The decomposition of a generic diatomic element in its standard state is represented by the equation

$\frac{1}{2}{x}_2(g)longrightarrowx(g)$

Assume that the standard molar Gibbs energy of formation of $x(g)$ is $5\mathrm{.}74kJ*mo{l}^{-1}$ at $2000.K$ and $-49\mathrm{.}75kJ*mo{l}^{-1}$ at $3000.$ K$.$ Determine the value of the thermodynamic equilibrium constant, $K,$ at each temperature.

At $2000.K,G_f=5\mathrm{.}74kJ*mo{l}^{-1}.$ What is $K$ at that temperature?

$K$ at $2000.K=$

At $3000.K,G_f=-49\mathrm{.}75kJ*mo{l}^{-1}.$ What is $K$ at that temperature?

$K$ at $3000.K=$