Equilibrium composition:

Chemical reaction for the formation of $H_{2}O$ is given by:

$H_2+\frac{1}{2}{O}_2{H}_{2}O$

If the equilibrium constant $K_p=3\mathrm{.}486{10}^3$ at a pressure of $p_{\text{t}\text{o}\text{t}\text{a}\text{l}}=1$atm and temperature $T=2000K$

a$)$ Write a set of equations to determine the mole fractions of all species $({}_{H_2},{}_{O_2},{}_{H_{2}O})$ at equilibrium

BONUS: Use a programming tool $($calculator$,$ matlab, etc$)$ to calculate the mole fractions if the ratio of number of moles of $H$ atoms and $O$ atoms initially is $1.$

Hints and formulae:

Use atom conservation equations of $H$ and $O$ and take the ratio of the equations.