A system formed initially of $2molC{O}_2,5mol{H}_2,$ and $1$molCO undergoes the reactions:

$C{O}_2(g)+3H_2(g)C{H}_{3}OH(g)+H_{2}O(g)$

$C{O}_2(g)+H_2(g)CO(g)+H_{2}O(g)$

$($a$)$ Develop expressions for the mole fractions of the reacting species as functions of the

reaction coordinates for the two reactions.

$($b$)$ Determine the equilibrium composition of the system if the reaction occurs at $500K$

and $3$ bar.