Chapter 18.7, Problem 2Q

Interpretation Introduction

Interpretation:

The mathematical relationship between ${\text{Δ}}_{\text{r}}{\text{G}}^{\text{°}}$ and ${\text{Δ}}_{\text{r}}{\text{G}}^{\text{°}}{}^{\text{'}}$ for the given reaction should be identified.

Concept introduction:

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

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

${\text{Δ}}_{\text{r}}{\text{G}}^{\text{o}}$ is related to ${\text{Δ}}_{\text{r}}{\text{G}}^{\text{°}}{}^{\text{'}}$ by the expression,

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

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

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