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Ch.6 - Gases
Tro - Chemistry: A Molecular Approach 6th Edition
Tro6th EditionChemistry: A Molecular ApproachISBN: 9780137832217Not the one you use?Change textbook
All textbooksTro 6th EditionCh.6 - GasesProblem 82
Chapter 6, Problem 82

Oxygen gas reacts with powdered aluminum according to the reaction: 4 Al(s) + 3 O2(g) → 2 Al2O3(s) What volume of O2 gas (in L), measured at 782 mmHg and 25 °C, completely reacts with 53.2 g Al?

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1
Calculate the moles of aluminum (Al) using its molar mass. The molar mass of Al is approximately 26.98 g/mol.
Use the stoichiometry of the balanced chemical equation to find the moles of oxygen gas (O2) needed. According to the equation, 4 moles of Al react with 3 moles of O2.
Convert the moles of O2 to volume using the ideal gas law equation: PV = nRT. First, convert the pressure from mmHg to atm (1 atm = 760 mmHg).
Convert the temperature from Celsius to Kelvin by adding 273.15 to the Celsius temperature.
Substitute the values into the ideal gas law equation to solve for the volume (V) of O2 gas. Use R = 0.0821 L·atm/mol·K as the ideal gas constant.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions based on the balanced equation. It allows us to determine the proportions of substances involved in a reaction. In this case, the balanced equation shows that 4 moles of aluminum react with 3 moles of oxygen gas, which is essential for calculating the amount of O2 needed for the given mass of Al.
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Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. This law is crucial for converting the amount of oxygen gas from moles to volume under specific conditions of temperature and pressure. Understanding how to manipulate this equation will help in finding the volume of O2 required for the reaction.
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Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is essential for converting grams of a substance to moles, which is necessary for stoichiometric calculations. For aluminum, the molar mass is approximately 26.98 g/mol, and knowing this allows us to determine how many moles of Al are present in 53.2 g, which is the first step in solving the problem.
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Related Practice
Textbook Question

Consider the chemical reaction:

C(s) + H2O(g) → CO(g) + H2(g)

How many liters of hydrogen gas are formed from the complete reaction of 22.5 g C? Assume that the hydrogen gas is collected at a pressure of 1.00 atm and a temperature of 355 K.

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Textbook Question

Lithium reacts with nitrogen gas according to the reaction: 6 Li(s) + N2(g) → 2 Li3N(s) What mass of lithium (in g) reacts completely with 58.5 mL of N2 gas at STP?

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Textbook Question

CH3OH can be synthesized by the reaction: CO(g) + 2 H2(g) → CH3OH( g) What volume of H2 gas (in L), at 748 mmHg and 86 °C, is required to synthesize 25.8 g CH3OH? How many liters of CO gas, measured under the same conditions, are required?

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Textbook Question

Automobile air bags inflate following a serious impact. The impact triggers the chemical reaction: 2 NaN3(s) → 2 Na(s) + 3 N2(g) If an automobile air bag has a volume of 11.8 L, what mass of NaN3 (in g) is required to fully inflate the air bag upon impact? Assume STP conditions.

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Textbook Question

Consider the chemical reaction: 2 H2O(l) → 2 H2(g) + O2(g) What mass of H2O is required to form 1.85 L of O2 at a temperature of 315 K and a pressure of 0.981 atm?

Textbook Question

Hydrogen gas (a potential future fuel) can be formed by the reaction of methane with water according to the equation: CH4(g) + H2O(g) → CO(g) + 3 H2(g) In a particular reaction, 25.5 L of methane gas (measured at a pressure of 732 torr and a temperature of 25 °C) mixes with 22.8 L of water vapor (measured at a pressure of 702 torr and a temperature of 125 °C). The reaction produces 26.2 L of hydrogen gas at STP. What is the percent yield of the reaction?

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