independent of pressure. The change in molar Gibbs free energy, in units of J mol^-1, when the pressure is increased from 1 bar to 3 bars is

Concept:-

The molar Gibbs free energy (Gibbs energy) is a thermodynamic property of a substance that describes its potential to do non-mechanical work (such as chemical reactions) at constant temperature and pressure. It is denoted by the symbol "G" and is usually measured in joules per mole (J/mol) or sometimes in kilojoules per mole (kJ/mol).

Mathematically, the molar Gibbs free energy is defined as:

G = H - TS

dG = dH - Tds -SdT

dG = Vdp - SdT.....(1)

where:

• G is the molar Gibbs free energy,
• H is the molar enthalpy (total heat content) of the system,
• T is the absolute temperature in Kelvin,
• S is the molar entropy (a measure of randomness or disorder) of the system.

During phase change, the temperature of the system remains constant. dT=0

Thus, from equation (1) we get,

dG = Vdp

\(\left ( \frac{\partial G}{\partial n} \right )=V_mdp\)

\(\mu =V_mdp\).......(2)

Explanation:-

• Given, During the phase transition, at constant temperature, of a solid from one form to another, the change in molar volume, ΔVm = 1.0 cm3 mol-1 is independent of pressure.
• When the pressure is increased from 1 bar to 3 bars is, from equation (2) we get

\(\mu =V_mdp\)

\(\mu \) = 1.0 cm3 mol-1 × (3 bar - 1 bar)

= 1.0 × 2 cm3. mol-1. bar

= 2 × 10^-3 lit. atm. mol-1 (1cm3 = 10-3 lit and 1 atm = 1 bar)

= 2 × 10-3 × 10² J mol-1 (1 lit.atm = 100 J)

= 2 × 10-1J mol-1 

Conclusion:-

Hence, The change in molar Gibbs free energy, in units of J mol-1, when the pressure is increased from 1 bar to 3 bars is 2 × 10-1J mol-1