In the blast furnace, C + CO2 -> 2CO and Fe2O3 + 3CO -> 2Fe + 3CO2 operate in a cycle, so that the carbon is consumed only in the net change 2Fe2O3 + 3C -> 4Fe + 3CO2. The mass of coke containing 90% carbon needed to reduce 640 kg of Fe2O3 completely by this net change (Fe 56, O 16, C 12) is

JEE Advanced levelSingle correct optionDifficulty 3 of 3mt108

In the blast furnace, $C + CO X_{2} 2 CO$ and $Fe X_{2} O X_{3} + 3 CO 2 Fe + 3 CO X_{2}$ operate in a cycle, so that the carbon is consumed only in the net change $2 Fe X_{2} O X_{3} + 3 C 4 Fe + 3 CO X_{2}$ . The mass of coke containing $90%$ carbon needed to reduce $640 kg$ of $Fe X_{2} O X_{3}$ completely by this net change (Fe 56, O 16, C 12) is

640 kg

Fe X_{2} O X_{3}

640/160 = 4

kmol. The net equation needs 3 mol C for every 2 mol

Fe X_{2} O X_{3}

, so 6 kmol C

= 72

kg. With

90%

carbon, coke

= 72/0.9 = 80.0 kg