Chapter 18, Problem 82IL

Interpretation Introduction

Interpretation:

The equilibrium constant for the formation of $\text{NiO}$ at $\text{1627 }°\text{C}$ should be calcualted under given conditions.

Concept introduction:

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

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

${\text{Δ}}_{\text{f}}{\text{G}}^{\text{o}}$ is related to the equilibrium constant $\text{K}$ by the equation,

  ${\text{Δ}}_{\text{f}}{\text{G}}^{\text{o}}{\text{= -RTlnK}}_{\text{p}}$

The rearranged expression is,

  ${\text{K}}_{\text{p}}{\text{= e}}^{\text{-}\frac{{\text{Δ}}_{\text{f}}{\text{G}}^{\text{o}}}{\text{RT}}}$

${\text{Δ}}_{\text{f}}{\text{G}}^{\text{o}}$ is also related to the reaction quotient $\text{Q}$ by the expression,

  ${\text{Δ}}_{\text{f}}{\text{G = Δ}}_{\text{f}}{\text{G}}^{\text{°}}\text{+RTlnQ}$

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

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