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Chapter 4: Problem 17

In the thermite reaction, iron(III) oxide is reduced by aluminum to give molten iron. $$\mathrm{Fe}_{2} \mathrm{O}_{3}(\mathrm{s})+2 \mathrm{Al}(\mathrm{s}) \rightarrow 2 \mathrm{Fe}(\ell)+\mathrm{Al}_{2} \mathrm{O}_{3}(\mathrm{s})$$ If you begin with \(10.0 \mathrm{g}\) of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) and \(20.0 \mathrm{g}\) of \(\mathrm{Al}\), (a) Which reactant is limiting? (b) What mass of Fe can be produced? (c) What mass of the excess reactant remains after the limiting reactant is consumed? (d) Set up an amounts table for this problem.

Short Answer

Expert verified
(a) The limiting reactant is Fe2O3. (b) 6.99 g of Fe can be produced. (c) 16.62 g of Al remains. (d) An amounts table is set up accordingly.

Step by step solution

01

Determine Molar Masses

To solve this problem, we first need to calculate the molar masses of the compounds involved. - Molar mass of Fe2O3 = 2(55.85) + 3(16.00) = 159.7 g/mol - Molar mass of Al = 26.98 g/mol - Molar mass of Fe = 55.85 g/mol
02

Convert Grams to Moles

Convert the masses of Fe2O3 and Al to moles using their molar masses.- Moles of Fe2O3 = \( \frac{10.0\ \text{g}}{159.7\ \text{g/mol}} = 0.0626\ \text{mol} \)- Moles of Al = \( \frac{20.0\ \text{g}}{26.98\ \text{g/mol}} = 0.741\ \text{mol} \)
03

Identify Limiting Reactant

Using the stoichiometry of the balanced equation, identify the limiting reactant. From the equation, we know:- 1 mole of Fe2O3 reacts with 2 moles of Al.- Moles of Al required for 0.0626 moles of Fe2O3 = \( 0.0626\ \text{mol} \times 2 = 0.1252\ \text{mol} \)Since we have 0.741 moles of Al and need only 0.1252 moles, Fe2O3 is the limiting reactant.
04

Calculate Mass of Iron Produced

Use the moles of the limiting reactant to calculate the mass of iron produced.- From the balanced equation, 1 mole of Fe2O3 produces 2 moles of Fe.- Moles of iron = \( 0.0626\ \text{mol Fe2O3} \times 2 = 0.1252\ \text{mol Fe} \)- Mass of iron = \( 0.1252\ \text{mol} \times 55.85\ \text{g/mol} = 6.99\ \text{g} \)
05

Calculate Mass of Excess Reactant Remaining

To find the remaining mass of Al after the reaction:- Moles of Al reacted = 0.1252 moles- Moles of excess Al = 0.741 - 0.1252 = 0.6158 moles- Mass of remaining Al = \( 0.6158\ \text{mol} \times 26.98\ \text{g/mol} = 16.62\ \text{g} \)
06

Set Up Amounts Table

Create an initial, change, and final amounts table for the reaction: | | Fe2O3 | Al | Fe | Al2O3 | |--------|-------|------|--------|-------| | Initial| 0.0626| 0.741| 0 | 0 | | Change | -0.0626| -0.1252| +0.1252| +0.0626| | Final | 0 | 0.6158| 0.1252| 0.0626|

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Thermite Reaction
The thermite reaction is a type of exothermic oxidation-reduction chemical reaction, highly favored for its high temperature output and the ability to produce molten metals. In this particular reaction, aluminum serves as the reducing agent, while iron(III) oxide acts as the oxidizing agent. When these two reactants come together, aluminum reduces iron(III) oxide to produce elemental iron and aluminum oxide. The reaction is represented by the balanced chemical equation:
  • Fe2O3(s) + 2Al(s) 鈫� 2Fe(l) + Al2O3(s)
A key feature of this reaction is its ability to produce intense heat, often used for welding and creating metal alloys.
Despite its industrial utility, the thermite reaction is central in various chemistry problems, allowing students to explore concepts like limiting reactants, stoichiometry, and molar mass calculations.
Stoichiometry
Stoichiometry is a branch of chemistry focusing on the amount of substances involved in chemical reactions. It uses the balanced chemical equations to connect the quantities of reactants and products. In our thermite reaction example, stoichiometry helps determine how much of each reactant is needed and the expected amount of each product. It accomplishes this through the mole ratio, which is derived from the coefficients in the balanced equation:
  • 1 mole of Fe2O3 requires 2 moles of Al to form 2 moles of Fe and 1 mole of Al2O3.
To solve problems related to the thermite reaction:
  • First, convert all given reactant amounts to moles.
  • Use the stoichiometric ratios to find the limiting reactant and calculate the resulting products.
Understanding stoichiometry thus allows for precise predictions about chemical reactions.
Molar Mass Calculation
Molar mass is a fundamental concept in chemistry, crucial for converting grams of a substance to moles and vice versa. Each element's molar mass (derived from their atomic weights in atomic mass units) is found on the periodic table. For our thermite reaction:
  • The molar mass of Fe2O3 is calculated as 2 times the molar mass of iron plus 3 times the molar mass of oxygen, which is 159.7 g/mol.
  • The molar mass of aluminum is 26.98 g/mol.
These calculations are the cornerstone for translating the mass of each reactant into moles, a necessary step in stoichiometry to solve for reactants' and products' quantities. When tackling exercises, take care to perform accurate molar mass calculations, as errors can mislead your solution.
Excess Reactant
In chemical reactions, reactants are often not consumed completely, leading to excess reactants. Identifying the excess reactant is crucial, as it provides insights into the reaction's efficiency and economy. For the thermite reaction, the excess reactant is found using the limiting reactant concept:
  • Calculate moles of each reactant.
  • Use stoichiometry to find which reactant runs out first (the limiting reactant).
  • Subtract the moles of the limiting reactant from the initial moles of other reactants to find the leftover or excess amount.
In our specific problem, aluminum acts as the excess reactant. After reacting with all available iron(III) oxide, not all aluminum is consumed, resulting in leftover aluminum. By calculating the precise amount of the remaining reactant, students better grasp the reaction's dynamics and efficiency.

