Answer to Question #118164 in General Chemistry for Emma

Question

Iron exists as iron ore in Earth’s crust as iron(III) oxide. To obtain pure iron, the ore must be “smelted” using a chemical reaction. Modern iron smelting combines carbon monoxide with the iron ore at temperatures exceeding 1000 ०C in a series of reactions that results in (unbalanced):

Fe2O3 (s) + CO (g) ➝ Fe (l) + CO2 (g)


Josiah, a chemical engineer, is calibrating the equipment used for smelting at the Iron Ore Company of Canada in Labrador City, Newfoundland and Labrador. Because the smelting process produces carbon dioxide as a byproduct, Canadian climate law dictates that he must measure the amount of carbon dioxide produced by his plant. The standards are reported in terms of molecules of CO2 output per day. If Josiah's plant produces an average of 1.500 x 1028 molecules of CO2 per day, calculate the mass of iron ore smelted by the plant per day.

Answer 1

Josiah's plant produces an average of 1.500 x 10²⁸ molecules of CO2 per day.

n(CO2) = N/Na = 1.500 x 10²⁸ molecules / 6.02 x 10²³ mol-1 = 0.2492 x 10⁵ mol

Fe2O3 (s) + 3CO (g) ➝ 2Fe (l) + 3CO2 (g) 

According to the equation:

n(Fe) = 0.2492*10⁵*2/3 = 0.1661 x 10⁵ mol

The mass of iron ore smelted by the plant per day:

m(Fe) = n*M = 0.1661 x 10⁵ mol*56g/mol = 9.3 x 10^{5 }g = 9.3 x 10² kg