One mol of $CO,1$mol of $H2O,$ and $\frac{1}{2}$mol of oxygen are mixed and heated to a temperature of $3600K$ at a pressure of $1$ atm. Assume the products consist of $CO2,CO,O2,O,H2O,OH$ and $H2.$ You will need to use Table $G\mathrm{.}9$ from Thermodynamics by Black and Hartley for part c$.$ of this problem or some other source of $Kp$ values such as the charts in your text.

a$.$ How many unknowns are there?

b$.$ Write the atom balances for $C,O,$ and $H.$

c$.$ Write expressions for $\frac{C}{O}$ and $\frac{H}{O}$ in terms of the product mol fractions.

d$.$ Write $K_p$ equations involving $($in terms of product mol fractions$)$

i$.CO2,CO,$ and $O2$

ii$.O2$ and $O$

iii. $H2$ and $H$

iv$.H2,OH,$ and $H2O$

e$.$ Write an expression for ${\displaystyle \underset{?}{\overset{?}{}}}{}_i=1.$

f$.$ Determine the unknown equilibrium product compositions using the equations above.

g$.$ Explain what would happen to the mol fraction of $O2$ and $CO2$ if the pressure were raised to $10$ atm

h$.$ Explain what would happen if the temperature were lowered to $2500K$

i$.$ Compare your results with those from the Mattingly software EQL