Chapter 18, Problem 32PS

(a)

Interpretation Introduction

Interpretation:

The ${\text{Δ}}_{\text{r}}{\text{G}}^{\text{°}}$ value for given reaction should be calculated by using ${\text{Δ}}_{\text{f}}{\text{G}}^{\text{o}}$ and should be identified that whether the given reaction is product favoured at equilibrium.

Concept introduction:

The Gibbs free energy or the free energy change is a thermodynamic quantity represented by ${\text{Δ}}_{\text{r}}{\text{G}}^{\text{°}}$. It can be calculated in a similar manner as entropy and enthalpy. The expression for the free energy change is:

  ${\text{Δ}}_{\text{r}}{\text{G}}^{\text{°}}\text{= }\sum {\text{nΔ}}_{\text{f}}{\text{G}}^{\text{°}}\left(\text{products}\right)\text{- }\sum {\text{nΔ}}_{\text{f}}{\text{G}}^{\text{°}}\left(\text{reactants}\right)$   

${\text{Δ}}_{\text{r}}{\text{G}}^{\text{°}}$ is related to the reaction quotient $\text{Q}$ by the expression,

  ${\text{Δ}}_{\text{r}}{\text{G = Δ}}_{\text{r}}{\text{G}}^{\text{°}}\text{+ RT lnQ}$

For a general reaction, $\text{aA + bB}\to \text{cC + dD}$

  $\text{Q = }\frac{{\left[\text{C}\right]}^{\text{c}}{\left[\text{D}\right]}^{\text{d}}}{{\left[\text{A}\right]}^{\text{a}}{\left[\text{B}\right]}^{\text{b}}}$

(b)

Interpretation Introduction

Interpretation:

The ${\text{Δ}}_{\text{r}}{\text{G}}^{\text{°}}$ value for given reaction should be calculated when partial pressure of carbon dioxide is $\text{0}\text{.10}\text{atm}$ in presence of both calcium carbonate and calcium oxide and identified that reaction is spontaneous under such given conditions.

Concept introduction:

The Gibbs free energy or the free energy change is a thermodynamic quantity represented by ${\text{Δ}}_{\text{r}}{\text{G}}^{\text{°}}$. It can be calculated in a similar manner as entropy and enthalpy. The expression for the free energy change is:

  ${\text{Δ}}_{\text{r}}{\text{G}}^{\text{°}}\text{= }\sum {\text{nΔ}}_{\text{f}}{\text{G}}^{\text{°}}\left(\text{products}\right)\text{- }\sum {\text{nΔ}}_{\text{f}}{\text{G}}^{\text{°}}\left(\text{reactants}\right)$   

${\text{Δ}}_{\text{r}}{\text{G}}^{\text{°}}$ is related to the reaction quotient $\text{Q}$ by the expression,

  ${\text{Δ}}_{\text{r}}{\text{G = Δ}}_{\text{r}}{\text{G}}^{\text{°}}\text{+ RT lnQ}$

For a general reaction, $\text{aA + bB}\to \text{cC + dD}$

  $\text{Q = }\frac{{\left[\text{C}\right]}^{\text{c}}{\left[\text{D}\right]}^{\text{d}}}{{\left[\text{A}\right]}^{\text{a}}{\left[\text{B}\right]}^{\text{b}}}$