Example $13\mathrm{.}13$

A bed of coal $($assume pure carbon$)$ in a coal gasifier is fed with steam and air,

and produces a gas stream containing $H_2,CO,O_2,H_{2}O,C{O}_2,$ and $N_2.$ If the feed to

the gasifier consists of $1$mol of steam and $2\mathrm{.}38$mol of air, calculate the equilibrium

composition of the gas stream at $P=20$ bar for temperatures of $1000,1100,1200,$

$1300,1400,$ and $1500K.$ Available data are listed in the accompanying table.

Solution $13\mathrm{.}13$

The feed stream to the coal bed consists of $1$mol of steam and $2\mathrm{.}38$mol of air,

containing:

$O_2$:$(0\mathrm{.}21)(2\mathrm{.}38)=0\mathrm{.}5$mol,$N_2$:$(0\mathrm{.}79)(2\mathrm{.}38)=1\mathrm{.}88$mol

The species present at equilibrium are $C,H_2,CO,O_2,H_{2}O,C{O}_2,$ and $N_2.$ The

formation reactions for the compounds present are:

$H_2+\frac{1}{2}{O}_2{H}_{2}O$

$C+\frac{1}{2}{O}_{2}CO$

$C+O_{2}C{O}_2$

Since elements hydrogen, oxygen, and carbon are themselves presumed present

in the system, this set of three independent reactions is a complete set.