Question

For each of the following reactions, give the balanced chemical equation for the reaction and state the meaning of the cquation in terms of individual molecules and in terms of moles of molecules. a. \(\mathrm{MnO}_{2}(s)+\mathrm{Al}(s) \rightarrow \mathrm{Mn}(s)+\mathrm{Al}_{2} \mathrm{O}_{3}(s)\) b. \(\mathrm{B}_{2} \mathrm{O}_{3}(s)+\mathrm{CaF}_{2}(s) \rightarrow \mathrm{BF}_{3}(g)+\mathrm{CaO}(s)\) c. \(\mathrm{NO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l) \rightarrow \mathrm{HNO}_{3}(a q)+\mathrm{NO}(g)\) d. \(\mathrm{C}_{6} \mathrm{H}_{6}(g)+\mathrm{H}_{2}(g) \rightarrow \mathrm{C}_{6} \mathrm{H}_{12}(g)\)

Short answer

a. 3MnO₂(s) + 4Al(s) → 3Mn(s) + 2Al₂O₃(s) Individual molecules: Three molecules of manganese dioxide (MnO₂) react with four molecules of aluminum (Al) to produce three molecules of manganese (Mn) and two molecules of aluminum oxide (Al₂O₃). Moles of molecules: 3 moles of MnO₂ react with 4 moles of Al to produce 3 moles of Mn and 2 moles of Al₂O₃. b. B₂O₃(s) + 3CaF₂(s) → 2BF₃(g) + 3CaO(s) Individual molecules: One molecule of boron trioxide (B₂O₃) reacts with three molecules of calcium fluoride (CaF₂) to produce two molecules of boron trifluoride (BF₃) and three molecules of calcium oxide (CaO). Moles of molecules: 1 mole of B₂O₃ reacts with 3 moles of CaF₂ to produce 2 moles of BF₃ and 3 moles of CaO. c. 2NO₂(g) + H₂O(l) → HNO₃(aq) + NO(g) Individual molecules: Two molecules of nitrogen dioxide (NO₂) react with one molecule of water (H₂O) to produce one molecule of nitric acid (HNO₃) and one molecule of nitrogen monoxide (NO). Moles of molecules: 2 moles of NO₂ react with 1 mole of H₂O to produce 1 mole of HNO₃ and 1 mole of NO. d. C₆H₆(g) + 3H₂(g) → C₆H₁₂(g) Individual molecules: One molecule of benzene (C₆H₆) reacts with three molecules of hydrogen (H₂) to produce one molecule of cyclohexane (C₆H₁₂). Moles of molecules: 1 mole of C₆H₆ reacts with 3 moles of H₂ to produce 1 mole of C₆H₁₂.

Step-by-step solution

Equation a

MnO₂(s) + Al(s) → Mn(s) + Al₂O₃(s) To balance this equation: a. Count the number of atoms of each element on both sides of the equation. b. Multiply the molecules by the necessary coefficients to balance atoms for each element. c. Verify that both sides of the equation are now balanced. By following these steps: - 1 Mn, 2 O, and 1 Al on the left side - 1 Mn, 3 O, and 2 Al on the right side a. Multiply MnO₂ by 2 and Al by 3: 3MnO₂(s) + 4Al(s) → 3Mn(s) + 2Al₂O₃(s) Now, the number of Mn, O, and Al atoms is matching on both sides.

Equation a - Meaning

Individual molecules: Three molecules of manganese dioxide (MnO₂) react with four molecules of aluminum (Al) to produce three molecules of manganese (Mn) and two molecules of aluminum oxide (Al₂O₃). Moles of molecules: 3 moles of MnO₂ react with 4 moles of Al to produce 3 moles of Mn and 2 moles of Al₂O₃. 2. Balancing the second chemical equation:

Equation b

B₂O₃(s) + CaF₂(s) → BF₃(g) + CaO(s) To balance this equation, follow the same steps as before: - 2 B, 3 O, 1 Ca and 2 F on the left side - 1 B, 3 F, 1 Ca and 1 O on the right side a. Multiply BF₃ by 2: B₂O₃(s) + 3CaF₂(s) → 2BF₃(g) + 3CaO(s) Now, the number of B, O, Ca, and F atoms is matching on both sides.

