At \(298\,K\), for the reaction
\[
N_2(g)+3H_2(g)\rightleftharpoons 2NH_3(g)
\]
\[
\Delta H=-92.4\ \text{kJ}
\]
and
\[
\log K_c=5.75.
\]
What is the entropy change \((\Delta S)\) (in J K\(^{-1}\)) for this reaction at the same temperature?
\[
(R=8.3\ \text{J K}^{-1}\text{mol}^{-1})
\]