Calcium hydride is a convenient, portable source of hydrogen that is used, among other things, to inflate weather balloons. If the reaction of CaH2 with water is used to inflate a balloon with 2.0 * 10^5 L of H2 gas at 25 °C and 1.00 atm pressure, how many kilograms of CaH2 are needed?

Verified step by step guidance

1. Step 1: Write the balanced chemical equation for the reaction between calcium hydride (CaH2) and water (H2O). The reaction is: \[ \text{CaH}_2 + 2\text{H}_2\text{O} \rightarrow \text{Ca(OH)}_2 + 2\text{H}_2 \]
2. Step 2: Use the ideal gas law to calculate the number of moles of hydrogen gas (H2) produced. The ideal gas law is given by \( PV = nRT \), where \( P \) is the pressure, \( V \) is the volume, \( n \) is the number of moles, \( R \) is the ideal gas constant (0.0821 L·atm/mol·K), and \( T \) is the temperature in Kelvin.
3. Step 3: Convert the temperature from Celsius to Kelvin by adding 273.15 to the Celsius temperature. For 25 °C, the temperature in Kelvin is \( 25 + 273.15 = 298.15 \text{ K} \).
4. Step 4: Rearrange the ideal gas law to solve for \( n \), the number of moles of hydrogen gas: \( n = \frac{PV}{RT} \). Substitute the known values (\( P = 1.00 \text{ atm} \), \( V = 2.0 \times 10^5 \text{ L} \), \( R = 0.0821 \text{ L·atm/mol·K} \), \( T = 298.15 \text{ K} \)) into the equation to find \( n \).
5. Step 5: Use stoichiometry to determine the mass of CaH2 needed. From the balanced equation, 1 mole of CaH2 produces 2 moles of H2. Calculate the moles of CaH2 required and then convert this to mass using the molar mass of CaH2 (42.09 g/mol). Finally, convert the mass from grams to kilograms.

Key Concepts

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions based on the balanced chemical equation. It allows us to determine the amount of one substance needed to react with a given amount of another. In this case, understanding the stoichiometric relationship between calcium hydride (CaH2) and hydrogen gas (H2) produced from their reaction with water is essential for calculating the required mass of CaH2.

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 crucial for determining the number of moles of hydrogen gas produced in the reaction, given the volume (2.0 * 10^5 L), temperature (25 °C), and pressure (1.00 atm). By calculating the moles of H2, we can then use stoichiometry to find the mass of CaH2 needed.

Molar Mass

Molar mass is the mass of one mole of a substance, expressed in grams per mole (g/mol). For calcium hydride (CaH2), the molar mass is calculated by summing the atomic masses of calcium and hydrogen. Knowing the molar mass is essential for converting between moles of CaH2 and grams, allowing us to determine how many kilograms of CaH2 are required to produce the desired volume of hydrogen gas.