[Vicstar]

When one knows the equillibrium constants at two different temperatures, is there a formula which one can use to calculate the dS of the equilibrium reaction?

[Yggdrasil]

You can relate K to ΔG, but relating this to ΔS requires knowledge of ΔH.

[0000000]

If the reaction is at standard state conditions is easy. Because the process is at equilibrium dG is 0 and in the formula there is only dG(standard) and the corelation is
dG(standard)=-RTlnK
from here you can calculate dG(standard), after that you need to determinate dH(standard) from H-tables (if you do not know how to do that reply an I will tell you). Finally the corelation between them is
dG(standard)=dH(standard)-TdS(standard)