Intemal combustion engines are used to bum hydrocarbon fuels, but this often results in simultaneous N$*$O$\_\{$x$\}$ formation. N$*$O$\_\{$x$\}$ gases are undesired because they react in the atmosphere to produce acid rain and smog. Catalytic convertors are used to capture these gases in the exhaust of automobiles. You are doing research to understand this process. The formation of nitrogen dioxide follous this reaction:

N $2($g$)+2$O $2($g$)$ leftrightarrow $25$O$\_\{2\}($g$)$

Assume that the reaction mixture behaves as an ideal gas with a molar heat capacity of C g $^$ prime $=$ a $+$ bT $+$ epsilon $*$ T $^2+$ d $*$ T $^2+$ epsilon T$^-2$ J$/$ mol for the relevant temperature range. Assume no other equilibrium reactions occur simultaneously.

Species

Delta$\_\{$t$\}$ subseteq$^-$

$0$

H$\text{'}$V

$0$

$27\mathrm{.}318$

$6\mathrm{.}23$

angle$*10^7$

X $10$

$\backslash$mathcal$\{$N$\}\_\{2\}(\backslash$mathfrak$\{$g$\}))$

$0$

$28\mathrm{.}167$

$-9\mathrm{.}50$

$0$

$6\mathrm{.}30$

$-7\mathrm{.}50$

NO

$90\mathrm{.}25$ kJ$/$mol

$27\mathrm{.}034$

$9\mathrm{.}87$

$-32\mathrm{.}2$

$-22\mathrm{.}9$

$86\mathrm{.}58$ kJ$/$mol

NO: $($g$)$

$51\mathrm{.}3$kJ$/$mol

$1*10^2$

$33\mathrm{.}2$ kJ$/$mol

$22\mathrm{.}929$

$57\mathrm{.}11$

$-351\mathrm{.}9$

i$\text{'}*10^5$

$7\mathrm{.}866$

$2.$ Calculate Delta$\_\{$m$\}*$G $,$ Delta min H$^-,$ and K$.$ at $298\mathrm{.}15$ K and $1$ atm.

b$.$ Calculate K$,$ at $1200$ K and $150$ bar.

c$.$ Starting with $2$ moles of nitrogen and $4$ moles of oxygen, the reaction is conducted at $1200$ K and $150$ bar. Calculate the molar compositions at equilibrium

d$.$ After equilibrium is attained at $1200$ K and $150$ bar, you increase the temperature to $1500$ K$.$ Would you expect to increase the mole fraction of nitrogen dioxide by doing so$?$ Why or why not?

e$.$ After equilibrium is attained at $1200$ K and $150$ bar, a reactor malfunction causes the pressure to drop to $10$ bar. What happens to the mole fraction of nitrogen dioxide when equilibrium is ze$-$established at $10$ bar? Explain

f$.$ Your colleague encourages you to introduce $2$ moles of argon into the reactor after reaching equilibrium while keeping temperature and pressure constant at $1200$ K and $150$ bar. If you take your colleague's advice, what would happen to the conversion to nitrogen dioxide? Justify briefly.

g$.$ If you were instead investigating the production of nitric oxide, NO$,$ in our reactor at $1200$ K and $150$ bar, what would be the effect of adding $2$ moles of argon on the equilibrium conversion to NO