Question

Write a balanced equation for the neutralization of each of the following: a. \(\mathrm{H}_{2} \mathrm{SO}_{4}(a q)\) and \(\mathrm{NaOH}(a q)\) b. \(\mathrm{HCl}(a q)\) and \(\mathrm{Fe}(\mathrm{OH})_{3}(s)\) c. \(\mathrm{H}_{2} \mathrm{CO}_{3}(a q)\) and \(\mathrm{Mg}(\mathrm{OH})_{2}(s)\)

Short answer

a. \( \mathrm{H}_{2}\mathrm{SO}_{4}(aq) + 2\mathrm{NaOH}(aq) \rightarrow \mathrm{Na}_{2}\mathrm{SO}_{4}(aq) + 2\mathrm{H}_{2}\mathrm{O}(l) \)b. \( 3\mathrm{HCl}(aq) + \mathrm{Fe(OH)}_{3}(s) \rightarrow \mathrm{FeCl}_{3}(aq) + 3\mathrm{H}_{2}\mathrm{O}(l) \)c. \( \mathrm{H}_{2}\mathrm{CO}_{3}(aq) + \mathrm{Mg(OH)}_{2}(s) \rightarrow \mathrm{MgCO}_{3}(aq) + 2\mathrm{H}_{2}\mathrm{O}(l) \)

Step-by-step solution

Identify Reactants

List the given reactants for each neutralization reaction. These include an acid and a base for each case:a. \( \mathrm{H}_{2}\mathrm{SO}_{4}(aq) \) (acid) and \( \mathrm{NaOH}(aq) \) (base)b. \( \mathrm{HCl}(aq) \) (acid) and \( \mathrm{Fe(OH)}_{3}(s) \) (base)c. \( \mathrm{H}_{2}\mathrm{CO}_{3}(aq) \) (acid) and \( \mathrm{Mg(OH)}_{2}(s) \) (base)

Write Unbalanced Equations

For each pair of reactants, write the initial, unbalanced chemical equation for their reaction that produces water and a salt:a. \( \mathrm{H}_{2}\mathrm{SO}_{4}(aq) + \mathrm{NaOH}(aq) \rightarrow \mathrm{Na}_{2}\mathrm{SO}_{4}(aq) + \mathrm{H}_{2}\mathrm{O}(l) \)b. \( \mathrm{HCl}(aq) + \mathrm{Fe(OH)}_{3}(s) \rightarrow \mathrm{FeCl}_{3}(aq) + \mathrm{H}_{2}\mathrm{O}(l) \)c. \( \mathrm{H}_{2}\mathrm{CO}_{3}(aq) + \mathrm{Mg(OH)}_{2}(s) \rightarrow \mathrm{MgCO}_{3}(aq) + \mathrm{H}_{2}\mathrm{O}(l) \)

Balance the Equations

Balance each equation by making sure the number of atoms for each element is the same on both sides:a. \[\mathrm{H}_{2}\mathrm{SO}_{4}(aq) + 2\mathrm{NaOH}(aq) \rightarrow \mathrm{Na}_{2}\mathrm{SO}_{4}(aq) + 2\mathrm{H}_{2}\mathrm{O}(l)\]b. \[3\mathrm{HCl}(aq) + \mathrm{Fe(OH)}_{3}(s) \rightarrow \mathrm{FeCl}_{3}(aq) + 3\mathrm{H}_{2}\mathrm{O}(l)\]c. \[\mathrm{H}_{2}\mathrm{CO}_{3}(aq) + \mathrm{Mg(OH)}_{2}(s) \rightarrow \mathrm{MgCO}_{3}(aq) + 2\mathrm{H}_{2}\mathrm{O}(l)\]

Key concepts

balanced chemical equations

Balanced chemical equations represent a chemical reaction where both sides have the same number of atoms for each element. This indicates that mass is conserved during the reaction. In neutralization reactions, ensuring that each atom is balanced is essential. For example, in the unbalanced equation for the reaction between sulfuric acid (H₂SO₄) and sodium hydroxide (NaOH):
\[ \text{H}_{2}\text{SO}_{4}(aq) + \text{NaOH}(aq) \rightarrow \text{Na}_{2}\text{SO}_{4}(aq) + \text{H}_2\text{O}(l) \]
we observe that the atoms are not balanced right away. By carefully counting and balancing these atoms, we arrive at:
\[ \text{H}_{2}\text{SO}_{4}(aq) + 2\text{NaOH}(aq) \rightarrow \text{Na}_{2}\text{SO}_{4}(aq) + 2\text{H}_2\text{O}(l) \]

This balanced equation shows that the same number of H, S, O, and Na atoms is present on both sides. As this example demonstrates, balancing chemical equations helps ensure we adhere to the law of conservation of mass.

acid-base reactions

Acid-base reactions are a type of chemical reaction where an acid and a base react to form water and a salt. This process is called a neutralization reaction. Let's break it down a bit:

• Acids are substances that release hydrogen ions (H⁺) in solution.
• Bases are substances that release hydroxide ions (OH⁻) in solution.

When an acid and a base come together, the hydrogen ion from the acid reacts with the hydroxide ion from the base to form water, a much less reactive substance:
\[ \text{H}^+ + \text{OH}^- \rightarrow \text{H}_2\text{O} \]

For instance, in the reaction between hydrochloric acid (HCl) and iron(III) hydroxide (Fe(OH)₃), we begin with an unbalanced equation:
\[ \text{HCl}(aq) + \text{Fe(OH)}_{3}(s) \rightarrow \text{FeCl}_{3}(aq) + \text{H}_2\text{O}(l) \]
After balancing, we get:
\[ 3\text{HCl}(aq) + \text{Fe(OH)}_{3}(s) \rightarrow \text{FeCl}_{3}(aq) + 3\text{H}_2\text{O}(l) \]
This shows how the acid (HCl) and the base (Fe(OH)₃) react to produce a salt (FeCl₃) and water (H₂O).

stoichiometry

Stoichiometry is the branch of chemistry that deals with the calculation of reactants and products in chemical reactions. It helps in determining the proportions in which substances react and the amounts of products formed. When solving neutralization reactions, understanding stoichiometry is crucial for balancing equations and predicting the quantities of each product and reactant.

Take, for example, the reaction between carbonic acid (H₂CO₃) and magnesium hydroxide (Mg(OH)₂). The initial unbalanced equation is:
\[ \text{H}_{2}\text{CO}_3(aq) + \text{Mg(OH)}_{2}(s) \rightarrow \text{MgCO}_3(aq) + \text{H}_2\text{O}(l) \]
Balancing this involves using stoichiometric principles to ensure that there are equal numbers of each type of atom on both sides. This is achieved by balancing:
\[ \text{H}_{2}\text{CO}_3(aq) + \text{Mg(OH)}_{2}(s) \rightarrow \text{MgCO}_3(aq) + 2\text{H}_2\text{O}(l) \]
This balanced equation shows one molecule of H₂CO₃ reacting with one molecule of Mg(OH)₂ to produce one molecule of MgCO₃ and two water molecules (H₂O). Mastering stoichiometry ensures precise and accurate chemical reactions and predictions.