Problem 11 - Chemistry: The Central Science in SI Units, Global Edition

Question

Balance the following equations: (a) \(\mathrm{SiCl}_{4}(l)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{Si}(\mathrm{OH})_{4}(s)+\mathrm{HCl}(a q)\) (b) \(\mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s)+\mathrm{O}_{2}(g)\) (c) \(\mathrm{Al}(\mathrm{OH})_{3}(s)+\mathrm{H}_{2} \mathrm{SO}_{4}(l) \longrightarrow \mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}(s)+\mathrm{H}_{2} \mathrm{O}(l)\) (d) \(\mathrm{H}_{3} \mathrm{PO}_{4}(a q) \longrightarrow \mathrm{H}_{4} \mathrm{P}_{2} \mathrm{O}_{7}(a q)+\mathrm{H}_{2} \mathrm{O}(l)\)

Step-by-Step Solution

Answer

The balanced equations are: (a) SiCl\(_4\) + 4H\(_2\)O \(\longrightarrow\) Si(OH)\(_4\) + 4HCl (b) 6CO\(_2\) + 6H\(_2\)O \(\longrightarrow\) C\(_6\)H\(_{12}\)O\(_6\) + 6O\(_2\) (c) 2Al(OH)\(_3\) + 3H\(_2\)SO\(_4\) \(\longrightarrow\) Al\(_2\)(SO\(_4\))\(_3\) + 6H\(_2\)O (d) 2H\(_3\)PO\(_4\) \(\longrightarrow\) H\(_4\)P\(_2\)O\(_7\) + H\(_2\)O

Step 1: Identify the elements

Identify the elements present in the reactants and products: Si, Cl, H, and O.

Step 2: Count the atoms

Count the atoms of each element in both the reactants and products: Reactants: 1 Si, 4 Cl, 2 H, 1 O Products: 1 Si, 4 H, 4 O, 1 Cl

Step 3: Balance the equation

Adding coefficients to balance the atoms in the equation: SiCl\(_4\) + 4H\(_2\)O \(\longrightarrow\) Si(OH)\(_4\) + 4HCl Now, the balanced equation has 1 Si, 4 Cl, 8 H, and 4 O on both sides. (b) \(\mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s)+\mathrm{O}_{2}(g)\)

Step 1: Identify the elements

Identify the elements present in the reactants and products: C, H, and O.

Step 2: Count the atoms

Count the atoms of each element in both the reactants and products: Reactants: 1 C, 2 H, 3 O Products: 6 C, 12 H, 18 O

Step 3: Balance the equation

Adding coefficients to balance the atoms in the equation: 6CO\(_2\) + 6H\(_2\)O \(\longrightarrow\) C\(_6\)H\(_{12}\)O\(_6\) + 6O\(_2\) Now, the balanced equation has 6 C, 12 H, and 18 O on both sides. (c) \(\mathrm{Al}(\mathrm{OH})_{3}(s)+\mathrm{H}_{2} \mathrm{SO}_{4}(l) \longrightarrow \mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}(s)+\mathrm{H}_{2} \mathrm{O}(l)\)

Step 1: Identify the elements

Identify the elements present in the reactants and products: Al, O, H, and S.

Step 2: Count the atoms

Count the atoms of each element in both the reactants and products: Reactants: 1 Al, 3 O, 3 H, 1 S Products: 2 Al, 12 O, 6 H, 3 S

Step 3: Balance the equation

Adding coefficients to balance the atoms in the equation: 2Al(OH)\(_3\) + 3H\(_2\)SO\(_4\) \(\longrightarrow\) Al\(_2\)(SO\(_4\))\(_3\) + 6H\(_2\)O Now, the balanced equation has 2 Al, 6 H, and 12 O on both sides. (d) \(\mathrm{H}_{3} \mathrm{PO}_{4}(a q) \longrightarrow \mathrm{H}_{4} \mathrm{P}_{2} \mathrm{O}_{7}(a q)+\mathrm{H}_{2} \mathrm{O}(l)\)

Step 1: Identify the elements

Identify the elements present in the reactants and products: H, P, and O.

Step 2: Count the atoms

Count the atoms of each element in both the reactants and products: Reactants: 3 H, 1 P, 4 O Products: 6 H, 2 P, 9 O

Step 3: Balance the equation

Adding coefficients to balance the atoms in the equation: 2H\(_3\)PO\(_4\) \(\longrightarrow\) H\(_4\)P\(_2\)O\(_7\) + H\(_2\)O Now, the balanced equation has 6 H, 2 P, and 9 O on both sides.

Key Concepts

Stoichiometry

Stoichiometry is a key concept in chemistry that revolves around the quantitative relationships within a chemical reaction. It allows chemists to predict how much of each reactant is needed and how much product will be formed in a given reaction. Stoichiometry involves using balanced chemical equations to perform calculations. This ensures that the number of atoms of each element is conserved, satisfying the law of conservation of mass.

When balancing chemical equations, one must adjust the coefficients (the numbers placed before the molecules) to ensure the same number of each type of atom appears on both sides of the equation. For example, in the first equation provided in the exercise: \( \text{SiCl}_4(l) + \text{H}_2\text{O}(l) \rightarrow \text{Si(OH)}_4(s) + \text{HCl}(aq) \), adding coefficients such as 1 Si, 4 H, and 4 Cl ensure the equation is balanced. The balanced equation reflects the stoichiometric relationships, where coefficients relate the moles of reactants and products.

• Coefficients denote mole ratios.
• Reactant and product atoms are conserved.
• Stoichiometry assists in determining theoretical yield of a reaction.

Chemical Reactions

Chemical reactions describe the transformation of substances into different substances. This involves the breaking and forming of chemical bonds, leading to new materials with new properties. Balanced chemical reactions not only show what substances are involved, but also how they are transformed.

In the reactions provided, balancing indicates the stoichiometry required to maintain conservation of mass and charge. For example, consider the reaction of carbon dioxide and water to form glucose and oxygen: \( 6\text{CO}_2(g) + 6\text{H}_2\text{O} \rightarrow \text{C}_6\text{H}_{12}\text{O}_6(s) + 6\text{O}_2(g) \). This is a balanced equation, meaning it accurately represents the quantities needed to fully complete the reaction, demonstrating how matter is neither created nor destroyed.

• Reactants are transformed into products.
• Chemical bonds breaking and forming define reactions.
• Balancing ensures representation of quantities involved in reactions.

Chemistry Education

Understanding chemical equations and reactions is fundamental in chemistry education. It serves as a building block for more advanced topics. Mastery of these concepts helps students grasp more complex chemical processes and reactions.

Educators emphasize learning how to balance equations due to its critical role in understanding reaction mechanisms. Through step-by-step practice, students learn to identify reactants, products, and their respective quantities. This foundational skill allows students to see the interconnection between chemical formulas and real-world processes.

For instance, when solving a problem like \( 2\text{H}_3\text{PO}_4 \rightarrow \text{H}_4\text{P}_2\text{O}_7 + \text{H}_2\text{O} \), students are trained to count and match quantities, strengthening analytical and problem-solving skills. As students progress, this knowledge aids in exploring more complex areas, such as kinetics and thermodynamics.

• Balanced equations are essential for understanding chemical changes.
• Equation balancing enhances analytical skills.
• These skills are foundational for exploring advanced chemistry.