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Chapter 3: Problem 109

Over the years, the thermite reaction has been used for welding railroad rails, in incendiary bombs, and to ignite solid-fuel rocket motors. The reaction is $$ \mathrm{Fe}_{2} \mathrm{O}_{3}(s)+2 \mathrm{Al}(s) \longrightarrow 2 \mathrm{Fe}(l)+\mathrm{Al}_{2} \mathrm{O}_{3}(s) $$ What masses of iron(III) oxide and aluminum must be used to produce 15.0 \(\mathrm{g}\) iron? What is the maximum mass of aluminum oxide that could be produced?

Short Answer

Expert verified
To produce 15.0 g of iron, 21.45 g of iron(III) oxide and 14.49 g of aluminum must be used. The maximum mass of aluminum oxide that could be produced is 54.75 g.

Step by step solution

01

Determine the moles of iron required

First, let's convert the given mass of iron (15.0 g) into moles using its molar mass. The molar mass of iron (Fe) is 55.85 g/mol. Moles of iron = \(\frac{15.0\,\text{g}}{55.85\,\text{g/mol}}\) = 0.2685 mol
02

Determine the moles of iron(III) oxide and aluminum required

Now, let's determine the moles of iron(III) oxide (Fe2O3) and aluminum (Al) needed for the reaction, using the stoichiometry of the balanced chemical equation. Moles of Fe2O3 = \(\frac{1\,\text{mol of Fe2O3}}{2\,\text{mol of Fe}} × 0.2685\,\text{mol of Fe}\) = 0.1343 mol of Fe2O3 Moles of Al = \(\frac{2\,\text{mol of Al}}{2\,\text{mol of Fe}} × 0.2685\,\text{mol of Fe}\) = 0.537 mol of Al
03

Calculate the masses of iron(III) oxide and aluminum required

To calculate the masses of the reactants, we will multiply the moles obtained in Step 2 by their corresponding molar masses. Mass of Fe2O3 = 0.1343 mol of Fe2O3 × \(159.69\,\text{g/mol}\) = 21.45 g of Fe2O3 Mass of Al = 0.537 mol of Al × 26.98 g/mol = 14.49 g of Al
04

Calculate the maximum mass of aluminum oxide produced

Lastly, we will find the maximum mass of aluminum oxide (Al2O3) that can be produced by multiplying the moles of aluminum used (0.537 mol) by the molar mass of Al2O3. Mass of Al2O3 = 0.537 mol of Al × \(101.96\,\text{g/mol}\) = 54.75 g of Al2O3 #Conclusion# To produce 15.0 g of iron, 21.45 g of iron(III) oxide and 14.49 g of aluminum must be used. The maximum mass of aluminum oxide that could be produced is 54.75 g.

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Most popular questions from this chapter

Elixirs such as Alka-Seltzer use the reaction of sodium bicarbonate with citric acid in aqueous solution to produce a fizz: $$ 3 \mathrm{NaHCO}_{3}(a q)+\mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{7}(a q) \longrightarrow $$ $$ 3 \mathrm{CO}_{2}(g)+3 \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{Na}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}(a q) $$ a. What mass of \(\mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{7}\) should be used for every \(1.0 \times 10^{2} \mathrm{mg} \mathrm{NaHCO}_{3} ?\) b. What mass of \(\mathrm{CO}_{2}(g)\) could be produced from such a mixture?

The aspirin substitute, acetaminophen $\left(\mathrm{C}_{8} \mathrm{H}_{9} \mathrm{O}_{2} \mathrm{N}\right),$ is produced by the following three-step synthesis: $$ \mathrm{I} . \quad \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{3} \mathrm{N}(s)+3 \mathrm{H}_{2}(g)+\mathrm{HCl}(a q) \longrightarrow $$ $$ \mathrm{C}_{6} \mathrm{H}_{8} \mathrm{ONCl}(s)+2 \mathrm{H}_{2} \mathrm{O}(l) $$ $$ \mathrm{II}\quad \mathrm{C}_{6} \mathrm{H}_{8} \mathrm{ONCl}(s)+\mathrm{NaOH}(a q) \longrightarrow $$ $$ \mathrm{C}_{6} \mathrm{H}_{7} \mathrm{ON}(s)+\mathrm{H}_{2} \mathrm{O}(l)+\mathrm{NaCl}(a q) $$ $$ \mathrm{III.} \quad \mathrm{C}_{6} \mathrm{H}_{7} \mathrm{ON}(s)+\mathrm{C}_{4} \mathrm{H}_{6} \mathrm{O}_{3}(l) \longrightarrow $$ $$ \mathrm{C}_{8} \mathrm{H}_{9} \mathrm{O}_{2} \mathrm{N}(s)+\mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}(l) $$ The first two reactions have percent yields of 87\(\%\) and 98\(\%\) by mass, respectively. The overall reaction yields 3 moles of acetaminophen product for every 4 moles of \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{3} \mathrm{N}\) reacted. a. What is the percent yield by mass for the overall process? b. What is the percent yield by mass of Step III?

A given sample of a xenon fluoride compound contains molecules of the type \(\mathrm{XeF}_{n},\) where \(n\) is some whole number. Given that $9.03 \times 10^{20}\( molecules of \)\mathrm{XeF}_{n}\( weigh \)0.368 \mathrm{g},$ determine the value for \(n\) in the formula.

A potential fuel for rockets is a combination of $\mathrm{B}_{5} \mathrm{H}_{9}\( and \)\mathrm{O}_{2}$ The two react according to the following balanced equation: $$ 2 \mathrm{B}_{5} \mathrm{H}_{9}(l)+12 \mathrm{O}_{2}(g) \longrightarrow 5 \mathrm{B}_{2} \mathrm{O}_{3}(s)+9 \mathrm{H}_{2} \mathrm{O}(g) $$ If one tank in a rocket holds 126 \(\mathrm{g} \mathrm{B}_{5} \mathrm{H}_{9}\) and another tank holds \(192 \mathrm{g} \mathrm{O}_{2},\) what mass of water can be produced when the entire contents of each tank react together?

Ammonia is produced from the reaction of nitrogen and hydrogen according to the following balanced equation: $$ \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g) $$ a. What is the maximum mass of ammonia that can be produced from a mixture of \(1.00 \times 10^{3} \mathrm{g} \mathrm{N}_{2}\) and $5.00 \times 10^{2} \mathrm{g} \mathrm{H}_{2} ?$ b. What mass of which starting material would remain unreacted?
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