Question

What mass of CaH₂ is necessary to react with water to provide enough hydrogen gas to fill a balloon at 20 °C and 0.8 atm pressure with a volume of 4.5 L? The balanced equation is: CaH₂(s) + 2H₂O(l) ⟶ Ca(OH)₂(aq) + 2H₂(g)

a. 0.45 g
b. 2.25 g
c. 4.50 g
d. 9.00 g

Answer 1

To find the mass of CaH₂ necessary to react with water and provide enough hydrogen gas to fill a balloon, use the ideal gas law to calculate the moles of H₂ gas. Then, use the balanced equation to determine the stoichiometric ratio and convert the moles of H₂ gas to grams of CaH₂ using the molar mass.

Step-by-step explanation:

To find the mass of CaH₂ necessary to react with water and provide enough hydrogen gas to fill a balloon, we need to use stoichiometry. First, calculate the number of moles of H₂ gas required using the ideal gas law. Then, use the balanced equation to determine the stoichiometric ratio between CaH₂ and H₂ gas. Finally, convert the moles of H₂ gas to grams of CaH₂ using the molar mass of CaH₂.

Step 1: Calculate the moles of H₂ gas using the ideal gas law:

moles H₂ = PV / RT

Step 2: Calculate the stoichiometric ratio by using the balanced equation:

1 mole CaH₂ = 2 moles H₂

Step 3: Convert moles of H₂ gas to grams of CaH₂ using the molar mass:

grams CaH₂ = moles H₂ x molar mass CaH₂

Substitute the given values into the equations and calculate the mass of CaH₂:

mass CaH₂ = (0.8 atm x 4.5 L) / (0.0821 atm·L/mol·K x 293K) x (1 mol CaH₂ / 2 mol H₂) x (42.1 g CaH₂ / 1 mol CaH₂)

mass CaH₂ = 2.25 g