A methanol synthesis reaction will be run in a container with a moveable piston to allow for changes in volume. The gas phase reaction is illustrated below:

$CO(g)+2H_2(g)C{H}_{3}OH(g)$

At equilibrium, the reaction is run at $400K$ in a $10L$ flask; there are $3\mathrm{.}09$ moles of

$CO$ and $1\mathrm{.}11$ moles $H_2$ initially.

Calculate the equilibrium constant at $500K$ using this formula:

$ln(\frac{K_2}{K_1})=-\frac{H_{rxn}}{R}[\frac{1}{T_2}-\frac{1}{T_1}]$