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 of calcium hydride (CaH₂) with water (H₂O) is: CaH₂ + 2H₂O → Ca(OH)₂ + 2H₂ To form 4.500 g of hydrogen gas, 46.889 g of calcium hydride are needed.

Step 1: Write the unbalanced chemical equation

Write the chemical equation for the reaction between calcium hydride (CaH₂) and water (H₂O), forming calcium hydroxide (Ca(OH)₂) and hydrogen gas (H₂): CaH₂ + H₂O → Ca(OH)₂ + H₂

Step 2: Balance the chemical equation

Balance the chemical equation by placing coefficients in front of the chemical formulas to ensure equal numbers of atoms for each element on both sides of the equation: CaH₂ + 2H₂O → Ca(OH)₂ + 2H₂

Step 3: Calculate moles of hydrogen gas produced

To find out how many grams of calcium hydride are needed to form 4.500 g of hydrogen gas, first, we need to convert the mass of hydrogen gas into moles using the molar mass of hydrogen gas (2.02 g/mol): Moles of H₂ = \(\frac{4.500 \thinspace \text{g}}{2.02 \thinspace \text{g/mol}}\) = 2.228 moles H₂

Step 4: Relate the moles of hydrogen gas to moles of calcium hydride

Using the balanced chemical equation, determine the stoichiometric relationship between moles of hydrogen gas and moles of calcium hydride: 1 mol CaH₂ → 2 mol H₂ Therefore, for every mole of calcium hydride, 2 moles of hydrogen gas are produced. Using this stoichiometric relationship, we can find the moles of calcium hydride required to produce 2.228 moles of hydrogen gas: Moles of CaH₂ = \(\frac{1 \thinspace \text{mol CaH}_{2}}{2 \thinspace \text{mol H}_{2}}\) × 2.228 moles H₂ = 1.114 moles CaH₂

Step 5: Convert moles of calcium hydride to mass

Finally, convert the moles of calcium hydride into mass using the molar mass of calcium hydride (42.094 g/mol): Mass of CaH₂ = 1.114 moles CaH₂ × 42.094 \(\mathrm{\frac{g}{mol}}\) = 46.889 g CaH₂ So, 46.889 g of calcium hydride are needed to form 4.500 g of hydrogen gas.