Problem 66 - Chemistry: The Central Science

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 \(4.500 \mathrm{~g}\) of hydrogen?

Step-by-Step Solution

Answer

The balanced chemical equation for the reaction between calcium hydride (CaH2) and water (H2O) is: \[ \text{CaH}_2 + 2\text{H}_2\text{O} → \text{Ca(OH)}_2 + 2\text{H}_2 \] Approximately 46.978 g of calcium hydride are needed to form 4.500 g of hydrogen gas.

Step 1: Write the balanced chemical equation

First, let's write the unbalanced equation for the reaction between calcium hydride (CaH2) and water (H2O): \[ \text{CaH}_2 + \text{H}_2\text{O} → \text{Ca(OH)}_2 + \text{H}_2 \] Now, let's balance the equation. We can see that there are 2 moles of hydrogen in calcium hydride and 2 moles of hydrogen in water. In addition, there is one mole of oxygen in water and one mole of oxygen in calcium hydroxide. Thus, the balanced equation is: \[ \text{CaH}_2 + 2\text{H}_2\text{O} → \text{Ca(OH)}_2 + 2\text{H}_2 \]

Step 2: Determine the molar mass of hydrogen gas and calcium hydride

We will need to determine the molar mass of hydrogen gas (H2) and calcium hydride (CaH2) to find the mass of calcium hydride needed to form 4.500 g of hydrogen. The molar mass of hydrogen gas (H2) is approximately \(2 \times 1.008 = 2.016\,\text{g/mol}\). The molar mass of calcium hydride (CaH2) is approximately \(40.08 + 2\times 1.008 = 42.096\,\text{g/mol}\).

Step 3: Calculate the moles of hydrogen gas

We can now calculate the moles of hydrogen gas produced by using the mass of hydrogen gas given in the problem (4.500 g) and the molar mass of hydrogen gas (2.016 g/mol): \[ \text{moles of H}_2 = \frac{4.500\,\text{g}}{2.016\,\text{g/mol}} ≈ 2.232\,\text{mol}\]

Step 4: Calculate the moles of calcium hydride needed

From the balanced equation, we can see that 1 mole of calcium hydride (CaH2) is required for every 2 moles of hydrogen gas produced. Therefore, we can calculate the moles of calcium hydride needed: \[ \text{moles of CaH}_2 = \frac{\text{moles of H}_2}{2} = \frac{2.232\,\text{mol}}{2} ≈ 1.116\,\text{mol} \]

Step 5: Calculate the mass of calcium hydride needed

Now that we have the moles of calcium hydride needed, we can calculate the mass of calcium hydride required by using the molar mass of calcium hydride (42.096 g/mol): \[ \text{mass of CaH}_2 = 1.116\,\text{mol} × 42.096\,\text{g/mol} ≈ 46.978\,\text{g}\] Therefore, approximately 46.978 g of calcium hydride are needed to form 4.500 g of hydrogen gas.