Problem 69 - Chemistry

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

Step-by-Step Solution

Answer

Therefore, it will take about 13 million tons of sulfur to produce 26 million tons of sulfur dioxide.

Step 1: Understand the chemical equation

In the balanced equation \(S(s) + O_{2}(g) \rightarrow SO_{2}(g)\), one mole of sulfur reacts with one mole of oxygen to produce one mole of sulfur dioxide.

Step 2: Convert known quantity to moles

It is known that the production of sulfur dioxide is 26 million tons per year. Using the molar mass of sulfur dioxide (approximately 64.066 g/mol) and the fact that 1 metric ton equals 1000000 g, the amount of sulfur dioxide in moles can be calculated using the formula \(Number of moles = mass (tons) * (1000000 \ g/1 ton) * (1 \ mole/64.066 g)\). Using this formula, the quantity of sulfur dioxide translates to approximately \(4.06*10^{8}\) moles.

Step 3: Use stoichiometric ratio to find quantity of sulfur

Since stoichiometry of the given equation shows a 1:1 ratio between sulfur and sulfur dioxide, the amount (in moles) of the sulfur needed is equal to the amount of sulfur dioxide produced. Hence, the quantity of sulfur required is also \(4.06*10^{8}\) moles.

Step 4: Convert moles of sulfur to tons

The molar mass of sulfur (approximately 32.066 g/mol) is used in conjunction with the calculated amount of sulfur (in moles) to find the sulfur's mass in grams. The formula used here is \(mass (g) = number of moles * molar mass (g/mole)\). The resulting number is then converted from grams to tons by dividing by 1000000. Using this method, the mass of sulfur that would result in the given quantity of sulfur dioxide is found to be approximately 13 million tons.

Key Concepts

Chemical Reaction

In the realm of chemistry, a chemical reaction is a process where substances, known as reactants, are transformed into different substances, called products. This transformation involves the breaking and forming of chemical bonds. In our specific exercise, we're looking at the reaction:

• Reactants: Sulfur (\(S(s)\)) and Oxygen (\(O_{2}(g)\))
• Product: Sulfur Dioxide (\(SO_{2}(g)\))

The above equation represents a balanced reaction, meaning that the number of each type of atom (like sulfur or oxygen) is the same on both sides of the equation. This balance is crucial for correctly calculating the amounts of reactants and products. In our case, one mole of sulfur reacts with one mole of oxygen gas to produce one mole of sulfur dioxide. This 1:1:1 mole ratio will be very useful when conducting calculations related to this reaction.

Sulfur Dioxide

Sulfur dioxide (\(SO_{2}\)) is a colorless gas with a penetrating, choking odor. It is released naturally by volcanic activity and combustion of sulfur-containing fuels such as coal and oil. It plays a role in environmental pollution and acid rain. In the context of this exercise, sulfur dioxide is the product of the given chemical reaction. Our task is to determine how much sulfur results in the production of 26 million tons of sulfur dioxide.To calculate this, we rely on the balanced chemical equation, which tells us that one mole of sulfur reacts to produce one mole of sulfur dioxide. By utilizing the stoichiometric calculations mentioned earlier, we can convert mass to moles and predict the mass of sulfur involved in producing a certain amount of sulfur dioxide.

Molar Mass Calculation

Understanding molar mass is key to inter-converting between mass and moles. The molar mass is simply the mass of one mole of a substance. Every element on the periodic table has a molar mass based on its atomic mass. For sulfur dioxide (\(SO_{2}\)), the molar mass is calculated by summing the atomic masses of sulfur and oxygen:

• Sulfur (S): approximately 32.066 g/mol
• Oxygen (O): approximately 15.999 g/mol
  • Sulfur Dioxide (\(SO_{2}\)): Unlike water (H\(_2\)O), sulfur dioxide (\(SO_{2}\)) consists of one sulfur atom and two oxygen atoms.

Therefore, the molar mass of sulfur dioxide is 32.066 g/mol + (2 * 15.999 g/mol) = 64.066 g/mol. Calculating the molar mass correctly helps us accurately perform further conversions from mass to moles or vice versa.

Conversion Between Moles and Mass

Conversion between moles and mass is an essential skill in stoichiometry.When we know the mass of a substance, we can convert it to moles using the relationship:\[\text{moles} = \frac{\text{mass (grams)}}{\text{molar mass (g/mol)}}\]Conversely, to convert moles back to mass:\[\text{mass} (g) = \text{moles} \times \text{molar mass (g/mol)}\]In our chemical reaction exercise, we're focused on converting between the mass of sulfur and the mass of sulfur dioxide. Given that 26 million tons of sulfur dioxide are produced, we first convert this mass to moles using the molar mass of sulfur dioxide (\(64.066 \, \text{g/mol}\)).Once we know the number of moles of sulfur dioxide, we use the stoichiometric 1:1 mole ratio to determine the corresponding moles of sulfur used. Finally, using sulfur’s molar mass (\(32.066 \, \text{g/mol}\)), we convert sulfur moles back to mass, giving us the sulfur's mass required in tons.