Question

Balance the following equations: (a) \(\mathrm{Mg}+\mathrm{HNO}_{3} \longrightarrow \mathrm{H}_{2}+\mathrm{Mg}\left(\mathrm{NO}_{3}\right)_{2}\) (b) \(\mathrm{CaC}_{2}+\mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{Ca}(\mathrm{OH})_{2}+\mathrm{C}_{2} \mathrm{H}_{2}\) (c) \(\mathrm{S}+\mathrm{O}_{2} \longrightarrow \mathrm{SO}_{3}\) (d) \(\mathrm{UO}_{2}+\mathrm{HF} \longrightarrow \mathrm{UF}_{4}+\mathrm{H}_{2} \mathrm{O}\)

Short answer

(a) \(\mathrm{Mg} + 2\,\mathrm{HNO}_3 \rightarrow \mathrm{H}_2 + \mathrm{Mg}(\mathrm{NO}_3)_2\); (b) \(\mathrm{CaC}_{2} + 2\,\mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{Ca(OH)}_{2} + \mathrm{C}_{2} \mathrm{H}_{2}\); (c) \(2\,\mathrm{S} + 3\,\mathrm{O}_2 \rightarrow 2\,\mathrm{SO}_3\); (d) \(\mathrm{UO}_{2} + 4\,\mathrm{HF} \rightarrow \mathrm{UF}_{4} + 2\,\mathrm{H}_{2}\mathrm{O}\)."

Step-by-step solution

Balance Equation (a)

The unbalanced reaction is \( \mathrm{Mg} + \mathrm{HNO}_3 \rightarrow \mathrm{H}_2 + \mathrm{Mg}(\mathrm{NO}_3)_2 \). First, balance the magnesium (Mg) by including a coefficient of 1 for Mg on both sides: \( 1\,\mathrm{Mg} + \mathrm{HNO}_3 \rightarrow \mathrm{H}_2 + 1\,\mathrm{Mg}(\mathrm{NO}_3)_2 \). The reaction involves one Mg on each side, so they are balanced.Next, balance the nitrate ions (NO\(_3\)^-): on the right, there are two NO\(_3\)^- associated with the magnesium nitrate (Mg(NO\(_3\))_2), which requires two HNO\(_3\) molecules on the left: \( \mathrm{Mg} + 2\,\mathrm{HNO}_3 \rightarrow \mathrm{H}_2 + \mathrm{Mg}(\mathrm{NO}_3)_2 \).Now, balance hydrogen (H): there are 2 H's on the left (from 2 HNO\(_3\)) and 2 H's on the right (from H\(_2\)):\[\mathrm{Mg} + 2\,\mathrm{HNO}_{3} \rightarrow \mathrm{H}_{2} + \mathrm{Mg}(\mathrm{NO}_{3})_{2} \] This equation is now balanced.

Balance Equation (b)

The unbalanced equation is: \( \mathrm{CaC}_2 + \mathrm{H}_2 \mathrm{O} \rightarrow \mathrm{Ca(OH)}_2 + \mathrm{C}_2 \mathrm{H}_2 \). Start by balancing calcium (Ca): one Ca on each side requires a coefficient of 1 for calcium: \( 1\,\mathrm{CaC}_2 + \mathrm{H}_2 \mathrm{O} \rightarrow 1\,\mathrm{Ca(OH)}_2 + \mathrm{C}_2 \mathrm{H}_2 \).Now, balance the acetylene (C\(_2\)H\(_2\)): two carbon atoms on the left side (in one CaC\(_2\)), so those are balanced with the two carbons in C\(_2\)H\(_2\) on the right side.Next, balance hydrogen: There are two hydrogens from one molecule of water on the left, and two hydrogens from the C\(_2\)H\(_2\) on the right, plus an additional two hydrogens forming the hydroxide on the right, requiring a total of two water molecules: \( \mathrm{CaC}_2 + 2\,\mathrm{H}_2 \mathrm{O} \rightarrow \mathrm{Ca(OH)}_2 + \mathrm{C}_2 \mathrm{H}_2 \).The equation is balanced with:\[\mathrm{CaC}_{2} + 2\,\mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{Ca(OH)}_{2} + \mathrm{C}_{2} \mathrm{H}_{2}\]

Balance Equation (c)

The unbalanced equation is: \( \mathrm{S} + \mathrm{O}_2 \rightarrow \mathrm{SO}_3 \). Sulfur (S) is balanced with one atom on each side.Next, balance the oxygen atoms: there are two oxygen atoms on the left (\(\mathrm{O}_2\)) and three oxygen atoms in \(\mathrm{SO}_3\), requiring additional O\(_2\) on the left. Using a coefficient of 3/2 in front of O\(_2\) balances the oxygen as follows: \(\mathrm{S} + \frac{3}{2}\,\mathrm{O}_2 \rightarrow \mathrm{SO}_3\).For integer coefficients, multiply the entire equation by 2:\[2\,\mathrm{S} + 3\,\mathrm{O}_2 \rightarrow 2\,\mathrm{SO}_3\]

