The formic acid produced by oxidation of formaldehyde. However, under the reaction
conditions some undesirable reactions take place to produce CO$_2$, H$_2$, CO and H$_2$O. The
reactions that occur are:
CO$_2$ + H$_2$
k$_2$
k$_1$
HCHO + 1/2 O$_2$
HCOOH
k$_3$
CO + H$_2$O
The reaction rate for oxidation of formaldehyde reaction is first order for formaldehyde and
zero order for oxygen. These reactions are carried out in a batch reactor in which feed contains
67% HCHO and 33% O$_2$. The reaction rate constants $k_1$, $k_2$ and $k_3$ are 0.001 s$^{-1}$, 0.003 s$^{-1}$ and
0.002 s$^{-1}$, respectively.
a) Derive an equation for concentration of HCHO as a function of time and calculate the ratio
$C_{HCHO}$/$C_{HCHO,0}$ after 3 min.
b) Derive an equation for concentration of HCOOH as a function of time and calculate the
concentration of HCOOH after 4 min if $C_{HCHO}$ equals to 0.15 mol/dm$^3$ and $C_{O_2,0}$ equals to
0.07 mol/dm$^3$.
c) Sketch the concentrations as functions of time. What time gives the maximum concentration
of HCOOH?
d) If the series reaction is carried out in a CSTR, determine the reactor volume that will
maximize the production of HCOOH for a volumetric flow rate of 15 dm$^3$/min.
NOTE: Use numerical method (Classical RK-4) for your solutions.