Ch.10 - Gases

Brown - Chemistry: The Central Science 14th Edition

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Brown 14th Edition

Ch.10 - Gases

Problem 56

Chapter 10, Problem 56

Calcium hydride, CaH2, reacts with water to form hydrogengas:CaH21s2 + 2 H2O1l2¡Ca1OH221aq2 + 2 H21g2This reaction is sometimes used to inflate life rafts, weatherballoons, and the like, when a simple, compact means ofgenerating H2 is desired. How many grams of CaH2 areneeded to generate 145 L of H2 gas if the pressure of H2 is110 kPa at 21 °C?

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Identify the balanced chemical equation: \( \text{CaH}_2 + 2 \text{H}_2\text{O} \rightarrow \text{Ca(OH)}_2 + 2 \text{H}_2 \).

Use the ideal gas law \( PV = nRT \) to find the number of moles of \( \text{H}_2 \) gas. Convert the given pressure from kPa to atm and temperature from Celsius to Kelvin.

Calculate the number of moles of \( \text{H}_2 \) using \( n = \frac{PV}{RT} \), where \( R \) is the ideal gas constant (0.0821 L·atm/mol·K).

Use stoichiometry to determine the moles of \( \text{CaH}_2 \) needed. From the balanced equation, 1 mole of \( \text{CaH}_2 \) produces 2 moles of \( \text{H}_2 \).

Convert the moles of \( \text{CaH}_2 \) to grams using its molar mass (\( \text{CaH}_2 \) has a molar mass of approximately 42.09 g/mol).

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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 consumed and produced. In this case, the stoichiometric coefficients from the reaction of calcium hydride with water will help us relate the amount of CaH2 needed to produce a specific volume of hydrogen gas.

Ideal Gas Law

The Ideal Gas Law (PV = nRT) relates the pressure, volume, temperature, and number of moles of a gas. It allows us to calculate the amount of gas produced in a reaction under specific conditions. For this problem, we can use the Ideal Gas Law to find the number of moles of hydrogen gas generated, which can then be converted to the mass of calcium hydride required for the reaction.

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 between moles and grams in stoichiometric calculations. In this scenario, knowing the molar mass of calcium hydride (CaH2) will allow us to calculate how many grams are needed to produce the desired volume of hydrogen gas based on the moles determined from the Ideal Gas Law.

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Molar Mass Concept

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Textbook Question

In the Dumas-bulb technique for determining the molarmass of an unknown liquid, you vaporize the sample of aliquid that boils below 100 °C in a boiling-water bath anddetermine the mass of vapor required to fill the bulb. Fromthe following data, calculate the molar mass of the unknownliquid: mass of unknown vapor, 1.012 g; volume of bulb,354 cm3; pressure, 98.93 kPa; temperature, 99 °C.

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Textbook Question

The molar mass of a volatile substance was determined bythe Dumas-bulb method described in Exercise 10.53. Theunknown vapor had a mass of 2.55 g; the volume of thebulb was 500 mL, pressure 101.33 kPa, and temperature37 °C.Calculate the molar mass of the unknown vapor.

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Textbook Question

Magnesium can be used as a 'getter' in evacuated enclosuresto react with the last traces of oxygen. (The magnesium isusually heated by passing an electric current through a wireor ribbon of the metal.) If an enclosure of 5.67 L has a partialpressure of O2 of 7.066 mPa at 30 °C, what mass of magnesiumwill react according to the following equation?2 Mg1s2 + O21g2¡2 MgO1s2

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Textbook Question

Both Jacques Charles and Joseph Louis Guy-Lussac were avid balloonists. In his original flight in 1783, Jacques Charles used a balloon that contained approximately 31,150 L of H2. He generated the H2 using the reaction between iron and hydrochloric acid: Fe1s2 + 2 HCl1aq2 ¡ FeCl21aq2 + H21g2 How many kilograms of iron were needed to produce this volume of H2 if the temperature was 22 °C?

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Textbook Question

During a person's typical breathing cycle, the CO2 concentration in the expired air rises to a peak of 4.6% by volume.(a) Calculate the partial pressure of the CO2 in the expiredair at its peak, assuming 1 atm pressure and a body temperature of 37 °C.

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