Ch.10 - Gases

Brown - Chemistry: The Central Science 15th Edition

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Brown 15th Edition

Ch.10 - Gases

Problem 56

Chapter 10, Problem 56

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?

Verified step by step guidance

Convert the pressure from torr to atm using the conversion factor: 1 atm = 760 torr.

Use the ideal gas law equation, PV = nRT, to solve for the number of moles of H2 gas (n). Remember to convert the temperature from Celsius to Kelvin by adding 273.15.

Identify the stoichiometry of the reaction from the balanced chemical equation: 1 mole of CaH2 produces 2 moles of H2.

Calculate the moles of CaH2 needed using the stoichiometric relationship from the balanced equation.

Convert the moles of CaH2 to grams using the molar mass of CaH2.

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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. It involves using balanced chemical equations to determine the relationships between the quantities of substances involved. In this case, the stoichiometric coefficients from the reaction equation indicate that one mole of CaH2 produces two moles of H2 gas, which is essential for calculating the amount of CaH2 needed to generate a specific volume of H2.

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 allows us to calculate the number of moles of hydrogen gas produced in the reaction based on the given conditions of pressure and temperature. Understanding this concept is crucial for converting the volume of H2 gas into moles, which can then be used in stoichiometric calculations.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). For this problem, knowing the molar mass of CaH2 is necessary to convert moles of CaH2 into grams. The molar mass is calculated by summing the atomic masses of calcium and hydrogen, which allows for the final conversion needed to determine how many grams of CaH2 are required to produce the desired volume of hydrogen gas.

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Textbook Question

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?

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Textbook Question

Consider the apparatus shown in the following drawing. (a) When the valve between the two containers is opened and the gases are allowed to mix, what is the partial pressure of N2 after mixing?

1135

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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.