A haematite ore sample of mass 250 kg contains 76% Fe2O3 by mass, the rest being gangue. It is reduced by CO in a blast furnace according to Fe2O3 + 3CO -> 2Fe + 3CO2, and 92% of the iron present is recovered as metal. Using Fe = 56 and O = 16, calculate the mass of iron obtained in kg, to the nearest integer.

JEE Main levelNumerical answerDifficulty 2 of 3mt088

A haematite ore sample of mass $250 kg$ contains $76%$ $Fe X_{2} O X_{3}$ by mass, the rest being gangue. It is reduced by $CO$ in a blast furnace according to $Fe X_{2} O X_{3} + 3 CO 2 Fe + 3 CO X_{2}$ , and $92%$ of the iron present is recovered as metal. Using Fe = 56 and O = 16, calculate the mass of iron obtained in kg, to the nearest integer.

Numerical answer type, answer in kg, tolerance 0.5.

Mass of

Fe X_{2} O X_{3}

= 250 \times 0.76 = 190 kg

. Molar mass

Fe X_{2} O X_{3} = 160

, and it contains

112

g Fe per 160 g. Iron present

= 190 \times 112/160 = 133.0 kg

. Recovered iron

= 133.0 \times 0.92 = 122.36 kg \approx 122 kg