The decomposition of calcium carbonate

${\mathrm{CaCO}}_3\left(\mathrm{s}\right)\to \mathrm{CaO}\left(\mathrm{s}\right)+{\mathrm{CO}}_2\left(\mathrm{g}\right)$ does not take place at room temperature.

Explain in terms of entropy changes why heating the calcium carbonate to a high temperature increases the likelihood of this reaction taking place.

In a closed system at high temperatures, the reactants and products are in equilibrium.

${\mathrm{CaCO}}_3\left(\mathrm{s}\right)\to \mathrm{CaO}\left(\mathrm{s}\right)+{\mathrm{CO}}_2\left(\mathrm{g}\right)$.

Explain the meaning of the term closed system.

In a closed system at high temperature, the reactants and products are in equilibrium.

${\mathrm{CaCO}}_3\left(\mathrm{s}\right)\to \mathrm{CaO}\left(\mathrm{s}\right)+{\mathrm{CO}}_2\left(\mathrm{g}\right)$.

Explain, in terms of entropy changes, what happens when the pressure on this system is increased.

In a closed system at high temperatures, the reactants and products are in equilibrium.

${\mathrm{CaCO}}_3\left(\mathrm{s}\right)\to \mathrm{CaO}\left(\mathrm{s}\right)+{\mathrm{CO}}_2\left(\mathrm{g}\right)$.

What is the value of the standard total entropy change at equilibrium?

Calculate the standard Gibbs free energy of a given reaction, using the standard molar entropy values given. Express your answer to $3$ significant figures in kJ ${\mathrm{mol}}^{-1},$ and in each case state whether or not the reaction is spontaneous under standard conditions.

Given:

$$\begin{gathered} {\mathrm{H}}_2\left(\mathrm{g}\right)+{\mathrm{Cl}}_2\left(\mathrm{g}\right)\to 2\mathrm{HCl}\left(\mathrm{g}\right); ∆{\mathrm{H}}_{\mathrm{reaction}}^{⊝}=-184.6 \mathrm{kJ} {\mathrm{mol}}^{-1} \\ \mathrm{Values} \mathrm{for} {\mathrm{S}}^{⊝}\mathrm{in} \mathrm{J} {\mathrm{K}}^{-1} {\mathrm{mol}}^{-1}; \\ \mathrm{HCl}\left(\mathrm{g}\right)=186.8 \\ {\mathrm{H}}_2\left(\mathrm{g}\right)=130.6 \\ {\mathrm{Cl}}_2\left(\mathrm{g}\right)=165. \end{gathered}$$

Given:

$$\begin{gathered} {\mathrm{CH}}_4\left(\mathrm{g}\right)+2{\mathrm{O}}_2\left(\mathrm{g}\right)\to {\mathrm{CO}}_2\left(\mathrm{g}\right)+2{\mathrm{H}}_2\mathrm{O}; ∆{\mathrm{H}}_{\mathrm{reaction}}^{⊝}=-890.3 \mathrm{kJ} {\mathrm{mol}}^{-1} \\ \mathrm{Values} \mathrm{for} {\mathrm{S}}^{⊝}\mathrm{in} \mathrm{J} {\mathrm{K}}^{-1} {\mathrm{mol}}^{-1}; \\ {\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right)=69.9 \\ {\mathrm{CO}}_2\left(\mathrm{g}\right)=213.6 \\ {\mathrm{O}}_2\left(\mathrm{g}\right)=205.0 \\ {\mathrm{CH}}_4\left(\mathrm{g}\right)=186.2. \end{gathered}$$

Calculate the standard Gibbs free energy of a given reaction, using the standard molar entropy values given. Express your answer to $3$ significant figures in $\mathrm{kJ} {\mathrm{mol}}^{-1}$, and in each case state whether or not the reaction is spontaneous under standard conditions.

Given:

$$\begin{gathered} 2\mathrm{Na}\left(\mathrm{s}\right)+{\mathrm{O}}_2\left(\mathrm{g}\right)\to {\mathrm{Na}}_2{\mathrm{O}}_2\left(\mathrm{s}\right); ∆{\mathrm{H}}_{\mathrm{reaction}}^{⊝}=-510.9 \mathrm{kJ} {\mathrm{mol}}^{-1} \\ \mathrm{Values} \mathrm{for} {\mathrm{S}}^{⊝}\mathrm{in} \mathrm{J} {\mathrm{K}}^{-1} {\mathrm{mol}}^{-1}; \\ {\mathrm{Na}}_2{\mathrm{O}}_2\left(\mathrm{s}\right)=95.0 \\ \mathrm{Na}\left(\mathrm{s}\right)=51.2 \\ {\mathrm{O}}_2\left(\mathrm{g}\right)=205.0. \end{gathered}$$

Calculate the standard Gibbs free energy of a given reaction, using the standard molar entropy values given. Express your answer to $3$ significant figures in $\mathrm{kJ} {\mathrm{mol}}^{-1}$, and in each case state whether or not the reaction is spontaneous under standard conditions.

$$\begin{gathered} \mathrm{Mg}\left(\mathrm{s}\right)+{\mathrm{Cl}}_2\left(\mathrm{g}\right)\to {\mathrm{MgCl}}_2\left(\mathrm{s}\right); ∆{\mathrm{H}}_{\mathrm{reaction}}^{⊝}=-641.3 \mathrm{kJ} {\mathrm{mol}}^{-1} \\ \mathrm{Values} \mathrm{for} {\mathrm{S}}^{⊝}\mathrm{in} \mathrm{J} {\mathrm{K}}^{-1} {\mathrm{mol}}^{-1}; \\ {\mathrm{MgCl}}_2\left(\mathrm{s}\right)=89.6 \\ \mathrm{Mg}\left(\mathrm{s}\right)=37.2 \\ {\mathrm{Cl}}_2\left(\mathrm{g}\right)=165. \end{gathered}$$

Calculate the standard Gibbs free energy of a given reaction, using the standard molar entropy values given. Express your answer to three significant figures $\mathrm{kJ} {\mathrm{mol}}^{-1}$, and in each case state whether or not the reaction is spontaneous under standard conditions.

$$\begin{gathered} {\mathrm{Ag}}_2{\mathrm{CO}}_3\left(\mathrm{s}\right)\to {\mathrm{Ag}}_2\mathrm{O}\left(\mathrm{s}\right)+{\mathrm{CO}}_2; ∆{\mathrm{H}}_{\mathrm{reaction}}^{⊝}=+167.5 \mathrm{kJ} {\mathrm{mol}}^{-1} \\ \mathrm{Values} \mathrm{for} {\mathrm{S}}^{⊝}\mathrm{in} \mathrm{J} {\mathrm{K}}^{-1} {\mathrm{mol}}^{-1}; \\ {\mathrm{Ag}}_2\mathrm{O}\left(\mathrm{s}\right)=121.3 \\ {\mathrm{CO}}_2=213.6 \\ {\mathrm{Ag}}_2{\mathrm{CO}}_3\left(\mathrm{s}\right)=167.4. \end{gathered}$$