Chapter 21, Problem 75GQ

Interpretation Introduction

Interpretation: To calculate the value of standard Gibbs free energy of reaction $\left({\Delta }_r{\text{G}}^{\circ }\right)$ for given metal carbonates.

The relative tendency of given metal carbonates to decompose is to be stated also.

Concept introduction:

The change of Gibbs free energy to form one mole of a substance from its constituent elements when all the substances in the standard form is known as standard Gibbs free energy of formation $\left({\Delta }_f{\text{G}}^{\text{°}}\right)$.

The standard Gibbs free energy of reaction $\left({\Delta }_r{\text{G}}^{\circ }\right)$ in terms of standard Gibbs free energy of formation $\left({\Delta }_f{\text{G}}^{\text{°}}\right)$  is written as,

${\Delta }_r{\text{G}}^{\circ }={\displaystyle \sum {\Delta }_f{\text{G}}^{\circ }{}_{\text{products}}-{\displaystyle \sum {\Delta }_f{\text{G}}^{\circ }{}_{\text{reactants}}}}$ (1)

Answer to Problem 75GQ

The value of standard Gibbs free energy of reaction $\left({\Delta }_r{\text{G}}^{\circ }\right)$ for ${\text{MgCO}}_3$ is

 $64\text{.}9kJ\cdot mo{l}^{-1}$.

The value of standard Gibbs free energy of reaction $\left({\Delta }_r{\text{G}}^{\circ }\right)$ for ${\text{CaCO}}_{\text{3}}$ is

 $131\text{.}4kJ\cdot mo{l}^{-1}$.

The value of standard Gibbs free energy of reaction $\left({\Delta }_r{\text{G}}^{\circ }\right)$ for ${\text{BaCO}}_{\text{3}}$ is   

 $219\text{.}67kJ\cdot mo{l}^{-1}$.

The relative tendency of given carbonates to decompose is written as,

${\text{MgCO}}_{\text{3}}>{\text{CaCO}}_{\text{3}}>{\text{BaCO}}_{\text{3}}$

Explanation of Solution

If the value of standard Gibbs free energy of reaction $\left({\Delta }_r{\text{G}}^{\circ }\right)$ is positive then the reaction is reactant favored. If the value of standard Gibbs free energy of reaction $\left({\Delta }_r{\text{G}}^{\circ }\right)$ is negative then the reaction is product favored and spontaneous.

The value of standard Gibbs free energy of reaction $\left({\Delta }_r{\text{G}}^{\circ }\right)$ for the decomposition of given carbonates is calculated below.

Given:

Refer to the appendix L for the value of standard Gibbs free energy of formation $\left({\Delta }_f{\text{G}}^{\text{°}}\right)$.

The chemical reaction of decomposition of magnesium carbonate $\left({\text{MgCO}}_{\text{3}}\right)$ into $\text{MgO}$ and ${\text{CO}}_{\text{2}}$ is written as,

    ${\text{MgCO}}_{\text{3}}\left(\text{s}\right)\to \text{MgO}\left(\text{s}\right)+{\text{CO}}_{\text{2}}\left(\text{g}\right)$

The value of standard Gibbs free energy of formation $\left({\Delta }_f{\text{G}}^{\text{°}}\right)$ for $\text{MgO}$ is

$-568.93\text{kJ}\cdot {\text{mol}}^{-1}$.

The value of standard Gibbs free energy of formation $\left({\Delta }_f{\text{G}}^{\text{°}}\right)$ for ${\text{MgCO}}_3$ is

$-1028.2\text{kJ}\cdot {\text{mol}}^{-1}$.

The value of standard Gibbs free energy of formation $\left({\Delta }_f{\text{G}}^{\text{°}}\right)$ for ${\text{CO}}_{\text{2}}$ is

$-394.359\text{kJ}\cdot {\text{mol}}^{-1}$.

Substitute these values in equation (1) to calculate the value of standard Gibbs free energy of reaction $\left({\Delta }_r{\text{G}}^{\circ }\right)$ for ${\text{MgCO}}_3$

$\begin{array}{c}{\Delta }_r{\text{G}}^{\circ }=\left(-568.93\text{kJ}\cdot {\text{mol}}^{-1}\right)+\left(-394.359\text{kJ}\cdot {\text{mol}}^{-1}\right)-\left(1028.2\text{kJ}\cdot {\text{mol}}^{-1}\right)\\ =64.9\text{kJ}\cdot {\text{mol}}^{-1}\end{array}$

Therefore, the value of standard Gibbs free energy of reaction $\left({\Delta }_r{\text{G}}^{\circ }\right)$ for ${\text{MgCO}}_3$ is

 $64.9\text{kJ}\cdot {\text{mol}}^{-1}$.

The chemical reaction of decomposition of calcium carbonate $\left({\text{CaCO}}_{\text{3}}\right)$ into $\text{CaO}$ and ${\text{CO}}_{\text{2}}$ is written as,

    ${\text{CaCO}}_{\text{3}}\left(\text{s}\right)\to \text{CaO}\left(\text{s}\right)+{\text{CO}}_{\text{2}}\left(\text{g}\right)$

The value of standard Gibbs free energy of formation $\left({\Delta }_f{\text{G}}^{\text{°}}\right)$ for $\text{CaO}$ is

$-603.42\text{kJ}\cdot {\text{mol}}^{-1}$.

