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Chapter 3: Problem 62

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

Expert verified
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

01

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
02

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 \(= 40.08 + 2 脳 1.01 = 42.10 \mathrm{~g/mol}\) Molar mass of H2 \(= 2 脳 1.01 = 2.02 \mathrm{~g/mol}\)
03

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 (\(n_{CaH2}\)) \(= \frac{1}{2} \times 4.2079 \mathrm{~mol} = 2.10395 \mathrm{~mol}\)
04

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.

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