Question

Write a balanced chemical equation for the reaction that occurs when (a) calcium metal undergoes a combination reaction with ${\mathrm{O}}_2(g);$ (b) copper(II) hydroxide decomposes into copper(II) oxide and water when heated; (c) heptane, ${\mathrm{C}}_7{\mathrm{H}}_{16}(l),$ burns in air; (d) methyl tert-butyl ether, ${\mathrm{C}}_5{\mathrm{H}}_{12}\mathrm{O}(l)$ burns in air.

Short answer

(a) 2Ca + O₂ → 2CaO (b) Cu(OH)₂ → CuO + H₂O (c) C₇H₁₆ + 11O₂ → 7CO₂ + 8H₂O (d) C₅H₁₂O + 6O₂ → 5CO₂ + 6H₂O

Step-by-step solution

Reaction (a): Calcium metal and oxygen gas.

In this reaction, calcium metal (Ca) reacts with oxygen gas (O₂) to form calcium oxide (CaO). The unbalanced equation is: Ca + O₂ → CaO To balance the equation, we need to have 2 oxygen atoms on both sides. We can achieve this by placing a 2 in front of CaO: Ca + O₂ → 2CaO The balanced equation for this reaction is: 2Ca + O₂ → 2CaO

Reaction (b): Decomposition of copper(II) hydroxide.

Copper(II) hydroxide (Cu(OH)₂) decomposes upon heating to produce copper(II) oxide (CuO) and water (H₂O). The unbalanced equation is: Cu(OH)₂ → CuO + H₂O Balancing the equation, we realize that the number of atoms for each element is already equal on both sides. Therefore, the balanced equation for this reaction is: Cu(OH)₂ → CuO + H₂O

Reaction (c): Combustion of heptane.

Heptane (C₇H₁₆) reacts with oxygen gas (O₂) when burned in air to produce carbon dioxide (CO₂) and water (H₂O). The unbalanced equation is: C₇H₁₆ + O₂ → CO₂ + H₂O To balance the equation, first balance the carbon and hydrogen atoms: C₇H₁₆ + O₂ → 7CO₂ + 8H₂O Finally, balance the oxygen atoms by placing a 11 in front of O₂: C₇H₁₆ + 11O₂ → 7CO₂ + 8H₂O The balanced equation for this reaction is: C₇H₁₆ + 11O₂ → 7CO₂ + 8H₂O

Reaction (d): Combustion of methyl tert-butyl ether.

Methyl tert-butyl ether (C₅H₁₂O) reacts with oxygen gas (O₂) when burned in air to produce carbon dioxide (CO₂) and water (H₂O). The unbalanced equation is: C₅H₁₂O + O₂ → CO₂ + H₂O To balance the equation, first balance the carbon and hydrogen atoms: C₅H₁₂O + O₂ → 5CO₂ + 6H₂O Finally, balance the oxygen atoms by placing a 6 in front of O₂: C₅H₁₂O + 6O₂ → 5CO₂ + 6H₂O The balanced equation for this reaction is: C₅H₁₂O + 6O₂ → 5CO₂ + 6H₂O

Key concepts

Combination Reaction

A combination reaction, also known as a synthesis reaction, involves two or more substances reacting to form a single new product. These reactions are one of the simplest types of chemical reactions. An example from the exercise is the reaction of calcium metal with oxygen gas to form calcium oxide.

To write the balanced equation for this reaction, we start with the substances involved:

• Calcium (Ca) - the metal reactant.
• Oxygen (O₂) - the gaseous reactant.
• Calcium Oxide (CaO) - the product.

The unbalanced equation may look like this:$$\text{Ca}+\text{O₂}\to \text{CaO}$$
To balance the equation, count the atoms on each side and adjust the coefficients accordingly. In this case, balance the oxygen by placing a 2 in front of CaO, making it:$$\text{Ca}+\text{O₂}\to 2\text{CaO}$$
Further adjust the... by placing a 2 in front of Ca, resulting in:$$2\text{Ca}+\text{O₂}\to 2\text{CaO}$$This equation is now balanced, with equal numbers of Ca and O on both sides.

Combination reactions often release energy, making them exothermic. These reactions are common in forming compounds in nature.

Decomposition Reaction

Decomposition reactions are the opposite of combination reactions. In decomposition reactions, a single compound breaks down into two or more simpler substances. This type of reaction usually requires energy input, like heat, to occur.

An informative example from the given exercise is the decomposition of copper(II) hydroxide. When heated, it decomposes into copper(II) oxide and water.

• Copper(II) Hydroxide (Cu(OH)₂) - the compound undergoing decomposition.
• Copper(II) Oxide (CuO) - one of the products.
• Water (H₂O) - another product.

The initial unbalanced equation is:$$\text{Cu(OH)₂}\to \text{CuO}+\text{H₂O}$$
In this equation, notice the number of atoms for each element on both sides of the equation:

• 1 Copper atom on each side.
• 2 Oxygen atoms from Cu(OH)₂ turning into one CuO and one H₂O, totaling two Oxygen atoms.
• 2 Hydrogen atoms in the water molecule, matching the 2 from the hydroxide groups.

This equation is already balanced as is. Decomposition reactions are crucial in various applications, including recycling and the breakdown of organic materials.

Combustion Reaction

Combustion reactions are usually the burning of substances in the presence of oxygen. They generate heat and light, making them exothermic processes. In combustion, organic compounds often convert into carbon dioxide and water.

An example from the exercise is the combustion of heptane. Heptane, a hydrocarbon, reacts with oxygen to form carbon dioxide and water.

• Heptane (C₇H₁₆) - the hydrocarbon fuel.
• Oxygen (O₂) - the oxidizing agent causing the burn.
• Carbon Dioxide (CO₂) and Water (H₂O) - the products resulting from complete combustion.

The unbalanced reaction is:$$\text{C₇H₁₆}+\text{O₂}\to \text{CO₂}+\text{H₂O}$$
To balance it, adjust the carbon and hydrogen atoms first:$$\text{C₇H₁₆}+\text{O₂}\to 7\text{CO₂}+8\text{H₂O}$$
Then, ensure there are enough oxygen molecules by placing an 11 in front of O₂:$$\text{C₇H₁₆}+11\text{O₂}\to 7\text{CO₂}+8\text{H₂O}$$
Finally, your equation is balanced! Combustion reactions are vital for energy production in engines as well as cooking and heating processes. Proper balancing ensures an understanding of the stoichiometry involved, which is crucial for efficient energy use.