How many grams of calcium hydride (CaH2) are required to produce 4.56 L of hydrogen gas (H2) at 25.0 °C and 0.975 atm according to the reaction: CaH2(s) + 2H2O(l) → Ca(OH)2(aq) + 2H2(g)?

• A. 0.500 g
• B. 0.125 g
• C. 1.000 g
• D. 0.250 g

Answer: (A)

Verified step by step guidance

1. Start by using the ideal gas law to find the number of moles of hydrogen gas (H2) produced. The ideal gas law is given by the equation: \( PV = nRT \), 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.
2. Convert the temperature from Celsius to Kelvin by adding 273.15 to the Celsius temperature: \( T(K) = 25.0 + 273.15 \).
3. Rearrange the ideal gas law to solve for \( n \), the number of moles of hydrogen gas: \( n = \frac{PV}{RT} \). Substitute the given values for \( P \), \( V \), and \( T \) into the equation to calculate \( n \).
4. Use the stoichiometry of the balanced chemical equation to find the moles of calcium hydride (CaH2) needed. According to the equation, 1 mole of CaH2 produces 2 moles of H2. Therefore, divide the moles of H2 by 2 to find the moles of CaH2 required.
5. Finally, convert the moles of CaH2 to grams using its molar mass. The molar mass of CaH2 is approximately 42.09 g/mol. Multiply the moles of CaH2 by its molar mass to find the mass in grams.