Calculate the enthalpy of formation of acetic acid $\left({\mathrm{CH}}_3\mathrm{COOH}\right)$ if its enthalpy of combustion is $- 867 \mathrm{kJ} {\mathrm{mol}}^{-1}$. The enthalpies of formation of ${\mathrm{CO}}_2\left(\mathrm{g}\right)$ and ${\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right)$ are $- 393.5$ and $- 285.9 \mathrm{kJ} {\mathrm{mol}}^{-1}$ respectively.

It is planned to carry the reaction, ${\mathrm{CaCO}}_3\left(\mathrm{s}\right) \rightleftharpoons \mathrm{CaO}\left(\mathrm{s}\right) + {\mathrm{CO}}_2\left(\mathrm{g}\right)$ at $1273 \mathrm{K}$ and $1 \mathrm{bar}$. 

Is this reaction spontaneous at this temperature and pressure?

Given,

$$\begin{gathered} {\mathrm{\Delta }}_{\mathrm{f}}\mathrm{H}° \mathrm{values} (\mathrm{kJ} {\mathrm{mol}}^{-1}): {\mathrm{CaCO}}_3\left(\mathrm{s}\right)=-1206.9,\mathrm{CaO}\left(\mathrm{s}\right)=-635.1, \\ {\mathrm{CO}}_2\left(\mathrm{g}\right)=-393.5 \\ ∆\mathrm{S}° \mathrm{values} ({\mathrm{JK}}^{-1} {\mathrm{mol}}^{-1}), {\mathrm{CaCO}}_3\left(\mathrm{s}\right)=92.9,\mathrm{CaO}\left(\mathrm{s}\right)=39.8,{\mathrm{CO}}_2\left(\mathrm{g}\right)=213.7. \end{gathered}$$

It is planned to carry the reaction, ${\mathrm{CaCO}}_3\left(\mathrm{s}\right) \rightleftharpoons \mathrm{CaO}\left(\mathrm{s}\right) + {\mathrm{CO}}_2\left(\mathrm{g}\right)$ at $1273 \mathrm{K}$ and $1 \mathrm{bar}$. 

Calculate the value of ${\mathrm{K}}_{\mathrm{p}}$ at $1273 \mathrm{K}$ for the reaction.
Given,

$$\begin{gathered} {\mathrm{\Delta }}_{\mathrm{f}}\mathrm{H}° (\mathrm{kJ} {\mathrm{mol}}^{-1}): {\mathrm{CaCO}}_3\left(\mathrm{s}\right)=-1206.9, \mathrm{CaO}\left(\mathrm{s}\right)=-635.1, {\mathrm{CO}}_2\left(\mathrm{g}\right)=-393.5 \\ ∆\mathrm{S}° \left({\mathrm{JK}}^{-1}{\mathrm{mol}}^{-1}\right), {\mathrm{CaCO}}_3\left(\mathrm{s}\right)=92.9, \mathrm{CaO}\left(\mathrm{s}\right)=39.8, {\mathrm{CO}}_2\left(\mathrm{g}\right)=213.7. \end{gathered}$$

It is planned to carry the reaction, ${\mathrm{CaCO}}_3\left(\mathrm{s}\right) \rightleftharpoons \mathrm{CaO}\left(\mathrm{s}\right) + {\mathrm{CO}}_2\left(\mathrm{g}\right)$ at $1273 \mathrm{K}$ and $1 \mathrm{bar}$. 

Calculate the value of partial pressure of ${\mathrm{CO}}_2$, at equilibrium

Given,

$$\begin{gathered} {\mathrm{\Delta }}_{\mathrm{f}}\mathrm{H}° \mathrm{values} (\mathrm{kJ} {\mathrm{mol}}^{-1}): {\mathrm{CaCO}}_3\left(\mathrm{s}\right)=-1206.9,\mathrm{CaO}\left(\mathrm{s}\right)=-635.1, \\ {\mathrm{CO}}_2\left(\mathrm{g}\right)=-393.5 \\ ∆\mathrm{S}° \mathrm{values} \left({\mathrm{JK}}^{-1}{\mathrm{mol}}^{-1}\right), {\mathrm{CaCO}}_3\left(\mathrm{s}\right)=92.9,\mathrm{CaO}\left(\mathrm{s}\right)=39.8,{\mathrm{CO}}_2\left(\mathrm{g}\right)=213.7. \end{gathered}$$

Two moles of a perfect gas undergo the following processes :

(i) a reversible isobaric expansion from $(1.0 \mathrm{atm}, 20.0 \mathrm{L})$ to $(1.0 \mathrm{atm}, 40.0 \mathrm{L})$

(ii) a reversible isochoric change of state from $(1.0 \mathrm{atm}, 40.0 \mathrm{L})$ to $(0.5 \mathrm{atm}, 40.0 \mathrm{L})$

(iii) a reversible isothermal compression from $(0.5 \mathrm{atm}, 40.0 \mathrm{L})$ to $(1.0 \mathrm{atm}, 20.0\mathrm{L})$

Sketch with labels each of the processes on the same $\mathrm{p}-\mathrm{V}$ diagram.