Question

Complete and balance the equations for the following reactions. [Assume an excess of oxygen for (d).] (a) \(\mathrm{Na}(\mathrm{s})+\mathrm{Br}_{2}(\ell) \rightarrow\) (c) \(\mathrm{Al}(\mathrm{s})+\mathrm{F}_{2}(\mathrm{g}) \rightarrow\) (b) \(\mathrm{Mg}(\mathrm{s})+\mathrm{O}_{2}(\mathrm{g}) \rightarrow\) (d) \(\mathrm{C}(\mathrm{s})+\mathrm{O}_{2}(\mathrm{g}) \rightarrow\)

Short answer

Equations: (a) \(2\mathrm{Na} + \mathrm{Br}_2 \rightarrow 2\mathrm{NaBr}\); (c) \(2\mathrm{Al} + 3\mathrm{F}_2 \rightarrow 2\mathrm{AlF}_3\); (b) \(2\mathrm{Mg} + \mathrm{O}_2 \rightarrow 2\mathrm{MgO}\); (d) \(\mathrm{C} + \mathrm{O}_2 \rightarrow \mathrm{CO}_2\).

Step-by-step solution

Understand the Reaction Types

The reactions given are simple synthesis reactions where elements combine to form compounds. The task is to write the correct product chemical formulas and balance the equations according to the law of conservation of mass.

Write the Chemical Formulas of Products

For each reaction, identify the product based on the reactants:(a) Sodium reacts with bromine to form sodium bromide: \(\mathrm{NaBr}\).(c) Aluminum reacts with fluorine to form aluminum fluoride: \(\mathrm{AlF}_3\).(b) Magnesium reacts with oxygen to form magnesium oxide: \(\mathrm{MgO}\).(d) Carbon reacts with excess oxygen to form carbon dioxide: \(\mathrm{CO}_2\).

Write Unbalanced Equations

Using the products identified, write the unbalanced chemical equations:(a) \(\mathrm{Na} + \mathrm{Br}_2 \rightarrow \mathrm{NaBr}\)(c) \(\mathrm{Al} + \mathrm{F}_2 \rightarrow \mathrm{AlF}_3\)(b) \(\mathrm{Mg} + \mathrm{O}_2 \rightarrow \mathrm{MgO}\)(d) \(\mathrm{C} + \mathrm{O}_2 \rightarrow \mathrm{CO}_2\)

Balance Each Equation

Apply the law of conservation of mass by ensuring the number of atoms of each element is equal on both sides of the equation:(a) \(2\mathrm{Na} + \mathrm{Br}_2 \rightarrow 2\mathrm{NaBr}\)(c) \(2\mathrm{Al} + 3\mathrm{F}_2 \rightarrow 2\mathrm{AlF}_3\)(b) \(2\mathrm{Mg} + \mathrm{O}_2 \rightarrow 2\mathrm{MgO}\)(d) \(\mathrm{C} + \mathrm{O}_2 \rightarrow \mathrm{CO}_2\) (already balanced).

Key concepts

Reaction Balancing

Balancing chemical equations is an essential skill for understanding and analyzing chemical reactions. When balancing a chemical equation, we aim to have the same number of each type of atom on both sides of the equation. This process ensures that the equation abides by the law of conservation of mass.
When given an unbalanced equation, you'll start by counting the atoms of each element on both sides of the equation. For instance, in the reaction of sodium with bromine to form sodium bromide, the unbalanced equation is:

• Unbalanced: \(\mathrm{Na} + \mathrm{Br}_2 \rightarrow \mathrm{NaBr} \)

If you count the atoms, you'll notice two bromine atoms on the left but only one on the right. To balance, you'll place a coefficient of 2 in front of \(\mathrm{NaBr}\) and \(\mathrm{Na}\), ensuring equal numbers:

• Balanced: \(2\mathrm{Na} + \mathrm{Br}_2 \rightarrow 2\mathrm{NaBr}\)

It's like solving a puzzle, adjusting coefficients in front of compounds to equalize atom counts, always working methodically to minimize changes.

Synthesis Reactions

Synthesis reactions, a fundamental type of chemical reaction, involve two or more reactants combining to form a single product. These reactions are typically straightforward and are a common way new compounds are formed from elements.
For example, let's look at the synthesis reaction between aluminum and fluorine:

• \( \mathrm{Al} + \mathrm{F}_2 \rightarrow \mathrm{AlF}_3 \)

In this case, one aluminum atom reacts with fluorine to form aluminum fluoride, a single compound. Such reactions are characterized by forming one compound product from simpler reactants, whether elements or compounds.
Synthesis reactions are prevalent not just in laboratories but also in industrial chemistry and nature, such as in the formation of water from hydrogen and oxygen.

• General formula: \(A + B \rightarrow AB\)

They exemplify how simple combinations can lead to a more complex result, showcasing chemical reactivity's beautiful simplicity.

Law of Conservation of Mass

The law of conservation of mass is a foundational principle in chemistry and states that in a closed system, mass is conserved over time. This means that the mass of the reactants must equal the mass of the products.
When balancing chemical equations, this principle guides us to ensure that atoms are neither created nor destroyed in a reaction. By balancing an equation such as the reaction between magnesium and oxygen:

• Unbalanced: \(\mathrm{Mg} + \mathrm{O}_2 \rightarrow \mathrm{MgO}\)

We ensure that by balancing, the amount of magnesium and oxygen on the reactant side matches exactly what appears in the product:

• Balanced: \(2\mathrm{Mg} + \mathrm{O}_2 \rightarrow 2\mathrm{MgO}\)

This equality maintains the conservation of mass, as every atom can be accounted for in the resulting products.
Understanding this law is crucial for predicting the outcomes of chemical reactions and for carrying out reactions efficiently, whether in a scientific or industrial setting. It assures us that no matter the change that occurs, the total mass involved in any given reaction remains constant.