Lawrie Ryan and Roger Norris Solutions for Chapter: Entropy and Gibbs Free Energy, Exercise 10: Question

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:

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

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:

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

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.

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

Methanol reacts with hydrogen bromide.

$$\begin{gathered} {\mathrm{CH}}_3\mathrm{OH}\left(\mathrm{l}\right)+\mathrm{HBr}\left(\mathrm{g}\right)\to {\mathrm{CH}}_3\mathrm{Br}\left(\mathrm{g}\right)+{\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right);∆{\mathrm{H}}^{⊝}=-46 \mathrm{kJ} {\mathrm{mol}}^{-1}. \\ \mathrm{Standard} \mathrm{molar} \mathrm{entropy} \mathrm{values}(\mathrm{in} \mathrm{J} {\mathrm{mol}}^{-1}{\mathrm{K}}^{-1}) \mathrm{are}: \\ {\mathrm{CH}}_3\mathrm{OH}\left(\mathrm{l}\right)=239.7, \mathrm{HBr}\left(\mathrm{g}\right)=98.6, {\mathrm{CH}}_3\mathrm{Br}\left(\mathrm{g}\right)=246.3, {\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right)=69.9 \\ \mathrm{Which} \mathrm{one} \mathrm{of} \mathrm{these} \mathrm{values} \mathrm{is} \mathrm{the} \mathrm{correct} \mathrm{values} \mathrm{of} ∆\mathrm{G} \mathrm{for} \mathrm{this} \mathrm{reaction} \mathrm{at} 25°\mathrm{C}? \end{gathered}$$