Problem $3$: CSTR vs$.$ PBR for a catalyzed reaction

You are given the rate equation, $-$rA$=$ kA$$ cA for the reaction A$->$ B$.$ The inlet flow rate

is $200$ mol$/$s of pure A$.$ Pure A has a density of $500$ kg$/$m$3$ and a molar mass of $500$ g$/$

mol. The rate constant is $10-6$ m$/$s$.$ The reactor has a catalyst of surface area Sg of $5$ m$2/$

g$,$ and the catalyst density in the reactor is $30$ kg$/$m$3.$

a$.$ To achieve $40\%$ conversion in an isothermal, steady$-$state, liquid phase CSTR$,$

what is the volume required? $[0\mathrm{.}9$ m$3]$

b$.$ What volume is required for the same conversion in an isothermal, steady$-$state,

liquid phase PBR$?[0\mathrm{.}7$ m$3]$Problem $3$: CSTR vs$.$ PBR for a catalyzed reaction

You are given the rate equation, $-r_A^{\text{'}\text{'}}=k_A^{\text{'}\text{'}}{C}_A$ for the reaction $AB.$ The inlet flow rate

is $200mo\frac{l}{s}$ of pure A$.$ Pure A has a density of $500k\frac{g}{m^3}$ and a molar mass of $500\frac{g}{?}$

mol. The rate constant is ${10}^{-6}\frac{m}{s}.$ The reactor has a catalyst of surface area $S_g$ of $5\frac{m^2}{?}$

$g,$ and the catalyst density in the reactor is $30k\frac{g}{m^3}.$

a$.$ To achieve $40\%$ conversion in an isothermal, steady$-$state, liquid phase CSTR$,$

what is the volume required? $0\mathrm{.}9m^3$

b$.$ What volume is required for the same conversion in an isothermal, steady$-$state,

liquid phase PBR$?[0\mathrm{.}7$ m$^3]$