The decomposition of dinitrogen pentoxide proceeds according to the following reaction:

$2N_2{O}_5(g)4N{O}_2(g)+O_2(g)$

The reaction is first order with a rate constant $k=1\mathrm{.}7{10}^{-3}{s}^{-1}$ when the temperature is $55C.$

a$.$ Determine the reaction rate with respect to $N_2{O}_5$ when the fractional conversion $x$ is $0,0\mathrm{.}5$ and $1,$

given that the initial concentration of $N_2{O}_5$ is $0\mathrm{.}03M.$

$x=0$;$r=5\mathrm{.}1{10}^{-5}(mol)l^{-1}{s}^{-1}$:$x=0\mathrm{.}5$;$r=2\mathrm{.}55{10}^{-5}(mol)l^{-1}{s}^{-1}$:$x=1$;$r=0$

b$.$ Determine the reaction rate with respect to the $N{O}_2$ and $O_2$ for the same values of fractional

conversion in part a

$[x=0$:$r_{NO2}=1\mathrm{.}02{10}^{-4}(mol)l^{-1}{s}^{-1}$;$r_{O2}=2\mathrm{.}55{10}^{-5}(mol)l^{-1}{s}^{-1}]$

$[x=0\mathrm{.}5$:$r_{NO2}=5\mathrm{.}1{10}^{-5}(mol)l^{-1}{s}^{-1}$;$r_{O2}=1\mathrm{.}28{10}^{-5}(mol)l^{-1}{s}^{-1}]$

$[x=1$:$r_{NO2}=0$;$r_{O2}=0]$

c$.$ Use the ideal gas law to express the initial concentration of $N_2{O}_5$ in terms of pressure.

d$.$ Calculate the partial pressure and mole fraction of each gas component at $x=0\mathrm{.}5.$

$[p_{N2O5}=40905(Pa)$;$p_{NO2}=81810(Pa)$;$p_{O2}=20452(Pa)]$

$[y_{N2O5}=0\mathrm{.}286$;$y_{NO2}=0\mathrm{.}571$;$y_{O2}=0\mathrm{.}143]$