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Multiple Choice
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
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.
Convert the temperature from Celsius to Kelvin by adding 273.15 to the Celsius temperature: \( T(K) = 25.0 + 273.15 \).
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 \( n \).
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.
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.