Chapter 18, Problem 18.47QP

Interpretation Introduction

Interpretation:

Equilibrium pressure of $C{O}_2$ due to the decomposition of magnesium carbonate $\left(MgC{O}_3\right)$  at $25°C$ has to be calculated.

Concept Information:

Free energy change$\left(\Delta G\right)$: Change in the free energy takes place while reactants convert to product.

The value of standard free energy change ${\text{ΔG}}^{\text{ο}}$ of the given reaction is calculated by the formula,

${\text{ΔG}}^{\text{ο}}\text{=}{{\displaystyle \sum {\text{n}}_{\text{p}}{\text{ΔG}}_{\text{f}}^{\text{ο}}}}_{\left(\text{products}\right)}-{{\displaystyle \sum {\text{n}}_{\text{r}}{\text{ΔG}}_{\text{f}}^{\text{ο}}}}_{\left(\text{reactants}\right)}$

Where,

$\begin{array}{c}{\text{ΔG}}_{\text{f}}^{\text{ο}}{}_{\left(\text{reactants}\right)}\text{=}\text{the standard free energy of formation for the reactants}\\ {\text{ΔG}}_{\text{f}}^{\text{ο}}{}_{\left(\text{products}\right)}\text{=}\text{the standard free energy of formation for the products}\\ {\text{n}}_{\text{p}}\text{=}\text{number of products molecule}\\ {\text{n}}_{\text{r}}\text{=}\text{number of reactants molecule}\end{array}$

Change in the free energy can be determined by equilibrium pressure as follows:

$\begin{array}{c}\text{ΔG}°\text{=}-\text{RTln}{\text{K}}_P\\ \\ \text{where,}\\ \text{ΔG}°=\text{Standard free energy}\\ \text{R}\text{=}\text{Gas}\text{Constant}(\text{8}\text{.314 J/K mol})\\ T=\text{Temperature}\\ {\text{K}}_P\text{=}\text{Equlibrium}\text{Constant}at\text{constant}\text{pressure}\end{array}$