Question

When the hydroxide compound of many metals is heated, water is driven off and the oxide of the metal remains. For example, if cobalt(II) hydroxide is heated, cobalt(II) oxide is produced. $$\mathrm{Co}(\mathrm{OH})_{2}(s) \rightarrow \operatorname{CoO}(s)+\mathrm{H}_{2} \mathrm{O}(g)$$ What mass of cobalt(II) oxide would remain if \(5.75 \mathrm{g}\) of cobalt(II) hydroxide were heated strongly?

Short answer

If 5.75 g of cobalt(II) hydroxide were heated strongly, 4.63 g of cobalt(II) oxide would remain.

Step-by-step solution

Calculate the molar mass of cobalt(II) hydroxide and cobalt(II) oxide

First, we need to find the molar mass of each compound. To do this, we sum the molar mass of each element in the compound according to its chemical formula. For cobalt(II) hydroxide, Co(OH)₂: Molar mass of Co = 58.93 g/mol Molar mass of O = 16.00 g/mol Molar mass of H = 1.01 g/mol Molar mass of Co(OH)₂ = 58.93 + 2(16.00 + 1.01) = 58.93 + 34.02 = 92.95 g/mol For cobalt(II) oxide, CoO: Molar mass of Co = 58.93 g/mol Molar mass of O = 16.00 g/mol Molar mass of CoO = 58.93 + 16.00 = 74.93 g/mol

Convert the mass of cobalt(II) hydroxide to moles

Now, we will convert the given mass of cobalt(II) hydroxide (5.75 g) to moles using its molar mass (92.95 g/mol). Moles of Co(OH)₂ = (5.75 g) / (92.95 g/mol) = 0.0618 mol

Determine the moles of cobalt(II) oxide produced

Using the stoichiometry of the balanced chemical equation, we can determine the moles of cobalt(II) oxide produced. The balanced equation tells us that 1 mole of Co(OH)₂ produces 1 mole of CoO. Moles of CoO = moles of Co(OH)₂ = 0.0618 mol

Convert the moles of cobalt(II) oxide to mass

Finally, we will convert the moles of cobalt(II) oxide (0.0618 mol) to mass using its molar mass (74.93 g/mol). Mass of CoO = (0.0618 mol) * (74.93 g/mol) = 4.63 g Therefore, 4.63 g of cobalt(II) oxide would remain if 5.75 g of cobalt(II) hydroxide were heated strongly.

Key concepts

Molar Mass Calculation

Molar mass calculation plays a crucial role in understanding how to convert between mass and moles in chemistry. Each element in the periodic table has a unique atomic mass, which is expressed in grams per mole, representing the mass of one mole of atoms of that element. When calculating the molar mass of a compound, we add the atomic masses of each element within the compound's formula, considering the number of atoms of each element present.
For example, in cobalt(II) hydroxide, Co(OH)₂, the molar mass calculation involves adding the atomic mass of cobalt, oxygen, and hydrogen. With the atomic masses of cobalt (58.93 g/mol), oxygen (16.00 g/mol), and hydrogen (1.01 g/mol), the formula for Co(OH)₂ translates to a molar mass of 92.95 g/mol, calculated as follows:

• Cobalt: 58.93 g/mol
• Oxygen: 2 atoms x 16.00 g/mol = 32.00 g/mol
• Hydrogen: 2 atoms x 1.01 g/mol = 2.02 g/mol

The sum gives us 92.95 g/mol for Co(OH)₂. Understanding molar mass allows us to relate the mass of substances in chemical reactions to the amounts in moles, facilitating stoichiometric calculations.

Chemical Reactions

Chemical reactions involve the rearrangement of atoms to form new substances. This is represented by a chemical equation where reactants are converted into products. These reactions must be balanced, meaning the number of each type of atom is the same on both sides of the equation, reflecting the law of conservation of mass.
For the reaction of cobalt(II) hydroxide decomposing into cobalt(II) oxide and water, the balanced equation is:\[\mathrm{Co}(\mathrm{OH})_{2}(s) \rightarrow \operatorname{CoO}(s)+\mathrm{H}_{2} \mathrm{O}(g)\]This equation indicates that one mole of cobalt(II) hydroxide will produce one mole of cobalt(II) oxide and one mole of water, illustrating the 1:1:1 ratio in this reaction. This stoichiometric relationship is essential for determining the quantities of each substance involved.
When we calculate the reaction outcomes, we start by determining the moles of the reactants and then use the balanced equation to find the moles of products formed, making stoichiometry a powerful tool in chemical analysis.

Thermal Decomposition

Thermal decomposition is a chemical process where a single compound breaks down into two or more simpler substances upon heating. This type of reaction usually requires heat to initiate, as it involves breaking chemical bonds, which consumes energy.
In our example, cobalt(II) hydroxide undergoes thermal decomposition when heated, resulting in the formation of cobalt(II) oxide and water:\[\mathrm{Co}(\mathrm{OH})_{2}(s) \rightarrow \operatorname{CoO}(s)+\mathrm{H}_{2} \mathrm{O}(g)\]During this process, heat provides the energy needed to break the bonds within Co(OH)₂, shifting atoms into new arrangements to form CoO and H₂O. This type of reaction is common with metal hydroxides, oxides, and carbonates as they often release water, oxygen, or carbon dioxide when decomposed.
Understanding thermal decomposition reactions helps predict the behavior of compounds under heat and their potential products, an essential aspect in both academic studies and industrial applications.