Question

(Sig Figs) Iron(III) oxide reacts with carbon monoxide according to the equation:
Fe₂O₃(s)+3CO(g)→2Fe(s)+3CO₂(g)
A reaction mixture initially contains 22.20 g Fe₂O₃ and 14.00 g CO.

The online website said the answer is m = 2.32g ( 3 sig figs)
While my answer was 2.318 ( 4 sig figs)

Heres my calculations

22.20 g Fe₂O₃ / 159.69 = 0.13901934999060680067631035130565 mols of Fe₂O₃
14.00 g CO / 28.01 = 0.49982149232416993930739021777936 mols of  CO
0.13901934999060680067631035130565 x 3 = 0.41705804997182040202893105391696 mols of Fe₂O₃ needed to react with 3 mols of CO

CO is the excess compound so:
0.49982149232416993930739021777936 mols of Fe₂O₃ - 0.41705804997182040202893105391696 mols of CO =
0.0827634423523495372784591638624 moles of CO in excess
0.0827634423523495372784591638624 mol co * 28.01g / mol CO = 2.31820402.....

4 sig figs = 2.318g of CO

I thought our professors told us not to round before the end, and the stupid peason book now wants us to round early?

Answer 1

Moles of Fe2O3 = mass / molar mass = 22.20 / 159.69 = 0.1390 mol

Moles of CO = 14.00 / 28.01 = 0.4998 mol

From the balanced equation,

1 mol Fe2O3 needs 3 mol CO

Then, 0.1390 mol Fe2O3 needs 3 * 0.1390 = 0.4170 mol

But we have 0.4998 mol of CO. Hence CO is excess reagent.

Excess moles of CO = 0.4998 - 0.4170 = 0.0828 mol

NOTE: Here you did mistake. According to significant rules of addition and substraction, the answer must have that many decimal places as the number that has least decimal places.

So, in both the substracting numbers the decimal plcases are 4 and hence the answer should also has 4 decimal places, so it is 0.0828 but not 0.08280.

Hence, 0.0828 has only 3 significant figures.

Mass of Excess CO = 0.0828 * 28.01 = 2.32 g.

NOTE: According to significant rules of multiplication and division, the answer must have that many significant figures ans the number that has least significant figures. Hence the answer must have only 3 significant figures ans one of the multiplying numbers as only 3 significant figures.

Hope you understand.