$$ Prob. $(4)$: An iron blast furnace smelts ore of the composition $($ Fe $3$ O $470\%,$Fe $2$ O $35\%,$SiO $210\%,$P $2$ O $51\%,$MnO $24\%,$H $2$ O$10\%).$ It produces per day $800$ metric tons of pig iron. Enough flux is used to give a slag containing $25\%$CaO. The flux is pure limestone$.0\mathrm{.}5$ ton of coke is used per ton of ore. The coke is $85\%$C$,10\%$SiO $2,5\%$H $2$ O$.$ All the P charged, one$-$half the Mn$,$ and one$-$fifth the Si are reduced and go in the pig iron, which also contains by analysis $4\%$ C$.88\%$ of the carbon of the coke is burned at the tuyeres. Assume that $2\%$ of the iron is in the slag. Find: a$)$ The percentage composition of the pig iron b$)$ The weight of ore smelted per day c$)$ The weight of the flux used per day d$)$ The percentage composition of the flue gases Prob. $(4)$: An iron blast furnace smelts ore of the composition $($ Fe $3$ O $470\%,$Fe $2$ O $35\%,$SiO $210\%,$P $2$ O $51\%,$MnO $24\%,$H $2$ O$10\%).$ It produces per day $800$ metric tons of pig iron. Enough flux is used to give a slag containing $25\%$CaO. The flux is pure limestone$.0\mathrm{.}5$ ton of coke is used per ton of ore. The coke is $85\%$C$,10\%$SiO $2,5\%$H $2$ O$.$ All the P charged, one$-$half the Mn$,$ and one$-$fifth the Si are reduced and go in the pig iron, which also contains by analysis $4\%$ C$.88\%$ of the carbon of the coke is burned at the tuyeres. Assume that $2\%$ of the iron is in the slag. Find: a$)$ The percentage composition of the pig iron b$)$ The weight of ore smelted per day c$)$ The weight of the flux used per day d$)$ The percentage composition of the flue gases