Question

For each of the following reactions, give the balanced chemical equation for the reaction and state the meaning of the equation 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. \(C_{6} H_{6}(g)+H_{2}(g) \rightarrow C_{6} H_{12}(g)\)

Short answer

a. \(3MnO_2(s) + 4Al(s) \rightarrow 3Mn(s) + 2Al_2O_3(s)\) Three moles of manganese(IV) oxide and four moles of aluminum react to produce three moles of manganese and two moles of aluminum oxide. b. \(B_2O_3(s) + 6CaF_2(s) \rightarrow 2BF_3(g) + 3CaO(s)\) One mole of boron(III) oxide and six moles of calcium fluoride react to produce two moles of boron trifluoride and three moles of calcium oxide. c. \(3NO_2(g) + H_2O(l) \rightarrow 2HNO_3(aq) + NO(g)\) Three moles of nitrogen dioxide and one mole of water react to produce two moles of nitric acid and one mole of nitrogen monoxide. d. \(C_6H_6(g) + 6H_2(g) \rightarrow C_6H_{12}(g)\) One mole of benzene and six moles of hydrogen react to produce one mole of cyclohexane.

Step-by-step solution

a. Balancing the first chemical equation

\(MnO_2(s) + Al(s) \rightarrow Mn(s) + Al_2O_3(s)\) To balance this equation, we must first count the atoms of each element on both sides: - Left side: 1 Mn, 2 O, and 1 Al - Right side: 1 Mn, 3 O, and 2 Al We can balance the equation by adjusting the coefficients: \(3MnO_2(s) + 4Al(s) \rightarrow 3Mn(s) + 2Al_2O_3(s)\) Now it is balanced. Meaning in terms of individual molecules: Three manganese(IV) oxide molecules and four aluminum atoms react to form three manganese atoms and two aluminum oxide molecules. Meaning in terms of moles: Three moles of manganese(IV) oxide and four moles of aluminum react to produce three moles of manganese and two moles of aluminum oxide.

b. Balancing the second chemical equation

\(B_2O_3(s) + CaF_2(s) \rightarrow BF_3(g) + CaO(s)\) To balance this equation: - Left side: 2 B, 3 O, 1 Ca, and 2 F - Right side: 1 B, 3 F, 1 Ca, and 1 O We can balance the equation by adjusting the coefficients: \(B_2O_3(s) + 6CaF_2(s) \rightarrow 2BF_3(g) + 3CaO(s)\) Meaning in terms of individual molecules: One boron(III) oxide molecule and six calcium fluoride molecules react to form two boron trifluoride molecules and three calcium oxide molecules. Meaning in terms of moles: One mole of boron(III) oxide and six moles of calcium fluoride react to produce two moles of boron trifluoride and three moles of calcium oxide.

c. Balancing the third chemical equation

\(NO_2(g) + H_2O(l) \rightarrow HNO_3(aq) + NO(g)\) To balance this equation: - Left side: 1 N, 2 O, 2 H - Right side: 2 N, 4 O, 1 H We can balance the equation by adjusting the coefficients: \(3NO_2(g) + H_2O(l) \rightarrow 2HNO_3(aq) + NO(g)\) Meaning in terms of individual molecules: Three nitrogen dioxide molecules and one water molecule react to form two nitric acid molecules and one nitrogen monoxide molecule. Meaning in terms of moles: Three moles of nitrogen dioxide and one mole of water react to produce two moles of nitric acid and one mole of nitrogen monoxide.

d. Balancing the fourth chemical equation

\(C_6H_6(g) + H_2(g) \rightarrow C_6H_{12}(g)\) To balance this equation: - Left side: 6 C, 6 H - Right side: 6 C, 12 H We can balance the equation by adjusting the coefficients: \(C_6H_6(g) + 6H_2(g) \rightarrow C_6H_{12}(g)\) Meaning in terms of individual molecules: One benzene molecule and six hydrogen molecules react to form one cyclohexane molecule. Meaning in terms of moles: One mole of benzene and six moles of hydrogen react to produce one mole of cyclohexane.

Key concepts

Stoichiometry

Stoichiometry is the section of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It involves calculations that predict the amount of substances consumed and produced in a given chemical reaction. Central to these calculations is the balanced chemical equation, which provides the ratio of molecules and moles involved.

For instance, in the balanced equation
\[3\mathrm{MnO}_2(s) + 4\mathrm{Al}(s) \rightarrow 3\mathrm{Mn}(s) + 2\mathrm{Al}_2\mathrm{O}_3(s)\]
it is implied that for every three moles of manganese(IV) oxide reacted, four moles of aluminum are required, resulting in three moles of manganese and two moles of aluminum oxide as products. This mole ratio forms the core of stoichiometric calculations, allowing chemists to determine the exact proportions of reactants needed to achieve a complete reaction without excess.

Understanding this concept is crucial, since it not only helps in predicting the yield of a chemical process but also in scaling reactions for industrial applications and minimizing waste.

Mole Concept

The mole concept is a fundamental idea in chemistry that provides a bridge between the atomic scale and the macroscopic world. One mole is defined as the amount of a substance that contains as many entities (like atoms or molecules) as there are atoms in 12 grams of pure carbon-12, which is approximately \(6.022 \times 10^{23}\) entities, also known as Avogadro's number.

When dealing with chemical equations and reactions, the mole concept allows us to count particles by weighing them. For example, one mole of \(\mathrm{H}_2\mathrm{O}\) (water) contains exactly \(6.022 \times 10^{23}\) water molecules and weighs about 18 grams. Using the mole concept, we can easily convert between the mass of a substance and the number of moles, providing a powerful tool for chemists to use in laboratory and industry settings.

Moreover, in the reaction \(\mathrm{C}_6\mathrm{H}_6(g) + 6\mathrm{H}_2(g) \rightarrow \mathrm{C}_6\mathrm{H}_{12}(g)\), the balanced equation tells us that for every mole of benzene, six moles of hydrogen are needed. Using the mole concept, we can calculate the mass of hydrogen gas required to completely react with a known mass of benzene.

Chemical Reactions

Chemical reactions are processes in which substances, known as reactants, are transformed into different substances called products. Each chemical reaction is characterized by a balanced chemical equation, which ensures that the same number of atoms of each element is present on both sides, reflecting the Law of Conservation of Mass.

Different types of chemical reactions include synthesis, decomposition, single replacement, double replacement, and combustion reactions. Each type of reaction follows specific patterns in how molecules or ions interact with each other.

Understanding a Chemical Equation

The equation \(3\mathrm{NO}_2(g) + \mathrm{H}_2\mathrm{O}(l) \rightarrow 2\mathrm{HNO}_3(aq) + \mathrm{NO}(g)\) signifies that, in presence of water, nitrogen dioxide gas reacts to form nitric acid in aqueous solution and nitrogen monoxide gas. This gives insight into the reaction types, the states of matter involved and provides direct information on how to control a reaction, predict its products, and understand the transformation taking place at the molecular level. Chemical reactions are the core of understanding material changes in chemistry and have countless applications in real-world scenarios from manufacturing to environmental science.