The hydrate of sodium carbonate decomposes according to the following equation: [ mathrm{Na}_{2} mathrm{CO}_{3} cdot mathrm{H}_{2} mathrm{O}(mathrm{s})

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The hydrate of sodium carbonate decomposes according to the following equation:

\[ \mathrm{Na}_{2} \mathrm{CO}_{3} \cdot \mathrm{H}_{2} \mathrm{O}(\mathrm{s}) \rightarrow \mathrm{Na}_{2} \mathrm{CO}_{3}(\mathrm{~s})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \]

The equilibrium pressure of water vapour in this reaction is given by the following equation:

where

\[ \log P=7.944-\frac{3000}{T} \]

\(P=\) Pressure in atm

\(T=\) Temperature in \(\mathrm{K}\).

Derive an expression for the standard free energy change \(\Delta G^{0}\) of this reaction.

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