Question

Balance these equations. (a) \(\mathrm{MgO}(\mathrm{s})+\mathrm{Fe}(\mathrm{s}) \longrightarrow \mathrm{Fe}_{2} \mathrm{O}_{3}(\mathrm{~s})+\mathrm{Mg}(\mathrm{s})\) (b) \(\mathrm{H}_{3} \mathrm{BO}_{3}(\mathrm{~s}) \longrightarrow \mathrm{B}_{2} \mathrm{O}_{3}(\mathrm{~s})+\mathrm{H}_{2} \mathrm{O}(\ell)\) (c) \(\mathrm{NaNO}_{3}(\mathrm{~s})+\mathrm{H}_{2} \mathrm{SO}_{4}(\mathrm{aq}) \longrightarrow \mathrm{Na}_{2} \mathrm{SO}_{4}(\mathrm{aq})+\mathrm{HNO}_{3}(\mathrm{~g})\)

Short answer

(a) \(3\mathrm{MgO}+2\mathrm{Fe} \rightarrow \mathrm{Fe}_{2}\mathrm{O}_{3}+3\mathrm{Mg}\) (b) \(2\mathrm{H}_{3}\mathrm{BO}_{3} \rightarrow \mathrm{B}_{2}\mathrm{O}_{3}+3\mathrm{H}_{2}\mathrm{O}\) (c) \(2\mathrm{NaNO}_{3}+\mathrm{H}_{2}\mathrm{SO}_{4} \rightarrow \mathrm{Na}_{2}\mathrm{SO}_{4}+2\mathrm{HNO}_{3}\)

Step-by-step solution

Understanding the Equation (a)

Given the unbalanced equation: \(\mathrm{MgO}(\mathrm{s})+\mathrm{Fe}(\mathrm{s}) \longrightarrow \mathrm{Fe}_{2} \mathrm{O}_{3}(\mathrm{~s})+\mathrm{Mg}(\mathrm{s})\). Count the number of each type of atom on both sides of the equation.

Balancing Magnesium Atoms (a)

The equation is \(\mathrm{MgO}(\mathrm{s})+\mathrm{Fe}(\mathrm{s}) \longrightarrow \mathrm{Fe}_{2} \mathrm{O}_{3}(\mathrm{~s})+\mathrm{Mg}(\mathrm{s})\). Place a coefficient of 1 for \(\mathrm{MgO}\) and \(\mathrm{Mg}\), as there is one magnesium atom on each side.

Balancing Iron and Oxygen Atoms (a)

For oxygen, we have 1 on the reactant side (from MgO) and 3 on the product side (from \(\mathrm{Fe}_2\mathrm{O}_3\)). Consider adding coefficients to balance oxygen: 3 \(\mathrm{MgO}(\mathrm{s})+2\mathrm{Fe}(\mathrm{s}) \longrightarrow \mathrm{Fe}_{2} \mathrm{O}_{3}(\mathrm{~s})+3\mathrm{Mg}(\mathrm{s})\).

Check for Accuracy (a)

Verify if all elements are balanced: 3 Mg, 3 O, 2 Fe on both sides. Equation is balanced.

Equation (a) Balanced:

The balanced equation is: \(3\mathrm{MgO}(\mathrm{s})+2\mathrm{Fe}(\mathrm{s}) \longrightarrow \mathrm{Fe}_{2}\mathrm{O}_{3}(\mathrm{~s})+3\mathrm{Mg}(\mathrm{s})\).

Understanding the Equation (b)

Given equation: \(\mathrm{H}_3\mathrm{BO}_3(\mathrm{~s}) \longrightarrow \mathrm{B}_2\mathrm{O}_3(\mathrm{~s})+\mathrm{H}_2\mathrm{O}(\ell)\). Count atoms: H, B, and O.

Balancing Boron Atoms (b)

Boron needs to be balanced from the given B atoms: 2 in \(\mathrm{B}_2\mathrm{O}_3\). Multiply \(\mathrm{H}_3\mathrm{BO}_3\) by 2: \(2\mathrm{H}_3\mathrm{BO}_3 \longrightarrow \mathrm{B}_2\mathrm{O}_3+\mathrm{H}_2\mathrm{O}\).

Balancing Hydrogen and Oxygen Atoms (b)

Check hydrogens and oxygens after balancing boron. Correct to: \(2\mathrm{H}_3\mathrm{BO}_3(\mathrm{~s}) \longrightarrow \mathrm{B}_2\mathrm{O}_3(\mathrm{~s})+3\mathrm{H}_2\mathrm{O}(\ell)\).

