Question

Calcium hydride reacts with water to form calcium hydroxide and hydrogen gas. (a) Write a balanced chemical equation for the reaction. (b) How many grams of calcium hydride are needed to form \(8.500 \mathrm{~g}\) of hydrogen?

Short answer

The balanced chemical equation for the reaction between calcium hydride (CaH2) and water (H2O) is: CaH2 + 2H2O -> Ca(OH)2 + 2H2 To form \(8.500 \mathrm{~g}\) of hydrogen gas, \(88.566 \mathrm{~g}\) of calcium hydride is needed.

Step-by-step solution

Write the balanced chemical equation

For the reaction between Calcium Hydride (CaH2) and water (H2O), it forms Calcium Hydroxide (Ca(OH)2) and Hydrogen gas (H2). The unbalanced equation is: CaH2 + H2O -> Ca(OH)2 + H2 To balance the equation, we need to make sure that the number of atoms of each element on both sides of the equation is equal. In our case, we will need 2 moles of water molecules to balance the hydrogen atoms and the balanced chemical equation will be: CaH2 + 2H2O -> Ca(OH)2 + 2H2

Determine the molar mass of elements and compounds

We need to calculate the molar mass of calcium hydride (CaH2) and hydrogen gas (H2). Molar mass of Calcium (Ca) = \(40.08 \mathrm{~g/mol}\) Molar mass of Hydrogen (H) = \(1.01 \mathrm{~g/mol}\) Molar mass of CaH2 \(= 40.08 + 2 × 1.01 = 42.10 \mathrm{~g/mol}\) Molar mass of H2 \(= 2 × 1.01 = 2.02 \mathrm{~g/mol}\)

Perform stoichiometry calculations

Using the balanced chemical equation, we know that 1 mole of CaH2 reacts with 2 moles of H2O to produce 1 mole of Ca(OH)2 and 2 moles of H2. Hence, the mole ratio of CaH2 to H2 is 1:2. Given that we want to form \(8.500 \mathrm{~g}\) of hydrogen gas, let's determine the moles of hydrogen produced: Moles of hydrogen (\(n_{H2}\)) \(= \frac{8.500 \mathrm{~g}}{2.02 \mathrm{~g/mol}} = 4.2079 \mathrm{~mol}\) Now we will use the mole ratio to determine the moles of CaH2 needed: Moles of CaH2 (\(n_{CaH2}\)) \(= \frac{1}{2} \times 4.2079 \mathrm{~mol} = 2.10395 \mathrm{~mol}\)

Calculate mass of calcium hydride needed

To find the mass of CaH2 needed, multiply the moles of CaH2 by its molar mass: Mass of CaH2 \(= n_{CaH2} \times M_{CaH2} = 2.10395 \mathrm{~mol} \times 42.10 \mathrm{~g/mol} = 88.566 \mathrm{~g}\) So, \(88.566 \mathrm{~g}\) of calcium hydride is needed to form \(8.500 \mathrm{~g}\) of hydrogen gas.