Equation b - Meaning

Individual molecules: One molecule of boron trioxide (B₂O₃) reacts with three molecules of calcium fluoride (CaF₂) to produce two molecules of boron trifluoride (BF₃) and three molecules of calcium oxide (CaO). Moles of molecules: 1 mole of B₂O₃ reacts with 3 moles of CaF₂ to produce 2 moles of BF₃ and 3 moles of CaO. 3. Balancing the third chemical equation:

Equation c

NO₂(g) + H₂O(l) → HNO₃(aq) + NO(g) To balance this equation, follow the same steps as before: - 1 N, 2 O, and 2 H on the left side - 2 N, 5 O, and 1 H on the right side a. Multiply NO₂ by 2: 2NO₂(g) + H₂O(l) → HNO₃(aq) + NO(g) Now, the number of N, O, and H atoms is matching on both sides.

Equation c - Meaning

Individual molecules: Two molecules of nitrogen dioxide (NO₂) react with one molecule of water (H₂O) to produce one molecule of nitric acid (HNO₃) and one molecule of nitrogen monoxide (NO). Moles of molecules: 2 moles of NO₂ react with 1 mole of H₂O to produce 1 mole of HNO₃ and 1 mole of NO. 4. Balancing the fourth chemical equation:

Equation d

C₆H₆(g) + H₂(g) → C₆H₁₂(g) To balance this equation, follow the same steps as before: - 6 C and 12 H on the left side - 6 C, and 14 H on the right side a. Multiply H₂ by 3: C₆H₆(g) + 3H₂(g) → C₆H₁₂(g) Now, the number of C and H atoms is matching on both sides.

Equation d - Meaning

Individual molecules: One molecule of benzene (C₆H₆) reacts with three molecules of hydrogen (H₂) to produce one molecule of cyclohexane (C₆H₁₂). Moles of molecules: 1 mole of C₆H₆ reacts with 3 moles of H₂ to produce 1 mole of C₆H₁₂.

Key concepts

Stoichiometry

Stoichiometry is the section of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. It is the calculation of the quantities or the proportions in which chemicals react with each other and form products. To understand stoichiometry, you need to be familiar with the mole concept, as stoichiometry relies on the mole ratio derived from the balanced chemical equation.

For instance, in our exercise where we have the reaction between manganese dioxide and aluminum to produce manganese and aluminum oxide, stoichiometry allows us to calculate how many moles of each reactant are needed to produce a certain amount of product. In the balanced chemical equation, we can see that 3 moles of MnO₂ react with 4 moles of Al to create 3 moles of Mn and 2 moles of Al₂O₃. Using the mole ratios (3:4:3:2), stoichiometry can be applied in real-life situations to determine the mass of reactants needed for a reaction, the mass of products that can be obtained, and the percentage yield of a chemical process.

To balance a chemical equation stoichiometrically, one must:

• Identify and write down the unbalanced equation.
• Determine the number of atoms of each element in both reactants and products.
• Adjust coefficients to balance the number of atoms for each element on both sides of the equation.
• Ensure that the total mass is conserved, following the law of conservation of mass.

Mole Concept

The mole concept is a fundamental principle in chemistry that relates the mass of substances to the number of particles contained in them. One mole is defined as 6.022 × 10²³ particles, which could be atoms, molecules, ions, or electrons. This number is known as Avogadro's number.

In the context of the balanced equations we're examining, the mole concept enables us to quantify substances in chemical reactions. We can't accurately measure individual atoms or molecules due to their minuscule size; instead, we use moles to describe amounts in bulk. For example, in the reaction where boron trioxide reacts with calcium fluoride to form boron trifluoride and calcium oxide (Equation b), we discuss moles of substances to convey measurable and usable quantities in the laboratory or industry.

To apply the mole concept effectively, remember these key points:

• The molar mass of a substance (mass per mole of particles) enables us to convert between grams and moles.
• Stoichiometric coefficients in a balanced equation give the mole ratio of reactants and products.
• Using the mole ratio, we can perform calculations to determine the masses or volumes of reactants or products involved.

Chemical Reactions

Chemical reactions describe the process by which substances, known as reactants, transform into new substances, called products. The essence of a chemical reaction is the breaking of old bonds and the formation of new ones, leading to changes in the molecular structure of the substances involved.

In the textbook exercises, the variety of chemical reactions provided show different types of transformations. For instance, the reaction of nitrogen dioxide with water to produce nitric acid and nitrogen monoxide (Equation c) is a type of redox reaction, where the transfer of electrons between species occurs. On the other hand, the addition of hydrogen to benzene to form cyclohexane (Equation d) is an example of a hydrogenation reaction, which is key in organic chemistry.

Understanding chemical reactions requires knowledge of:

• Reaction stoichiometry, which predicts product amounts.
• Energy changes, with some reactions being exothermic (releasing heat) and others endothermic (absorbing heat).
• The rate of reaction, influenced by factors such as temperature, concentration, and the presence of catalysts.
• Balancing chemical equations to uphold the principle of the conservation of matter.