The value of standard Gibbs free energy of formation $\left({\Delta }_f{\text{G}}^{\text{°}}\right)$ for ${\text{CaCO}}_{\text{3}}$ is

$-1129.16\text{kJ}\cdot {\text{mol}}^{-1}$.

The value of standard Gibbs free energy of formation $\left({\Delta }_f{\text{G}}^{\text{°}}\right)$ for ${\text{CO}}_{\text{2}}$ is

$-394.359\text{kJ}\cdot {\text{mol}}^{-1}$.

Substitute these values in equation (1) to calculate the value of standard Gibbs free energy of reaction $\left({\Delta }_r{\text{G}}^{\circ }\right)$ for ${\text{CaCO}}_{\text{3}}$

$\begin{array}{c}{\Delta }_r{\text{G}}^{\circ }=\left(-603.42\text{kJ}\cdot {\text{mol}}^{-1}\right)+\left(-394.359\text{kJ}\cdot {\text{mol}}^{-1}\right)-\left(1129.16\text{kJ}\cdot {\text{mol}}^{-1}\right)\\ =131.4\text{kJ}\cdot {\text{mol}}^{-1}\end{array}$

Therefore, the value of standard Gibbs free energy of reaction $\left({\Delta }_r{\text{G}}^{\circ }\right)$ for ${\text{CaCO}}_{\text{3}}$ is

 $131.4\text{kJ}\cdot {\text{mol}}^{-1}$.

The chemical reaction of decomposition of barium carbonate $\left({\text{BaCO}}_{\text{3}}\right)$ into $\text{BaO}$ and ${\text{CO}}_{\text{2}}$ is written as,

    ${\text{BaCO}}_{\text{3}}\left(\text{s}\right)\to \text{BaO}\left(\text{s}\right)+{\text{CO}}_{\text{2}}\left(\text{g}\right)$

The value of standard Gibbs free energy of formation $\left({\Delta }_f{\text{G}}^{\text{°}}\right)$ for $\text{BaO}$ is

$-520.38\text{kJ}\cdot {\text{mol}}^{-1}$.

The value of standard Gibbs free energy of formation $\left({\Delta }_f{\text{G}}^{\text{°}}\right)$ for ${\text{BaCO}}_{\text{3}}$ is

$-1134.41\text{kJ}\cdot {\text{mol}}^{-1}$.

The value of standard Gibbs free energy of formation $\left({\Delta }_f{\text{G}}^{\text{°}}\right)$ for ${\text{CO}}_{\text{2}}$ is

$-394.359\text{kJ}\cdot {\text{mol}}^{-1}$.

Substitute these values in equation (1) to calculate the value of standard Gibbs free energy of reaction $\left({\Delta }_r{\text{G}}^{\circ }\right)$ for ${\text{BaCO}}_{\text{3}}$

$\begin{array}{c}{\Delta }_r{\text{G}}^{\circ }=\left(-520.38\text{kJ}\cdot {\text{mol}}^{-1}\right)+\left(-394.359\text{kJ}\cdot {\text{mol}}^{-1}\right)-\left(1134.41\text{kJ}\cdot {\text{mol}}^{-1}\right)\\ =219.67\text{kJ}\cdot {\text{mol}}^{-1}\end{array}$

Therefore, the value of standard Gibbs free energy of reaction $\left({\Delta }_r{\text{G}}^{\circ }\right)$ for ${\text{BaCO}}_{\text{3}}$ is

 $219.67\text{kJ}\cdot {\text{mol}}^{-1}$.

The relative tendency of metal carbonates to decompose is depended upon the value of standard Gibbs free energy of reaction $\left({\Delta }_r{\text{G}}^{\circ }\right)$ of the carbonate. The lesser the value of standard Gibbs free energy of reaction $\left({\Delta }_r{\text{G}}^{\circ }\right)$ of the metal carbonate, higher the tendency of metal carbonate to decompose.

Therefore, magnesium carbonate relatively decomposes faster than calcium carbonate and barium carbonate and calcium carbonate decompose faster than the barium carbonate. Hence, the relative tendency of given carbonates to decompose is written as,

${\text{MgCO}}_{\text{3}}>{\text{CaCO}}_{\text{3}}>{\text{BaCO}}_{\text{3}}$

Conclusion

The value of standard Gibbs free energy of reaction $\left({\Delta }_r{\text{G}}^{\circ }\right)$ for ${\text{MgCO}}_3$ is

 $64\text{.}9kJ\cdot mo{l}^{-1}$.

The value of standard Gibbs free energy of reaction $\left({\Delta }_r{\text{G}}^{\circ }\right)$ for ${\text{CaCO}}_{\text{3}}$ is

 $131\text{.}4kJ\cdot mo{l}^{-1}$.

The value of standard Gibbs free energy of reaction $\left({\Delta }_r{\text{G}}^{\circ }\right)$ for ${\text{BaCO}}_{\text{3}}$ is

 $219\text{.}67kJ\cdot mo{l}^{-1}$.

The relative tendency of given carbonates to decompose is written as,

${\text{MgCO}}_{\text{3}}>{\text{CaCO}}_{\text{3}}>{\text{BaCO}}_{\text{3}}$