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.
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 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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