Question

For each of the following unbalanced chemical equations, write the corresponding chemical statement. (a) \(\mathrm{S}_{8}+\mathrm{O}_{2} \longrightarrow \mathrm{SO}_{2}\) (b) \(\mathrm{CH}_{4}+\mathrm{O}_{2} \longrightarrow \mathrm{CO}_{2}+\mathrm{H}_{2} \mathrm{O}\) (c) \(\mathrm{N}_{2}+\mathrm{H}_{2} \longrightarrow \mathrm{NH}_{3}\) (d) \(\mathrm{P}_{4} \mathrm{O}_{10}+\mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{H}_{3} \mathrm{PO}_{4}\) (e) \(\mathrm{S}+\mathrm{HNO}_{3} \longrightarrow \mathrm{H}_{2} \mathrm{SO}_{4}+\mathrm{NO}_{2}+\mathrm{H}_{2} \mathrm{O}\)

Short answer

The balanced equations are: (a) \( \mathrm{S}_{8} + 8\mathrm{O}_{2} \rightarrow 8\mathrm{SO}_{2} \), (b) \( \mathrm{CH}_{4} + 2\mathrm{O}_{2} \rightarrow \mathrm{CO}_{2} + 2\mathrm{H}_{2}\mathrm{O} \), (c) \( \mathrm{N}_{2} + 3\mathrm{H}_{2} \rightarrow 2\mathrm{NH}_{3} \), (d) \( \mathrm{P}_{4} \mathrm{O}_{10} + 6\mathrm{H}_{2}\mathrm{O} \rightarrow 4\mathrm{H}_{3}\mathrm{PO}_{4} \), and (e) \( \mathrm{S} + 6\mathrm{HNO}_{3} \rightarrow \mathrm{H}_{2}\mathrm{SO}_{4} + 2\mathrm{NO}_{2} + 2\mathrm{H}_{2}\mathrm{O} \).

Step-by-step solution

Balance Equation (a)

For the equation \( \mathrm{S}_{8} + \mathrm{O}_{2} \rightarrow \mathrm{SO}_{2} \), we need to balance the sulfur and the oxygen atoms. There are 8 sulfur atoms on the left, so we need 8 \( \mathrm{SO}_{2} \) molecules on the right. Also, to balance the oxygen on both sides, we need 8 times 2 (since there are two oxygen atoms in each \( \mathrm{SO}_{2} \)) = 16 oxygen atoms in total, which means we need 8 \( \mathrm{O}_{2} \) molecules on the left. The balanced equation is: \( \mathrm{S}_{8} + 8\mathrm{O}_{2} \rightarrow 8\mathrm{SO}_{2} \).

Balance Equation (b)

For the equation \( \mathrm{CH}_{4} + \mathrm{O}_{2} \rightarrow \mathrm{CO}_{2} + \mathrm{H}_{2}\mathrm{O} \), we first balance the carbon atoms: 1 \( \mathrm{C} \) on each side. Next, balance the hydrogen atoms: 4 hydrogens on the left, so we need 2 \( \mathrm{H}_{2}\mathrm{O} \) on the right. Finally, balance the oxygen atoms: we have 4 oxygens from 2 \( \mathrm{CO}_{2} \) and 2 from \( \mathrm{H}_{2}\mathrm{O} \), needing 2 \( \mathrm{O}_{2} \) molecules (4 oxygens). The balanced equation is: \( \mathrm{CH}_{4} + 2\mathrm{O}_{2} \rightarrow \mathrm{CO}_{2} + 2\mathrm{H}_{2}\mathrm{O} \).

Balance Equation (c)

For \( \mathrm{N}_{2} + \mathrm{H}_{2} \rightarrow \mathrm{NH}_{3} \), balance nitrogen atoms first: we have 2 \( \mathrm{N} \) on the left, so we need 2 \( \mathrm{NH}_{3} \) on the right to get 2 nitrogens. Next, balance the hydrogen atoms: 2 \( \mathrm{NH}_{3} \) results in 6 hydrogens, so we need 3 \( \mathrm{H}_{2} \). The balanced equation is: \( \mathrm{N}_{2} + 3\mathrm{H}_{2} \rightarrow 2\mathrm{NH}_{3} \).

