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 \(8.500 \mathrm{~g}\) of hydrogen?

Short answer

The balanced chemical equation for the reaction between calcium hydride and water is: CaH₂(s) + 2H₂O(l) → Ca(OH)₂(aq) + 2H₂(g). To produce 8.500 g of hydrogen gas, 88.759 g of calcium hydride are needed.

Step-by-step solution

Write the balanced chemical equation

The first step is to write down the unbalanced chemical equation for the reaction between calcium hydride (CaH₂) and water (H₂O). This will help us understand the stoichiometry of the reaction and find the balanced chemical equation. The unbalanced equation is: CaH₂ + H₂O → Ca(OH)₂ + H₂ To balance the chemical equation, we need to ensure that the number of atoms of each element on the reactant side is equal to the number on the product side. After balancing the equation, we obtain: CaH₂ + 2H₂O → Ca(OH)₂ + 2H₂ So, the balanced chemical equation is: CaH₂(s) + 2H₂O(l) → Ca(OH)₂(aq) + 2H₂(g)

Calculate the moles of hydrogen gas produced

We are given that 8.500 grams of hydrogen gas is produced in the reaction. To find out how many moles of hydrogen gas are produced, we need to use the molar mass of hydrogen gas (H₂). The molar mass of H₂ is 2.016 g/mol (since 1 mole of hydrogen has a mass of 1.008 g, and there are two hydrogen atoms in H₂). Now, we can calculate the moles of hydrogen gas produced as follows: moles of H₂ = (8.500 g) / (2.016 g/mol) = 4.220 moles of H₂

Use stoichiometry to find the moles of calcium hydride required

Now that we know the number of moles of hydrogen gas produced, we can use the stoichiometry given in the balanced chemical equation to find the number of moles of calcium hydride required for this reaction. From the balanced equation, we know that 1 mole of CaH₂ produces 2 moles of H₂. Therefore: moles of CaH₂ = (4.220 moles of H₂) / 2 = 2.110 moles of CaH₂

Calculate the mass of calcium hydride required

Finally, we will convert moles of calcium hydride to grams using its molar mass. The molar mass of CaH₂ is 42.094 g/mol (40.078 g/mol for calcium, 1.008 g/mol for hydrogen, so 40.078 + 2*1.008). mass of CaH₂ = (2.110 moles of CaH₂) * (42.094 g/mol) = 88.759 g Therefore, 88.759 grams of calcium hydride are needed to form 8.500 grams of hydrogen gas.

Key concepts

Balanced Chemical Equation

A balanced chemical equation represents a chemical reaction with the same number of atoms for each element on both sides of the equation. This ensures that mass is conserved, following the law of conservation of mass. To balance an equation, we adjust the coefficients (the numbers in front of chemical formulas) until each element has the same number of atoms on both the reactants and products side.

In our example, calcium hydride (\(\text{CaH}_2\)) reacts with water (\(\text{H}_2\text{O}\)) to form calcium hydroxide (\(\text{Ca(OH)}_2\)) and hydrogen gas (\(\text{H}_2\)). The unbalanced equation initially looks like this:

• \(\text{CaH}_2 + \text{H}_2\text{O} \rightarrow \text{Ca(OH)}_2 + \text{H}_2\)

To balance it, we ensure that the number of atoms for each element is equal on both sides:

• Balanced equation: \(\text{CaH}_2 + 2\text{H}_2\text{O} \rightarrow \text{Ca(OH)}_2 + 2\text{H}_2\)

This tells us that one molecule of calcium hydride reacts with two molecules of water to produce one molecule of calcium hydroxide and two molecules of hydrogen gas.

Moles and Molar Mass

Moles and molar mass are crucial concepts in chemistry that help us understand the amount of a substance in a given sample. The mole is a unit of measurement used to discuss the amount of substance, where one mole contains exactly \(6.022 \times 10^{23}\) entities, be it atoms, molecules, or ions.

The molar mass is the mass of one mole of a substance. It is expressed in grams per mole (\(g/mol\)). For example, the molar mass of hydrogen gas (\(\text{H}_2\)) is about \(2.016\ g/mol\), calculated by doubling the atomic mass of a hydrogen atom, as each molecule consists of two hydrogen atoms.

To convert grams of a substance to moles, we divide the mass of the substance by its molar mass. Using the example, when given \(8.500\ g\) of \(\text{H}_2\), the number of moles can be calculated using its molar mass:

• \( \text{Moles of } \text{H}_2 = \frac{8.500 \text{ g}}{2.016 \text{ g/mol}} = 4.220 \text{ moles} \)

This calculation helps us quantify how much of a substance is partaking in or forming in a chemical reaction.

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the relative quantities of reactants and products in chemical reactions. It relies heavily on the balanced chemical equation to provide a quantitative relationship between the different substances involved.

In the given reaction, the stoichiometry from the balanced equation indicates that 1 mole of calcium hydride generates 2 moles of hydrogen gas. Thus, if we know the number of moles of hydrogen gas produced, we can determine the number of moles of calcium hydride required.

For instance:

• We calculated that \(4.220\) moles of \(\text{H}_2\) are produced.
• According to stoichiometry, \(1\) mole of \(\text{CaH}_2\) forms \(2\) moles of \(\text{H}_2\).
• Thus, the required moles of \(\text{CaH}_2\) are \(\frac{4.220}{2} = 2.110\ moles\).

Stoichiometry helps in predicting the amounts of products formed in a reaction and the amounts of reactants needed.

Chemical Reactions

Chemical reactions describe how substances transform into new substances with different properties. These reactions involve the breaking and forming of chemical bonds. In this exercise, calcium hydride reacts with water, resulting in the formation of calcium hydroxide and hydrogen gas.

To understand chemical reactions, it is important to know the reactants (starting materials) and the products (resulting substances). In our case:

• Reactants: Calcium hydride (\(\text{CaH}_2\)) and water (\(\text{H}_2\text{O}\))
• Products: Calcium hydroxide (\(\text{Ca(OH)}_2\)) and hydrogen gas (\(\text{H}_2\))

Such reactions are characterized by changes in energy, typically in the form of heat, and are due to the reorganization of electrons in chemical bonds.

This example also illustrates a basic type of chemical reaction — a displacement reaction, where an element in one compound is replaced by another element, forming a new compound as a result.