Question

Write the following as balanced chemical equations. (a) Calcium hydroxide reacts with hydrogen chloride to form calcium chloride and water. (b) Silver nitrate and calcium chloride react to form calcium nitrate and silver chloride. (c) Lead(II) nitrate reacts with sodium sulfate to form lead(II) sulfate and sodium nitrate. (d) Iron(III) oxide and carbon react to form iron and carbon dioxide.

Short answer

\( Ca(OH)_2 + 2HCl \rightarrow CaCl_2 + 2H_2O \), \( 2AgNO_3 + CaCl_2 \rightarrow Ca(NO_3)_2 + 2AgCl \), \( Pb(NO_3)_2 + Na_2SO_4 \rightarrow PbSO_4 + 2NaNO_3 \), \( Fe_2O_3 + 3C \rightarrow 2Fe + 3CO_2 \)

Step-by-step solution

Balancing Reaction (a)

Start by writing the unbalanced equation with reactants and products: Calcium hydroxide + Hydrogen chloride \rightarrow Calcium chloride + Water Write the chemical formulas: \( Ca(OH)_2 + HCl \rightarrow CaCl_2 + H_2O \) Balance the number of atoms for each element on both sides of the reaction: \( Ca(OH)_2 + 2HCl \rightarrow CaCl_2 + 2H_2O \)

Balancing Reaction (b)

Start by writing the unbalanced equation with reactants and products: Silver nitrate + Calcium chloride \rightarrow Calcium nitrate + Silver chloride Write the chemical formulas: \( AgNO_3 + CaCl_2 \rightarrow Ca(NO_3)_2 + AgCl \) Balance the number of atoms for each element on both sides of the reaction: \( 2AgNO_3 + CaCl_2 \rightarrow Ca(NO_3)_2 + 2AgCl \)

Balancing Reaction (c)

Start by writing the unbalanced equation with reactants and products: Lead(II) nitrate + Sodium sulfate \rightarrow Lead(II) sulfate + Sodium nitrate Write the chemical formulas: \( Pb(NO_3)_2 + Na_2SO_4 \rightarrow PbSO_4 + NaNO_3 \) Balance the number of atoms for each element on both sides of the reaction: \( Pb(NO_3)_2 + Na_2SO_4 \rightarrow PbSO_4 + 2NaNO_3 \)

Balancing Reaction (d)

Start by writing the unbalanced equation with reactants and products: Iron(III) oxide + Carbon \rightarrow Iron + Carbon dioxide Write the chemical formulas: \( Fe_2O_3 + C \rightarrow Fe + CO_2 \) Balance the number of atoms for each element on both sides of the reaction: \( Fe_2O_3 + 3C \rightarrow 2Fe + 3CO_2 \)

Key concepts

Stoichiometry

Stoichiometry is akin to a recipe in cooking; it tells you how much of each reactant you need to produce a certain amount of product. Imagine baking cookies without a recipe; you would not know the number of eggs, flour, or sugar required. Similarly, stoichiometry provides the quantitative relationship between reactants and products in a chemical reaction. Understanding stoichiometry is crucial for predicting the outcome of reactions and for scaling those reactions up from laboratory to industrial scales.

Through stoichiometry, it's possible to calculate the amounts of substances consumed and produced in a reaction. This is based on the coefficients of the balanced chemical equation, which comply with the law of conservation of mass. For example, looking at reaction (b) from the problem given, the correct stoichiometry of the balanced equation, as seen in the step-by-step solution, tells us that two moles of silver nitrate react with one mole of calcium chloride to yield one mole of calcium nitrate and two moles of silver chloride.

An inherent concept within stoichiometry is the mole ratio, referring to the ratio between the amounts in moles of any two compounds in a reaction. Thus, stoichiometry is the cornerstone of chemistry, especially when considering reactions on a quantitative level.

Chemical Formulas

Reading and writing chemical formulas is fundamental to understanding and communicating in chemistry. Chemical formulas, such as those used in the solutions to the exercise mentioned, represent the composition of a substance. They indicate the types of atoms present and the relative number of these atoms. For instance, the formula for water, \( H_2O \) indicates that water is composed of two hydrogen atoms and one oxygen atom bonded together.

In balanced chemical equations, the chemical formulas of the reactants and products are crucial. They provide the base for balancing the equation, as one must account for each atom represented in these formulas. When reacting calcium hydroxide \( \text{Ca(OH)}_2 \) with hydrogen chloride \( \text{HCl} \) to form calcium chloride \( \text{CaCl}_2 \) and water \( \text{H}_2\text{O} \) as shown in reaction (a), appreciating the subtleties in chemical formulas is paramount. Correctly identifying and counting each atom within these formulas is a skill that underlies the act of balancing equations and stoichiometric calculations.

Law of Conservation of Mass

The law of conservation of mass is one of the fundamental principles in chemistry, which states that mass can neither be created nor destroyed in a chemical reaction. This law applies to all chemical reactions, such as the ones detailed in the exercise. It means that the total mass of the reactants must be equal to the total mass of the products.

For instance, in reaction (d) from the exercise, the iron(III) oxide \( \text{Fe}_2\text{O}_3 \) reacts with carbon \( \text{C} \) to produce iron \( \text{Fe} \) and carbon dioxide \( \text{CO}_2 \). The balancing of this equation ensures that the number of iron, oxygen, and carbon atoms are the same on both sides of the equation, thus adhering to the law of conservation of mass. This concept is not only crucial in academic settings but also in practical applications where precise measurements are essential, such as pharmaceutical compounding and chemical manufacturing.

Understanding this law is vital when learning to balance chemical equations as it sets the stage for the conservation of each element throughout a reaction. Students will find that mastering the law of conservation of mass makes the complex task of balancing equations far more logical and manageable.