Ch.10 - Gases

Problem 56

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Chapter 10, Problem 56

Calcium hydride, CaH2, reacts with water to form hydrogen gas: CaH21s2 + 2 H2O1l2¡Ca1OH221aq2 + 2 H21g2 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 110 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

Related Practice

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, 98.93 kPa; temperature, 99 °C.

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Textbook Question

The molar mass of a volatile substance was determined by the Dumas-bulb method described in Exercise 10.53. The unknown vapor had a mass of 2.55 g; the volume of the bulb was 500 mL, pressure 101.33 kPa, and temperature 37 °C.Calculate the molar mass of the unknown vapor.

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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 5.67 L has a partial pressure of O2 of 7.066 mPa at 30 °C, what mass of magnesium will react according to the following equation? 2 Mg1s2 + O21g2¡2 MgO1s2

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Open Question

The metabolic oxidation of glucose, C6H12O6, in our bodies produces CO2, which is expelled from our lungs as a gas: C6H12O6(aq) + 6 O2(g) → 6 CO2(g) + 6 H2O(l). (a) Calculate the volume of dry CO2 produced at normal body temperature, 37 °C, and 101.33 kPa when 10.0 g of glucose is consumed in this reaction. (b) Calculate the volume of oxygen you would need, at 100 kPa and 298 K, to completely oxidize 15.0 g of glucose.

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 expired air at its peak, assuming 1 atm pressure and a body temperature of 37 °C.

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