Question # $5(25$ points$)$

For the ammonia synthesis reaction, $\frac{1}{2}{N}_2(g)+\frac{3}{2}{H}_2(g)harrN{H}_3(g),2$ moles of nitrogen and $6$ moles of hydrogen are fed to the reactor. You may assume for this exam that the reaction occurs in the gas phase, which behaves ideally, and the heat of reaction is not a function of temperature.

i$.(4$ pts$)$ Determine the value of the equilibrium constant K for the above reaction, at $55C(298\mathrm{.}15K)$ and $1$ bar pressure.

ii$.(4$ pts$)$ Determine the value of the equiiibrium constant if the pressure is maintained at $1$ bar and the reaction temperature is raised $).$

iii. $(7$ pts$)$ Set up the equation$($s$)$ to solve for the reaction coordinate $($extent of reaction, or $)$ at equilibrium.

iv$.(5$ pts$)$ Determine the mole fractions of nitrogen, hydrogen, and ammonia at equilibrium if the reactor temperature and pressure are maintained at K$)$ and $275$ bar, respectively.

You may assume that the reaction coordinate was found to be $=2\mathrm{.}4819$ at these conditions.

$(5$ pts$)$ For the conditions of part $4.$ above, how much heat in kJ must be added or $.$ removed $($specify which it is$)$ from the reactor at equilibrium to maintain it at a constant temperature?