A plant utility gas can be produced by reacting powdered coal with steam and air $($Figure P$4\mathrm{.}19).$ In a given application a coal with ultimate analysis $68\%C,6\mathrm{.}5\%H,1\mathrm{.}5\%N,1\mathrm{.}2\%S,13\mathrm{.}8\%O,$ and $9\mathrm{.}0\%$ ash is converted to a gas with dry$-$basis analysis of $23\%H_2,3\mathrm{.}2\%C{H}_4,16\mathrm{.}2\%CO,13\%C{O}_2+H_{2}S,$ and $44\mathrm{.}6\%N_2.$

The conversion is carried out by using $0\mathrm{.}95lb$ steam per $1lb$ coal. The air fed is found to contain $1\mathrm{.}5$mol$\%H_{2}O$ and product gas $0\mathrm{.}24mol{H}_2\frac{O}{m}ol$ dry gas. Calculate the fraction of the carbon fed which remains in the ash residue.