Chapter 20, Problem 20.41P

(a)

Interpretation Introduction

Interpretation:

For the given $C{H}_{3}OH\left(l\right)$ formation reactions, the entropy ${\text{ΔS}}_{\text{rxn}}^{\text{o}}$ value has to be calculated.

Concept introduction:

Entropy is a thermodynamic quantity, which is the measure of randomness in a system.  The term entropy is useful in explaining the spontaneity of a process. For all spontaneous process in an isolated system there will be an increase in entropy. Entropy is represented by the letter ‘S’.  It is a state function.  The change in entropy gives information about the magnitude and direction of a process.  The entropy changes associated with a phase transition reaction can be found by the following equation.

  ${\text{ΔS}}_{\text{surr}}\text{}\text{=}\text{}\text{}\frac{{\text{ΔΗ}}_{\text{rxn}}^{\text{o}}}{\text{Τ}}$

Where,

  $\Delta {\rm H}$ 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

Entropy is the measure of randomness in the system.  Standard entropy change in a reaction is the difference in entropy of the products and reactants.  ${\text{(ΔS}}^{\text{°}}{}_{\text{rxn}}\text{)}$ can be calculated by the following equation.

  ${\text{ΔS}}^{\text{°}}{}_{\text{rxn}}\text{ = }{\displaystyle \sum \text{m }}{\text{S}}^{\text{°}}{}_{\text{Products}}-{\displaystyle \sum \text{n}}{\text{S}}^{\text{°}}{}_{\text{reactants}}$

Where,

  ${\text{S}}^{\text{°}}{}_{\text{reactants}}$ is the standard entropy of the reactants

  ${\text{S}}^{\text{°}}{}_{\text{Products}}$ is the standard entropy of the products

Standard entropy change in a reaction and entropy change in the system are same.

(b)

Interpretation Introduction

Interpretation:

The entropy ${\text{ΔS}}_{\text{univ}}^{\text{o}}$ has to be calculated and it has to be identified that whether the $C{H}_{3}OH\left(l\right)$ formation reaction is spontaneous at $298K$ or not.

Concept introduction:

Entropy$\left(\text{S}\right)$ : it is used to describe the disorder. It is the amount of arrangements possible in a system at a particular state. ${\text{ΔS}}_{\text{univ}}={\text{ΔS}}_{\text{sys}}+{\text{ΔS}}_{\text{surr}}$

Entropy is the measure of randomness in the system.  Standard entropy change in a reaction is the difference in entropy of the products and reactants.  ${\text{(ΔS}}^{\text{°}}{}_{\text{rxn}}\text{)}$ can be calculated by the following equation.

  ${\text{ΔS}}^{\text{°}}{}_{\text{rxn}}{\text{ = S}}^{\text{°}}{}_{\text{Products}}-{\text{ S}}^{\text{°}}{}_{\text{reactants}}$

Where,

  ${\text{S}}^{\text{°}}{}_{\text{reactants}}$ is the standard entropy of the reactants

  ${\text{S}}^{\text{°}}{}_{\text{Products}}$ is the standard entropy of the products

Standard entropy change in a reaction and entropy change in the system are same.

Enthalpy is the amount energy absorbed or released in a process.

The enthalpy change in a system $\text{(Δ}{{\rm H}}_{\text{sys}}\text{)}$ can be calculated by the following equation.

  ${\text{ΔH}}_{\text{rxn}}\text{ = }{\displaystyle \sum {\text{ΔH}}^{\text{°}}{}_{\text{produdcts}}}\text{-}{\displaystyle \sum {\text{ΔH}}^{\text{°}}{}_{\text{reactants}}}$

Where,

  ${\text{ΔH}}^{\text{°}}{}_{\text{reactants}}$ is the standard entropy of the reactants

  ${\text{ΔH}}^{\text{°}}{}_{\text{produdcts}}$ is the standard entropy of the products

Using the value for the change in enthalpy in a system and the temperature, we can calculate ${\text{ΔS}}_{\text{surr}}$

  ${\text{ΔS}}_{\text{surr}}\text{=-}\frac{{\text{ΔΗ}}_{\text{sys}}}{\text{T}}$   

Where,

  $\Delta {\rm H}$ 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