Question $5$: Ammonia undergoes a reaction with oxygen in the presence of a platinum catalyst to form nitric oxide and water. The reaction is carried out in a microreactor which results in a constant temperature. The reaction is $N{H}_3+\frac{5}{2}{O}_{2}NO+\frac{3}{2}{H}_{2}O$

The reaction occurs on the surface of a tube in the microreactor as governed by the following rate of reaction $($in gmol$/c{m}^{2}s)($Pignet and Schmidt, $1975).$ The partial pressures are in torr and the total pressure is maintained at $0\mathrm{.}115$ torr $($as an approximation$).$ The rate is in gmo$\frac{l}{c}{m}^{2}s$ :

$r_{N{H}_3}=\frac{A}{BxC},A-=3\mathrm{.}4{10}^{-8}$exp$(\frac{21,700}{RT})p_{N{H}_3}{p}_{O_2}^{\frac{1}{2}}$

$B-=1+8{10}^{-2}$exp$(\frac{4400}{RT})p_{O_2}^{\frac{1}{2}}$

$C-=1+1\mathrm{.}6{10}^{-3}$exp$(\frac{25500}{RT})p_{N{H}_3}$

The inlet stream contains ammonia and oxygen with partial pressures of $0\mathrm{.}046$ and $0\mathrm{.}068$ torr, respectively, and the flow rate is $100\frac{L}{h}.$ Solve the problem for a temperature of $($a$)473K$; $($b$)673K$; $($c$)800K$ and compare the results. The microreactor channel is $40300um,$ and its length is $1cm.$ The governing equations are

$\frac{d{F}_i}{dz}=P{v}_i{r}_{N{H}_3},F_i(0)=F_{i0}$

Where $u_i$ is the stoichiometric coefficient of the ith species; $P$ is the perimeter in $cm$;$F_i$ is the flow rate of ith species in gmo$\frac{l}{s}$;$F_{io}$ is the flow rate of ith species at inlet in gmo$\frac{l}{s}.$

In addition,

$F_T={\displaystyle \underset{i=1}{\overset{N}{}}}{F}_i,y_i=\frac{F_i}{F_T},p_i=y_i{p}_T$

Plot the molar flowrate of each specie as a function of the length of the reactor at the $3$ different temperatures.