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Most popular questions from this chapter

The metabolic disorder diabetes causes a buildup of acetone, \(\mathrm{CH}_{3} \mathrm{COCH}_{3,}\) in the blood. Acetone, a volatile compound, is exhaled, giving the breath of untreated diabetics a distinctive odor. The acetone is produced by a breakdown of fats in a series of reactions. The equation for the last step, the breakdown of acetoacetic acid to give acetone and \(\mathrm{CO}_{2},\) is $$\mathrm{CH}_{3} \mathrm{COCH}_{2} \mathrm{CO}_{2} \mathrm{H} \rightarrow \mathrm{CH}_{3} \mathrm{COCH}_{3}+\mathrm{CO}_{2}$$ What mass of acetone can be produced from \(125 \mathrm{mg}\) of acetoacetic acid?

An unknown metal reacts with oxygen to give the metal oxide, \(\mathrm{MO}_{2}\). Identify the metal if a \(0.356-\mathrm{g}\) sample of the metal produces \(0.452 \mathrm{g}\) of the metal oxide.

Sodium azide, an explosive chemical used in automobile airbags, is made by the following reaction: $$\mathrm{NaNO}_{3}+3 \mathrm{NaNH}_{2} \rightarrow \mathrm{NaN}_{3}+3 \mathrm{NaOH}+\mathrm{NH}_{3}$$ If you combine \(15.0 \mathrm{g}\) of \(\mathrm{NaNO}_{3}\) with \(15.0 \mathrm{g}\) of \(\mathrm{NaNH}_{2},\) what mass of \(\mathrm{NaN}_{3}\) is produced?

When an electric current is passed through an aqueous solution of \(\mathrm{NaCl}\), the valuable industrial chemicals \(\mathrm{H}_{2}(\mathrm{g}), \mathrm{Cl}_{2}(\mathrm{g}),\) and \(\mathrm{NaOH}\) are produced. $$2 \mathrm{NaCl}(\mathrm{aq})+2 \mathrm{H}_{2} \mathrm{O}(\ell) \rightarrow \mathrm{H}_{2}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g})+2 \mathrm{NaOH}(\mathrm{aq})$$ What mass of NaOH can be formed from 15.0 L of 0.35 M NaCl? What mass of chlorine is obtained?

Antacids are chemical compounds that can give immediate relief from indigestion or heartburn because they contain carbonate or hydroxide ions that neutralize stomach acids. Some common active ingredients include \(\mathrm{NaHCO}_{3}, \mathrm{KHCO}_{3}\), \(\mathrm{CaCO}_{3}, \mathrm{Mg}(\mathrm{OH})_{2},\) and \(\mathrm{Al}(\mathrm{OH})_{3} .\) Although these compounds give quick relief, they are not recommended for prolonged consumption. Calcium carbonate may contribute to the growth of kidney stones, and calcium carbonate and aluminum hydroxide may cause constipation. Magnesium hydroxide, on the other hand, is a mild laxative that can cause diarrhea. Antacids containing magnesium, therefore, are often combined with aluminum hydroxide since the aluminum counteracts the laxative properties of the magnesium. (a) Which of the compounds listed above produce gas-forming reactions when combined with HCl? (b) One tablet of Tums Regular Strength Antacid contains \(500 . \mathrm{mg} \mathrm{CaCO}_{3}\) . (i) Write a balanced chemical equation for the reaction of \(\mathrm{CaCO}_{3}\) and stomach acid \((\mathrm{HCl})\) (ii) What volume (in mL) of 0.500 \(\mathrm{M}\) HCl(aq) will react completely with one tablet of Tums? (c) The active ingredients in Rolaids are \(\mathrm{CaCO}_{3}\) and \(\mathrm{Mg}(\mathrm{OH})_{2}\). (i) Write a balanced chemical equation for the reaction of \(\mathrm{Mg}(\mathrm{OH})_{2}\) and \(\mathrm{HCl}\). (ii) If \(29.52 \mathrm{mL}\) of \(0.500 \mathrm{M} \mathrm{HCl}\) is required to titrate one tablet of Rolaids and the tablet contains \(550 \mathrm{mg}\) of \(\mathrm{CaCO}_{3},\) what mass of \(\mathrm{Mg}(\mathrm{OH})_{2}\) is present in one tablet? (d) Maalox may be purchased in either a liquid or solid form. One teaspoon of the liquid form of Maalox" contains a mixture of \(200 . \mathrm{mg}\) of \(\mathrm{Al}(\mathrm{OH})_{3}\) and \(200 . \mathrm{mg}\) of \(\mathrm{Mg}(\mathrm{OH})_{2} .\) What volume of 0.500 \(\mathrm{M} \mathrm{HCl}(\mathrm{aq})\) will react completely with one teaspoon of Maalox \(^{\pi / 2} ?\) (e) Which product neutralizes the greatest amount of acid when taken in the quantities presented above: one tablet of Tums" or Rolaids" or one teaspoon of Maalox"?
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