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Chapter 3: Problem 66

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 g of hydrogen?

Short Answer

Expert verified
(a) The balanced chemical equation for the reaction is: CaH_2 + 2 H_2O → Ca(OH)_2 + 2 H_2 (b) 46.955 g of calcium hydride is needed to form 4.500 g of hydrogen gas.

Step by step solution

01

Write the balanced chemical equation for the reaction

The reaction can be represented as follows: CaH_2 + 2 H_2O → Ca(OH)_2 + 2 H_2 This equation is already balanced, as there are an equal number of atoms of each element on both sides.
02

Convert the given mass of hydrogen gas to moles

To do this, we will use the molar mass of hydrogen gas. Hydrogen has a molar mass of 1.008 g/mol, so H_2 has a molar mass of 2.016 g/mol. Given mass of hydrogen = 4.500 g Molar mass of hydrogen (H_2) = 2.016 g/mol Number of moles = (given mass) / (molar mass) Number of moles of H_2 = 4.500 g / 2.016 g/mol = 2.232 moles
03

Use stoichiometry to find the moles of calcium hydride

From the balanced chemical equation, we can see that 1 mole of CaH_2 reacts to produce 2 moles of H_2. Now we can set up a proportion to find the moles of CaH_2 needed: 1 (mol CaH_2) / 2 (mol H_2) = x (mol CaH_2) / 2.232 (mol H_2) Solving for x, we find: x = (1 * 2.232) / 2 x = 1.116 moles of CaH_2
04

Convert moles of calcium hydride to grams

We will now use the molar mass of calcium hydride to convert the number of moles to grams. Calcium has a molar mass of 40.08 g/mol, and hydrogen has a molar mass of 1.008 g/mol, so CaH_2 has a molar mass of 42.096 g/mol. Molar mass of CaH_2 = 42.096 g/mol Moles of CaH_2 = 1.116 moles Mass of CaH_2 = (moles) × (molar mass) Mass of CaH_2 = 1.116 moles × 42.096 g/mol = 46.955 g
05

Provide the final answer

We found that 46.955 g of calcium hydride is needed to form 4.500 g of hydrogen gas.

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Most popular questions from this chapter

A sample of the male sex hormone testosterone, \(\mathrm{C}_{19} \mathrm{H}_{28} \mathrm{O}_{2}\) , contains \(3.88 \times 10^{21}\) hydrogen atoms. (a) How many atoms of carbon does it contain? (b) How many molecules of testosterone does it contain? (c) How many moles of testosterone does it contain? (d) What is the mass of this sample in grams?

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