A fuel oil is fed to a furnace and burned with 35.0% excess air. The oil contains 86.0 wt% C, 10.0% H, and 4.00% S. Analysis of the furnace exhaust gas shows only N2, O2, CO2, SO2, and H2O. The sulfur dioxide emission rate is to be controlled by passing the exhaust gas through a scrubber in which most of the SO2 is absorbed in an alkaline solution. The gases leaving the scrubber (all of the N2, O2, and CO2, and some of the H2O and SO2 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 SO2 in the gas fed to it, and the combined stack gas contains 612.5 ppm (parts per million) SO2 on a dry basis; that is, every million moles of dry stack gas contains 612.5 moles of SO2. Calculate the fraction of the exhaust bypassing the scrubber at this moment.