Question

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 \(\mathrm{SO}_{2}\) ?

Short answer

13 million tons of sulfur is required.

Step-by-step solution

Understand the Chemical Reaction

The problem provides us with a chemical reaction: \(\mathrm{S}(s) + \mathrm{O}_{2}(g) \rightarrow \mathrm{SO}_{2}(g)\). Here, sulfur (S) combines with oxygen (\(\mathrm{O}_2\)) to produce sulfur dioxide (\(\mathrm{SO}_2\)). Our goal is to determine how much sulfur is needed to produce 26 million tons of \(\mathrm{SO}_2\).

Molar Mass Calculations

First, calculate the molar masses. The molar mass of sulfur (S) is approximately 32.07 g/mol. The molar mass of sulfur dioxide (\(\mathrm{SO}_2\)) is the sum of the molar masses of sulfur and oxygen: 32.07 g/mol (for S) + 2 × 16.00 g/mol (for each O) = 64.07 g/mol for \(\mathrm{SO}_2\).

Determine Moles of \(\mathrm{SO}_2\)

To find the amount of sulfur needed, we first need to determine the number of moles of \(\mathrm{SO}_2\) produced. Using the molar mass of \(\mathrm{SO}_2\), convert 26 million tons to grams (1 ton = 1,000,000 grams) and then to moles: \[\text{Moles of } \mathrm{SO}_2 = \frac{26,000,000 \times 1,000,000 \text{ grams}}{64.07 \text{ g/mol}}\]

Calculate Moles of Sulfur

Because the reaction shows that one mole of sulfur produces one mole of \(\mathrm{SO}_2\), the moles of sulfur needed are the same as the moles of \(\mathrm{SO}_2\) being produced. Thus, the calculated moles from the previous step are directly the moles of sulfur required.

Calculate Mass of Sulfur

Convert the moles of sulfur back to mass using its molar mass (32.07 g/mol): \[\text{Mass of sulfur} = \text{Moles of sulfur} \times 32.07 \text{ g/mol}\] Convert the result from grams to tons (1 ton = 1,000,000 grams).

Final Result

After performing the calculations, we find that approximately 13 million tons of sulfur are needed to produce 26 million tons of \(\mathrm{SO}_2\).

Key concepts

Chemical Reactions

Chemical reactions describe a process where substances, known as reactants, are transformed into different substances, called products. In the exercise provided, the reaction involves sulfur (\(\mathrm{S}(s)\)), which reacts with oxygen (\(\mathrm{O}_{2}(g)\)) to form sulfur dioxide (\(\mathrm{SO}_{2}(g)\)).This specific reaction is an example of a synthesis reaction, where two or more simple substances combine to form a single, more complex compound.Understanding chemical reactions is crucial as it allows us to predict the substances produced after a reaction and quantify the amounts involved.To represent chemical reactions, we use balanced chemical equations. These equations use symbols to denote the reactants and products, ensuring that the number of atoms for each element is the same on both sides of the equation.

Molar Mass

Molar mass is a vital concept in chemistry used to convert between the mass of a substance and the amount in moles. It refers to the mass of one mole of a given substance, measured in grams per mole (g/mol).For sulfur, the molar mass is approximately 32.07 g/mol. This means that one mole of sulfur weighs 32.07 grams. For sulfur dioxide, the molar mass is calculated by adding the molar masses of its constituent elements. Thus, \(\mathrm{SO}_2 = 32.07 \text{ g/mol(S)} + 2 \times 16.00 \text{ g/mol(O)} = 64.07 \text{ g/mol}\).Grasping molar mass is essential as it provides the bridge between the macroscopic scale, which we can measure, and the microscopic scale, the level of individual molecules, essential for stoichiometric calculations.

Sulfur Dioxide Production

Sulfur dioxide (\(\mathrm{SO}_2\)) is produced through several natural and industrial processes. In the problem context, it's generated from burning sulfur-containing fuels like coal and oil.This gas is significant in the atmosphere because it can lead to acid rain when combined with water vapor. Understanding its production is important to mitigate environmental impacts associated with its release.The production of \(\mathrm{SO}_2\) is closely tied to the stoichiometry of the reaction shown in the exercise. By knowing the balanced chemical equation, we can predict how much \(\mathrm{SO}_2\) will form from a given amount of sulfur. This is particularly useful in industrial applications where controlling emissions is crucial.

Mass Conversion

Mass conversion in chemistry refers to the process of converting mass from one unit to another or from mass to moles using molar mass. In this scenario, the task involves converting the produced \(\mathrm{SO}_2\) from tons to grams and further to moles.Here's a simple process breakdown:

• First, convert the known mass of \(\mathrm{SO}_2\) from tons to grams (\(1 \text{ ton} = 1,000,000 \text{ grams}\)).
• Next, use the molar mass to convert grams to moles by dividing the mass in grams by the molar mass (\(64.07 \text{ g/mol for } \mathrm{SO}_2\)).
• Finally, utilize the stoichiometry of the reaction to determine the amount of sulfur needed, as one mole of sulfur produces one mole of \(\mathrm{SO}_2\).

Mass conversion allows the understanding of relationships between reactants and products, crucial for practical and theoretical chemical applications.