The annual production of sulfur dioxide from burning coal and fossil fuels, auto exhaust, and other sources is about 26 million tons. The equation for the reaction is $$ \mathrm{S}(s)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{SO}_{2}(g) $$ How much sulfur (in tons), present in the original materials, would result in that quantity of \(\mathrm{SO}_{2} ?\)

Understanding chemical equations is fundamental to studying chemical reactions, as they succinctly represent the reactants, products, and their proportions to one another. A chemical equation uses chemical symbols and formulas to convey a reaction. For instance, in the given exercise, the balanced equation \( \mathrm{S}(s) + \mathrm{O}_{2}(g) \longrightarrow \mathrm{SO}_{2}(g) \) shows how sulfur (S) and oxygen (\(\mathrm{O}_{2}\)) react to form sulfur dioxide (\(\mathrm{SO}_{2}\)). Here, the (s) and (g) denote the physical states of the substances, solid and gas, respectively.

Each component's coefficient in a balanced equation indicates the molar proportion in which substances react or are produced. In our example, one mole of solid sulfur combines with one mole of gaseous oxygen to yield one mole of sulfur dioxide gas. Balancing equations is a crucial skill, as it ensures the law of conservation of mass is upheld, meaning the mass of reactants equals the mass of the products in a chemical reaction.

The molecular mass (or molecular weight) is the sum of the atomic masses of all atoms in a molecule, typically expressed in atomic mass units (amu). It's a vital concept in stoichiometry as it allows us to convert between amounts of substance in moles and mass.

For instance, sulfur dioxide (\(\mathrm{SO}_{2}\)) has a molecular mass calculated by adding the atomic mass of sulfur (32 amu) to the mass of two oxygen atoms (2 \times 16 amu), resulting in 64 amu. When dealing with larger quantities like tons, understanding molecular mass enables us to establish the relationship between the mass of different substances involved in a reaction. The atomic mass of elements such as sulfur can be found on the periodic table and is crucial for these calculations.

Sulfur dioxide (\(\mathrm{SO}_{2}\)) is a significant byproduct of burning sulfur-containing compounds, such as coal and fossil fuels. It plays a prominent role in environmental chemistry as it contributes to air pollution and acid rain formation.

In this context, quantifying the sulfur dioxide production and understanding its stoichiometry in reactions is essential for environmental monitoring and regulations. The production of sulfur dioxide from sulfur can be described through the balanced chemical equation previously mentioned, showcasing a straightforward 1:1 ratio in the production process.

Theoretical yield refers to the maximum amount of product that could be formed from a given amount of reactants in a chemical reaction under perfect conditions. It is essential for efficiency analysis in industrial processes.

The problem at hand involves a real-world application of theoretical yield, requiring us to calculate how much sulfur must be burned to yield 26 million tons of sulfur dioxide. By using the molecular weight ratio of sulfur to sulfur dioxide (0.5), we can determine the theoretical yield of sulfur necessary to produce the desired amount of \(\mathrm{SO}_{2}\). The calculation in our exercise shows that to produce 26 million tons of sulfur dioxide, we would theoretically need 13 million tons of sulfur.