Balance Equation (d)

For \( \mathrm{P}_{4} \mathrm{O}_{10} + \mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{H}_{3} \mathrm{PO}_{4} \), first balance the phosphorus: 4 \( \mathrm{P} \) means we need 4 \( \mathrm{H}_{3}\mathrm{PO}_{4} \). To balance oxygen: we have 10 from \( \mathrm{P}_{4} \mathrm{O}_{10} \) and need 10 for the 4 \( \mathrm{H}_{3}\mathrm{PO}_{4} \). This already balances oxygen. Finally, for hydrogen, we need 6 \( \mathrm{H}_{2} \mathrm{O} \) to balance with 12 hydrogens in 4 \( \mathrm{H}_{3} \mathrm{PO}_{4} \). The balanced equation is: \( \mathrm{P}_{4} \mathrm{O}_{10} + 6\mathrm{H}_{2} \mathrm{O} \rightarrow 4\mathrm{H}_{3} \mathrm{PO}_{4} \).

Balance Equation (e)

For \( \mathrm{S} + \mathrm{HNO}_{3} \rightarrow \mathrm{H}_{2} \mathrm{SO}_{4} + \mathrm{NO}_{2} + \mathrm{H}_{2} \mathrm{O} \), balance the sulphur first: 1 sulfur on each side. Nitrogen is next: 2 \( \mathrm{HNO}_{3} \) provides 2 nitrogen atoms for 2 \( \mathrm{NO}_{2} \). For hydrogen, adjust to 2 \( \mathrm{H}_{2} \mathrm{O} \) to align total oxygens. This means balancing 8 oxygens, needing 6 oxygens from \( \mathrm{HNO}_{3} \), so 6 \( \mathrm{HNO}_{3} \) works. The balanced equation is: \( \mathrm{S} + 6\mathrm{HNO}_{3} \rightarrow \mathrm{H}_{2} \mathrm{SO}_{4} + 2\mathrm{NO}_{2} + 2\mathrm{H}_{2} \mathrm{O} \).

Key concepts

Chemical Reactions

Chemical reactions are the processes in which substances, known as reactants, are transformed into new substances, called products. This transformation involves the breaking and forming of chemical bonds, which results in the reorganization of atoms. It's important to note that during a chemical reaction, the mass of the reactants is conserved and equals the mass of the products. This is the essence of the Law of Conservation of Mass.
When observing a chemical reaction, certain clues can indicate that a reaction is taking place:

• Change in color
• Emission or absorption of heat
• Formation of a precipitate
• Emission of gas

Understanding these indicators can help identify the occurrence of a reaction, even for complex substances like those involving sulfur or methane. Mastery of these concepts is crucial for analyzing reactions in chemistry.

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It involves calculations based on balanced chemical equations to predict the proportions in which chemicals will react and the amounts of products that will be produced.
Stoichiometric calculations are essential in:

• Determining the amount of reactants needed
• Calculating the yield of a reaction
• Predicting the amounts of by-products

These calculations rely heavily on the concept of the mole, a fundamental unit in chemistry, which translates microscopic atomic measurements to macroscopic observable amounts. By using stoichiometry, one can efficiently use chemical substances without excess waste.

Chemical Equations

Chemical equations are symbolic representations of chemical reactions. They display the reactants, the products, and their relative proportions. For instance, the unbalanced reaction between elemental sulfur and oxygen yields sulfur dioxide, represented as: \[ \mathrm{S}_{8} + \mathrm{O}_{2} \rightarrow \mathrm{SO}_{2} \]
A balanced chemical equation ensures that the number of atoms of each element is the same on both sides of the equation, respecting the Law of Conservation of Mass. To balance a chemical equation:

• Start by balancing elements that appear in only one reactant and one product.
• Balance remaining elements, usually hydrogen and oxygen last due to their prevalence.
• Verify each element and make sure all coefficients are the smallest possible integers.

Balancing chemical equations is crucial for stoichiometric calculations and for understanding how different substances interact.

Sulfur Reactions

Sulfur reactions encompass a variety of chemical processes where sulfur atoms combine with other elements or compounds to form new products. A classic example is the reaction between sulfur and oxygen gas to form sulfur dioxide (\(\mathrm{S}_{8} + 8\mathrm{O}_{2} \rightarrow 8\mathrm{SO}_{2}\)), widely encountered in industrial processes and natural phenomena like volcanic eruptions.
Sulfur reactions are significant in fields such as:

• Industrial production of sulfuric acid (\(\mathrm{H}_{2}\mathrm{SO}_{4}\))
• Environmental science, due to their role in forming acid rain (\(\mathrm{H}_{2}\mathrm{SO}_{4}\) from sulfur dioxide)
• Biological systems, where sulfur is a vital element in amino acids

Understanding sulfur reactions is essential for managing industrial outputs and mitigating their environmental impacts.