Balance Equation (d)

The unbalanced equation is: \( \mathrm{UO}_2 + \mathrm{HF} \rightarrow \mathrm{UF}_4 + \mathrm{H}_2 \mathrm{O} \). Start by balancing uranium (U): one U on both sides requires no additional coefficients.Now, balance the fluorine atoms. There are four fluorines on the right in UF\(_4\), so we need four HF molecules:\[\mathrm{UO}_{2} + 4\,\mathrm{HF} \rightarrow \mathrm{UF}_{4} + \mathrm{H}_{2} \mathrm{O}\]Then, balance the hydrogen and oxygen: two hydrogens from two HF participate in forming one H\(_2\)O. Ensure the two oxygens are balanced with UO\(_2\) on the left. This yields:\[\mathrm{UO}_{2} + 4\,\mathrm{HF} \rightarrow \mathrm{UF}_{4} + 2\,\mathrm{H}_{2}\mathrm{O}\]The balanced equation is:\[\mathrm{UO}_{2} + 4\,\mathrm{HF} \rightarrow \mathrm{UF}_{4} + 2\,\mathrm{H}_{2}\mathrm{O}\]

Key concepts

Stoichiometry

Stoichiometry is a fascinating aspect of chemistry that involves the quantitative relationships between reactants and products in chemical reactions. Think of it as a recipe for a chemical reaction. Just like you need a precise amount of ingredients to bake a perfect cake, stoichiometry ensures that the right amount of elements and compounds reacts to form the desired product.

In stoichiometry, we use balanced chemical equations to understand these relationships. A balanced equation provides the exact ratio of molecules needed for the reaction to occur. It conserves mass, meaning the number of each type of atom is the same on both sides of the equation. This helps chemists predict the amounts of substances consumed and produced in a reaction.

For example, in the reaction \( \mathrm{Mg} + 2\,\mathrm{HNO}_3 \rightarrow \mathrm{H}_2 + \mathrm{Mg}(\mathrm{NO}_3)_2 \), the stoichiometric coefficients tell us that one atom of magnesium (Mg) reacts with two molecules of nitric acid (HNO\(_3\)) to produce one molecule of hydrogen (H\(_2\)) and one molecule of magnesium nitrate (Mg(NO\(_3\))\(_2\)).

Understanding stoichiometry is essential for accurately conducting experiments and scaling reactions from a laboratory setting to industrial production.

Chemistry Education

Chemistry education plays a crucial role in helping students grasp the principles of stoichiometry and chemical reactions. It involves much more than just memorizing formulas and equations. The goal is to foster an intuitive understanding of how substances interact on a molecular level.

Here are some strategies to improve chemistry education:

• Interactive experiments: Real-world experiments help students visualize abstract concepts. Performing stoichiometry experiments in labs reinforce theoretical knowledge.
• Visual aids: Diagrams and models can illustrate how molecules interact, making it easier to understand chemical processes.
• Step-by-step problem solving: Breaking down complex equations into smaller steps, like in balanced equations, aids comprehension and builds problem-solving skills.
• Incorporating technology: Tools like simulation software allow students to model chemical reactions themselves, explore different scenarios, and visualize outcomes.

With these tools, students can develop a strong foundation in chemistry that prepares them for advanced studies and real-world applications. Ensuring a clear understanding of the concepts can spark a lifelong interest in the sciences.

Chemical Reactions

Chemical reactions are processes where substances, known as reactants, are transformed into new substances called products. They are fundamental to both chemistry and life itself, powering everything from cellular processes to combustion engines.

In these reactions, atoms are reorganized as chemical bonds are broken and formed, resulting in new compounds. This process is what makes one substance completely change its identity. For example, in the equation \( \mathrm{CaC}_2 + 2\,\mathrm{H}_2 \mathrm{O} \rightarrow \mathrm{Ca(OH)}_2 + \mathrm{C}_2 \mathrm{H}_2 \), calcium carbide and water react to form calcium hydroxide and acetylene gas—both distinctly different from the original substances.

Each chemical reaction is driven by factors such as temperature, pressure, and the presence of catalysts. These factors can either increase or decrease the reaction rate, hence, understanding them is pivotal for controlling reactions in industrial and laboratory settings.

• Exothermic reactions: These release energy, usually in the form of heat, and can occur spontaneously.
• Endothermic reactions: These absorb energy, requiring an external source of heat to occur.

Ultimately, gaining an in-depth understanding of chemical reactions allows scientists to harness them in beneficial ways, from synthesizing new materials to understanding biological systems.