Write a balanced equation, including state symbols, for the thermal decomposition of calcium carbonate.

Use Figure 1 to estimate $\Delta_\mathrm r G^\circ$ at $1000\ \mathrm K$

Use Figure 1 to determine $\Delta_\mathrm r H^\circ$ and $\Delta_\mathrm r S^\circ$ for the decomposition. Give signs and units, and show how you obtain both values.

Using your values from (c), determine the temperature at which $\Delta_\mathrm r G^\circ=0$ State at which temperatures the forward decomposition is spontaneous under standard-state conditions.

At $1000\ \mathrm K$ a gas stream keeps the carbon dioxide partial pressure in the kiln at $0.10\ \mathrm{bar}$ For the reaction as written, take

with pure solids omitted from $Q$ Under these conditions,

where $R=8.31\ \mathrm{J\,K^{-1}\,mol^{-1}}$

Determine the carbon dioxide partial pressure at which $\Delta_\mathrm r G=0$ at $1000\ \mathrm K$ Hence decide whether the forward decomposition is spontaneous at $p(\mathrm{CO_2})=0.10\ \mathrm{bar}$ and assess the claim that a positive $\Delta_\mathrm r G^\circ$ at $1000\ \mathrm K$ means that the decomposition cannot be spontaneous.