Question

Which equations are balanced? a. \(\mathrm{Mg}(\mathrm{s})+2 \mathrm{HCl}(\mathrm{aq}) \rightarrow \mathrm{MgCl}_{2}(\mathrm{aq})+\mathrm{H}_{2}(\mathrm{~g})\) b. \(3 \mathrm{Al}(\mathrm{s})+3 \mathrm{Br}_{2}(\ell) \rightarrow \mathrm{Al}_{2} \mathrm{Br}_{3}(\mathrm{~s})\) c. \(2 \mathrm{HgO}(\mathrm{s}) \rightarrow 2 \mathrm{Hg}(\ell)+\mathrm{O}_{2}(\mathrm{~g})\)

Short answer

Equations a and c are balanced.

Step-by-step solution

Understand the Concept of a Balanced Equation

A chemical equation is balanced when the number of atoms for each element is the same on both sides of the equation. This follows the law of conservation of mass, which states that mass cannot be created or destroyed in a chemical reaction.

Identify and Count Atoms for Equation a

For equation a, count the number of atoms of each element on both sides: - Reactants: 1 Mg, 2 H, 2 Cl - Products: 1 Mg, 2 Cl, 2 H Equation a is balanced.

Identify and Count Atoms for Equation b

For equation b, count the number of atoms of each element on both sides: - Reactants: 3 Al, 6 Br - Products: 2 Al, 6 Br Equation b is not balanced because the number of aluminum atoms does not match on both sides.

Identify and Count Atoms for Equation c

For equation c, count the number of atoms of each element on both sides: - Reactants: 2 Hg, 2 O - Products: 2 Hg, 2 O Equation c is balanced.

Key concepts

The Law of Conservation of Mass

The **Law of Conservation of Mass** is a fundamental principle in chemistry. It states that mass in an isolated system is neither created nor destroyed by chemical reactions or physical transformations. In simpler terms, whatever mass you start with in a chemical reaction, you will have the same mass at the end.
Think of it like baking a cake: if you start with a certain amount of ingredients, you still have the same amount of substances after baking - they might be just in a different form. You put together flour, eggs, sugar, and milk, and although they transform into a cake, the total weight remains the same.
In chemical reactions, this means that the atoms on the reactants' side must equal the atoms on the products' side. Understanding this concept helps in balancing chemical equations, ensuring that no atoms are lost or gained during the reaction.

Atom Counting

Atom counting is a crucial step when dealing with chemical equations. It helps ensure that the chemical equation abides by the law of conservation of mass. When you count atoms, you verify that each element has the same number of atoms on both the reactant and the product side of the equation.
To count effectively, you should:

• First, write down the number of atoms for each element in the reactants.
• Then, write down the number on the products side.
• Compare the numbers: If they match for all elements, the equation is balanced. If not, you need to adjust the coefficients accordingly.

Using these steps will make it easier to spot any imbalances and help you know when you’ve achieved a balanced equation!

Chemical Reaction

A **chemical reaction** involves the transformation of one or more substances into new substances. It's a process that cannot be easily reversed and often involves changes in energy, which can be seen as light, heat, or gas production.
Chemical reactions happen all around us, from the rusting of iron to the digestion of food. In the world of equations, these reactions are represented with symbols showing the reactants (starting materials) and the products (substances formed).
The ability to understand and interpret chemical reactions is essential in many scientific fields. It helps chemists synthesize new materials, understand biological processes, and even develop new energy solutions.

Chemical Equation Examples

Chemical equations are a way to express chemical reactions. They show which molecules react and what products they form. Let's look at our examples:
In example **(a)**, \(\mathrm{Mg}(\mathrm{s})+2 \mathrm{HCl}(\mathrm{aq}) \rightarrow \mathrm{MgCl}_{2}(\mathrm{aq})+\mathrm{H}_{2}(\mathrm{~g})\) is balanced. The magnesium (Mg), hydrogen chloride (HCl), resulting magnesium chloride (MgCl₂), and hydrogen gas (H₂) all maintain the same number of atoms before and after the reaction.
Example **(b)**, \(3 \mathrm{Al}(\mathrm{s})+3 \mathrm{Br}_{2}(\ell) \rightarrow \mathrm{Al}_{2} \mathrm{Br}_{3}(\mathrm{~s})\) is not balanced because the aluminum atoms don't match on both sides. To balance it, you would need to adjust the coefficients, ensuring equal numbers of atoms.
Example **(c)**, \(2 \mathrm{HgO}(\mathrm{s}) \rightarrow 2 \mathrm{Hg}(\ell)+\mathrm{O}_{2}(\mathrm{~g})\), keeps the same count of mercury and oxygen atoms on both sides, demonstrating once again the importance of balancing chemical equations.
These examples illustrate how equilibrium in a chemical equation is crucial to accurately reflect what physically happens in a reaction.