A fuel oil is fed to a furnace and burned with $25\%$ excess air. The oil contains $87\mathrm{.}0wt\%C,10\mathrm{.}0\%H,$ and

$3\mathrm{.}0\%S.$ Analysis of the furnace exhaust gas shows only $N_2,O_2,C{O}_2,S{O}_2,$ and $H_{2}O.$ The sulphur dioxide

emission rate is to be controlled by passing the exhaust gas through a scrubber, in which most of the $S{O}_2$

is absorbed in an alkaline solution. The gases leaving the scrubber $($all the $N_2,O_2,$ and $C{O}_2,$ and some of

the $H_{2}O$ and $S{O}_2$ entering the unit$)$ pass out to a stack. The scrubber has a limited capacity, however, so

that a fraction of the furnace exhaust gas must be bypassed directly to the stack. At one point during the

operation of the process, the scrubber removes $90\%$ of the $S{O}_2$ in the gas fed to it$,$ and the combined

stack gas contains $612\mathrm{.}5ppm($parts per million$)S{O}_2$ on a dry basis; that is$,$ every million moles of dry

stack gas contain $612\mathrm{.}5$ moles of $S{O}_2.$ Calculate the fraction of the exhaust bypassing the scrubber at

this moment.

Note: the process is shown in the following block diagram.

Fuel Oil