A blast-furnace charge of 1000 kg ore contains 18.0% SiO2 as the only acidic gangue. It is fluxed with limestone which is 90.0% CaCO3 by mass (the rest is inert) so that the silica is converted entirely to CaSiO3. Taking Ca = 40, Si = 28, C = 12, O = 16, the mass of limestone required, to the nearest kg, is

JEE Advanced levelSingle correct optionDifficulty 3 of 3mt154

A blast-furnace charge of $1000 kg$ ore contains $18.0%$ $SiO X_{2}$ as the only acidic gangue. It is fluxed with limestone which is $90.0%$ $CaCO X_{3}$ by mass (the rest is inert) so that the silica is converted entirely to $CaSiO X_{3}$ . Taking Ca = 40, Si = 28, C = 12, O = 16, the mass of limestone required, to the nearest kg, is

SiO X_{2}

present is

180 kg

and

SiO X_{2}

has molar mass

60

. Reactions

CaCO X_{3} CaO + CO X_{2}

and

CaO + SiO X_{2} CaSiO X_{3}

need

1 mol

CaCO X_{3}

per mol of silica, so pure

CaCO X_{3}

needed is

(180/60) \times 100 = 300 kg

. Limestone at

90.0%

purity is

300/0.900 = 333.3 \approx 333 kg