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

Short Answer

Expert verified
The balanced chemical equation for the reaction between calcium hydride and water is: \(CaH_2 + H_2O -> Ca(OH)_2 + 2H_2\) To form 4.500 g of hydrogen gas, we need 47.25 g of calcium hydride.

Step by step solution

01

Write the balanced chemical equation

The unbalanced chemical equation for the reaction between calcium hydride (CaH₂) and water (H₂O) is: CaH₂ + H₂O -> Ca(OH)₂ + H₂ Now we need to balance the equation. There are two hydrogen atoms in CaH₂ and two hydrogen atoms in H₂O, making a total of 4 hydrogen atoms. To balance the hydrogen atoms, we will put a coefficient of 2 in front of H₂: CaH₂ + H₂O -> Ca(OH)₂ + 2H₂ Now the equation is balanced with the same number of atoms for each element on both sides.
02

Calculate the moles of hydrogen gas

In order to find out how many grams of calcium hydride we need to form 4.500 g of hydrogen gas, we first need to calculate the moles of hydrogen gas. The molar mass of hydrogen gas (H₂) is approximately 2 g/mol. We can use the formula: moles = mass / molar_mass moles_of_H₂ = 4.500 g / 2 g/mol = 2.250 mol So, there are 2.250 moles of hydrogen gas.
03

Use stoichiometry to find the moles of calcium hydride

From the balanced chemical equation, we know that one mole of calcium hydride reacts to produce one mole of calcium hydroxide and two moles of hydrogen gas. This means that the molar ratio between CaH₂ and H₂ is 1:2. We can set up a proportion to find the moles of calcium hydride needed: moles_of_CaH₂ / moles_of_H₂ = 1 / 2 moles_of_CaH₂ = (1 × 2.250 mol) / 2 = 1.125 mol So, we need 1.125 moles of calcium hydride to produce 2.250 moles of hydrogen gas.
04

Calculate the mass of calcium hydride

Now that we know how many moles of calcium hydride we need, we can calculate the mass of calcium hydride required. The molar mass of CaH₂ is approximately 42 g/mol (40 g/mol for Ca and 2 g/mol for two hydrogen atoms). We can use the equation: mass = moles × molar_mass mass_of_CaH₂ = 1.125 mol × 42 g/mol = 47.25 g So, we need 47.25 grams of calcium hydride to produce 4.500 grams of hydrogen gas.

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Most popular questions from this chapter

Propenoic acid, \(\mathrm{C}_{3} \mathrm{H}_{4} \mathrm{O}_{2},\) is a reactive organic liquid that is used in the manufacturing of plastics, coatings, and adhesives. An unlabeled container is thought to contain this liquid. A \(0.275-g\) sample of the liquid is combusted to produce \(0.102 \mathrm{~g}\) of water and \(0.374 \mathrm{~g}\) carbon dioxide. Is the unknown liquid propenoic acid? Support your reasoning with calculations.

Write balanced chemical equations for \((\mathbf{a})\) the complete combustion of acetone \(\left(\mathrm{CH}_{3} \mathrm{COCH}_{3}\right),\) a common organic solvent; (b) the decomposition of solid mercury (I) carbonate into carbon dioxide gas, mercury, and solid mercury oxide; (c) the combination reaction between sulphur dioxide gas and liquid water to produce sulfurous acid.

Sodium hydroxide reacts with carbon dioxide as follows: $$ 2 \mathrm{NaOH}(s)+\mathrm{CO}_{2}(g) \longrightarrow \mathrm{Na}_{2} \mathrm{CO}_{3}(s)+\mathrm{H}_{2} \mathrm{O}(l) $$ Which is the limiting reactant when \(1.85 \mathrm{~mol} \mathrm{NaOH}\) and \(1.00 \mathrm{~mol} \mathrm{CO}_{2}\) are allowed to react? How many moles of \(\mathrm{Na}_{2} \mathrm{CO}_{3}\) can be produced? How many moles of the excess reactant remain after the completion of the reaction?

(a) You are given a cube of silver metal that measures 1.000 \(\mathrm{cm}\) on each edge. The density of silver is \(10.5 \mathrm{~g} / \mathrm{cm}^{3} .\) How many atoms are in this cube? (b) Because atoms are spherical, they cannot occupy all of the space of the cube. The silver atoms pack in the solid in such a way that \(74 \%\) of the volume of the solid is actually filled with the silver atoms. Calculate the volume of a single silver atom. (c) Using the volume of a silver atom and the formula for the volume of a sphere, calculate the radius in angstroms of a silver atom.

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