A by$-$product in the reduction of iron is a gas that contains $CO,C{O}_2,H_2,$ and $H_{2}O.$ This "spent" gas can be reused by removing much of the $H_{2}O$ and $C{O}_2.$ To be reusable the gas quality, designated by $Q,$ in exiting stream $6$ must be less than $0\mathrm{.}08($see diagram below for stream numbers$).$ This gas quality, $Q,$ is defined as the sum of the mole fractions of $H_{2}O$ and $C{O}_2.$ The gas in stream $6$ is created by splitting the incoming spent gas $($stream $1)$ into a by pass stream $(2)$ and a stream $(3)$ from which $H_{2}O$ and $C{O}_2$ will be removed. If $2\%$ by mole of stream $1$ is diverted to the bypass stream $2$ what is the value of $Q$ for the operating conditions shown in the figure below.