Check for Accuracy (b)

Verify atom balance: 2 B, 6 H, 6 O on both sides. Equation is balanced.

Equation (b) Balanced:

The balanced equation is: \(2\mathrm{H}_3\mathrm{BO}_3(\mathrm{~s}) \longrightarrow \mathrm{B}_2\mathrm{O}_3(\mathrm{~s})+3\mathrm{H}_2\mathrm{O}(\ell)\).

Understanding the Equation (c)

Given equation: \(\mathrm{NaNO}_3(\mathrm{~s})+\mathrm{H}_2\mathrm{SO}_4(\mathrm{aq}) \longrightarrow \mathrm{Na}_2\mathrm{SO}_4(\mathrm{aq})+\mathrm{HNO}_3(\mathrm{~g})\). Count atoms: Na, N, O, H, S.

Balancing Sodium Atoms (c)

Sodium atoms need double the NaNO3 for \(\mathrm{Na}_2\mathrm{SO}_4\). Start with: \(2\mathrm{NaNO}_3+\mathrm{H}_2\mathrm{SO}_4 \longrightarrow \mathrm{Na}_2\mathrm{SO}_4+\mathrm{HNO}_3\).

Balancing Remaining Elements (c)

After sodium, balance other elements. Adjust H and N: \(2\mathrm{NaNO}_3+\mathrm{H}_2\mathrm{SO}_4 \longrightarrow \mathrm{Na}_2\mathrm{SO}_4+2\mathrm{HNO}_3\).

Check for Accuracy (c)

Verify atom balance: 2 Na, 2 N, 7 O, 2 H, and 1 S on both sides. Equation is balanced.

Equation (c) Balanced:

The balanced equation is: \(2\mathrm{NaNO}_3(\mathrm{~s})+\mathrm{H}_2\mathrm{SO}_4(\mathrm{aq}) \longrightarrow \mathrm{Na}_2\mathrm{SO}_4(\mathrm{aq})+2\mathrm{HNO}_3(\mathrm{~g})\).

Key concepts

Stoichiometry

Stoichiometry is a key concept in chemistry that involves the calculation of reactants and products in chemical reactions. It helps scientists determine the relative quantities of elements and compounds involved. This concept is crucial when balancing chemical equations as it ensures that the Law of Conservation of Mass is maintained, meaning the amount of each element is the same before and after a chemical reaction. To balance a reaction, you must ensure that the number of each type of atom on the reactant side equals the number on the product side. This involves adjusting coefficients, which are numbers placed in front of compounds in an equation. Here are steps to effectively use stoichiometry for balancing:

• Identify the reaction and write the unbalanced equation.
• List all elements involved and count the number of atoms for each element in both reactants and products.
• Adjust coefficients to balance the atoms one element at a time, usually starting with the element that appears in the fewest compounds.
• Re-check all elements to confirm balance, ensuring no fractional coefficients remain.

By mastering these steps, students can better understand the stoichiometry required in balancing chemical equations.

Chemical Reactions

Chemical reactions are processes where reactants transform into products. During this transformation, old chemical bonds break and new ones form. Understanding these reactions begins with understanding the reactants and products and how they interact. Balancing chemical reactions involves:

• Recognizing that the total mass of reactants equals the total mass of products, according to the Law of Conservation of Mass.
• Identifying each reactant and product in the equation, which helps track how atoms rearrange during the reaction.
• Knowing the physical states of compounds, which can impact the reaction conditions (e.g., solid, liquid, gas, aqueous).
• Different types of chemical reactions, such as synthesis, decomposition, single replacement, and double replacement, help categorize and predict reaction outcomes.

Recognizing these core elements of chemical reactions allows students to appreciate the intricate nature of chemical changes and the importance of balanced equations in describing chemical processes.

Chemistry Education

In the realm of chemistry education, concepts like balancing chemical equations are often challenging yet fundamental for students. A clear grasp of these concepts is crucial for success in not only chemistry but also various scientific fields. Effective chemistry education focuses on:

• Building foundational knowledge, such as atomic structure, chemical bonds, and reaction types, to create a strong understanding base.
• Offering hands-on practice through problems and laboratory experiments to apply theoretical knowledge to real-world scenarios.
• Utilizing visual aids, animations, and diagrams to illustrate abstract concepts like the rearrangement of atoms during reactions.
• Encouraging problem-solving skills and critical thinking to tackle complex questions and think scientifically.

By integrating these elements into educational frameworks, teachers can make chemistry more accessible and engaging, equipping students with essential skills to explore and understand the chemical world.