Chapter 4, Problem 4.2DQ

(a)

Interpretation Introduction

Interpretation:

Without doing calculation it should be checked that whether the presence of attractive interactions between gas molecules will raise or lower the molar Gibbs energy of a gas to its perfect value.

Concept introduction:

Free energy (Gibbs free energy) is the term that is used to explain the total energy content in a thermodynamic system that can be converted into work.  The free energy is represented by the letter G.  All spontaneous process is associated with the decrease of free energy in the system.  The equation given below helps us to calculate the change in free energy in a system.

  $\text{ΔG = }\Delta {\rm H}\text{- T}\Delta \text{S}$

Where,

  $\text{ΔG }$ is the change in free energy of the system

  $\Delta {\rm H}$ is the change in enthalpy of the system

  $\text{T}$ is the absolute value of the temperature

  $\Delta \text{S}$ is the change in entropy in the system

Gibb’s energy is an important factor which greatly affect the thermodynamic stability of a molecule or compound.

The relation between Gibbs energy with pressure is,

$\Delta G=V_{m}dP\boxed{\begin{array}{l}where,\\ P:pressure\\ V_m:Molarvolume\\ \Delta G:Gibbsenergychange\end{array}}$

Molar volume is related to the density,

$\text{Vm}\text{α}\frac{\text{1}}{\text{ρ}}\boxed{\begin{array}{l}\text{where,}\\ \text{Vm}\text{:}\text{molar}\text{volume}\\ \text{ρ}\text{:}\text{density}\end{array}}$

(b)

Interpretation Introduction

Interpretation:

Without doing calculation it should be checked that whether the presence of repulsive interactions between gas molecules will raise or lower the molar Gibbs energy of a gas to its perfect value.

Concept introduction:

Free energy (Gibbs free energy) is the term that is used to explain the total energy content in a thermodynamic system that can be converted into work.  The free energy is represented by the letter G.  All spontaneous process is associated with the decrease of free energy in the system.  The equation given below helps us to calculate the change in free energy in a system.

  $\text{ΔG = }\Delta {\rm H}\text{- T}\Delta \text{S}$

Where,

  $\text{ΔG }$ is the change in free energy of the system

  $\Delta {\rm H}$ is the change in enthalpy of the system

  $\text{T}$ is the absolute value of the temperature

  $\Delta \text{S}$ is the change in entropy in the system

Gibb’s energy is an important factor which greatly affect the thermodynamic stability of a molecule or compound.

The relation between Gibbs energy with pressure is,

$\Delta G=V_{m}dP\boxed{\begin{array}{l}where,\\ P:pressure\\ V_m:Molarvolume\\ \Delta G:Gibbsenergychange\end{array}}$

Molar volume is related to the density,

$\text{Vm}\text{α}\frac{\text{1}}{\text{ρ}}\boxed{\begin{array}{l}\text{where,}\\ \text{Vm}\text{:}\text{molar}\text{volume}\\ \text{ρ}\text{:}\text{density}\end{array}}$