Thermodynamics

For the reaction, X(s) \(\rightleftharpoons\) Y(s) + Z(g), the plot of \(\ln {{pz} \over {{p^\theta }}}\) versus \({{{{10}^4}} \over T}\) is given below (in solid line), where p_z is the pressure (in bar) of the gas Z at temperature T and \({{p^\theta }}\) = 1 bar.


(Given, \({{d(\ln K)} \over {d\left( {{1 \over T}} \right)}} = - {{\Delta {H^\theta }} \over R}\), where the equilibrium
constant, \(K = {{pz} \over {{p^\theta }}}\) and the gas constant, R = 8.314 J K^\(-\)1 mol^\(-\)1)

The value of \(\Delta\)S^\(\theta\) (in J K^\(-\)1 mol^\(-\)1) for the given reaction, at 1000 K is _________.