Ch.10 - Gases

Brown - Chemistry: The Central Science 15th Edition

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Brown 15th Edition

Ch.10 - Gases

Problem 55

Chapter 10, Problem 55

Magnesium can be used as a “getter” in evacuated enclosures to react with the last traces of oxygen. (The magnesium is usually heated by passing an electric current through a wire or ribbon of the metal.) If an enclosure of 0.452 L has a partial pressure of O2 of 3.5×10−6 torr at 27°C, what mass of magnesium will react according to the following equation?

Verified step by step guidance

Convert the given partial pressure of O2 from torr to atm using the conversion factor: 1 atm = 760 torr.

Use the ideal gas law equation, PV = nRT, to calculate the number of moles of O2. Here, P is the pressure in atm, V is the volume in liters, R is the ideal gas constant (0.0821 L·atm/mol·K), and T is the temperature in Kelvin (convert 27°C to Kelvin by adding 273.15).

From the balanced chemical equation, determine the stoichiometric relationship between moles of O2 and moles of Mg. The equation is: 2 Mg + O2 -> 2 MgO, which shows that 1 mole of O2 reacts with 2 moles of Mg.

Calculate the moles of Mg needed using the stoichiometric ratio from the balanced equation.

Convert the moles of Mg to mass using the molar mass of magnesium (24.31 g/mol).

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Key Concepts

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

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 essential for calculating the amount of gas present in a given volume and pressure, allowing us to determine how many moles of oxygen are available for reaction with magnesium in the enclosure.

Stoichiometry

Stoichiometry involves the calculation of reactants and products in chemical reactions based on balanced equations. Understanding stoichiometry is crucial for determining the mass of magnesium needed to react with a specific amount of oxygen, as it allows us to convert moles of oxygen to moles of magnesium using the coefficients from the balanced chemical equation.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole. Knowing the molar mass of magnesium is necessary to convert the number of moles of magnesium calculated from stoichiometry into grams, which is the final answer required for the problem.

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Textbook Question

(a) Calculate the density of NO₂gas at 0.970 atm and 35 °C.

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Textbook Question

Calcium hydride, CaH2, reacts with water to form hydrogen gas:

CaH2(𝑠)+2 H2O(𝑙)⟶Ca(OH)2(𝑎𝑞)+2 H2(𝑔)

This reaction is sometimes used to inflate life rafts, weather balloons, and the like, when a simple, compact means of generating H2 is desired. How many grams of CaH2 are needed to generate 145 L of H2 gas if the pressure of H2 is 825 torr at 21°C?

Textbook Question

Acetylene gas, C2H2(𝑔), can be prepared by the reaction of calcium carbide with water:

CaC2(𝑠)+2 H2O(𝑙)⟶Ca(OH)2(𝑎𝑞)+C2H2(𝑔)

Calculate the volume of C2H2 that is collected over water at 23°C by reaction of 1.524 g of CaC2 if the total pressure of the gas is 753 torr. (The vapor pressure of water is tabulated in Appendix B.)

Textbook Question

In the Dumas-bulb technique for determining the molar mass of an unknown liquid, you vaporize the sample of a liquid that boils below 100°C in a boiling-water bath and determine the mass of vapor required to fill the bulb. From the following data, calculate the molar mass of the unknown liquid: mass of unknown vapor, 1.012 g; volume of bulb, 354 cm3; pressure, 742 torr; temperature, 99°C.

Textbook Question

Calculate the molar mass of a vapor that has a density of 7.135 g/L at 12°C and 743 torr.