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Q. Solid $Ca \left( HCO _{3}\right)_{2}$ decomposes as
$Ca \left( HCO _{3}\right)_{2}( s ) \rightleftharpoons CaCO _{3}( s )+ CO _{2}( g )+ H _{2} O ( g )$
if the total pressure is $0.2$ bar at $420 \,K$, what is the standard free energy change for the given reaction $\left(\Delta_{r} G^{\circ}\right)$ ?

Equilibrium

Solution:

$P_{\text {total }}=0.2$ bar
At equilibrium
$P_{ CO _{2}}=P_{ H _{2} O }=0.1 bar$
$K_{P}=(0.1)^{2}=0.01$
$\Delta_{r} G^{\circ}=-R T \ln K_{P}$
$=-8.314 \times 420 \ln (0.01)$
$=16.083 \,kJ / mol$