Problem 65 - Chemistry The Science in Context

Question

Suppose 25 metric tons of coal that is \(3.0 \%\) sulfur by mass is burned at an electric power plant ( 1 metric ton \(=10^{3} \mathrm{kg}\) ). During combustion, the sulfur is converted into sulfur dioxide. How many tons of sulfur dioxide are produced?

Step-by-Step Solution

Answer

Question: Calculate the amount of sulfur dioxide produced when burning 25 metric tons of coal that is 3.0% sulfur by mass. Answer: To calculate the amount of sulfur dioxide produced, follow these steps: 1. Determine the mass of sulfur in the coal: mass_sulfur = (mass_coal) × (Percentage_sulfur) % 2. Convert mass of sulfur to moles: moles_sulfur = (mass_sulfur) / (molar_mass_sulfur) 3. Find the moles of sulfur dioxide produced: moles_sulfur_dioxide = moles_sulfur 4. Convert moles of sulfur dioxide back to mass: mass_sulfur_dioxide = (moles_sulfur_dioxide) * (molar_mass_sulfur_dioxide) 5. Convert mass of sulfur dioxide to metric tons: mass_sulfur_dioxide_metric_tons = mass_sulfur_dioxide / 1000 The mass of sulfur dioxide produced in metric tons will be the answer to the problem.

Step 1: Determine the amount of sulfur in the coal

Since the coal is given as 3.0% sulfur by mass, we can calculate the mass of sulfur in the 25 metric tons of coal: mass_sulfur = (mass_coal) × (Percentage_sulfur) % where mass_coal = 25 metric tons (and 1 metric ton \(=10^{3} \mathrm{kg}\) ) Percentage_sulfur = 3.0 %

Step 2: Convert mass of sulfur to moles

To convert the mass of sulfur to moles, we can use the molar mass of sulfur: moles_sulfur = (mass_sulfur) / (molar_mass_sulfur) where molar_mass_sulfur = 32.06 g/mol

Step 3: Find the moles of sulfur dioxide produced

When the sulfur in the coal is burned, it is converted into sulfur dioxide (SO₂). The balanced chemical equation for this reaction is given by: S + O₂ → SO₂ From the balanced equation, 1 mole of sulfur (S) will produce 1 mole of sulfur dioxide (SO₂). Therefore, the number of moles of sulfur dioxide produced is equal to the number of moles of sulfur: moles_sulfur_dioxide = moles_sulfur

Step 4: Convert moles of sulfur dioxide back to mass

To find the mass of sulfur dioxide produced, we can use the molar mass of sulfur dioxide: mass_sulfur_dioxide = (moles_sulfur_dioxide) * (molar_mass_sulfur_dioxide) where molar_mass_sulfur_dioxide = 64.06 g/mol (32.06 g/mol for S + 32.00 g/mol for O₂)

Step 5: Convert mass of sulfur dioxide to metric tons

Finally, to find the amount of sulfur dioxide produced in metric tons, we can convert the mass in grams to metric tons by dividing by 1000: mass_sulfur_dioxide_metric_tons = mass_sulfur_dioxide / 1000 The mass of sulfur dioxide produced in metric tons will be the answer to the problem.

Key Concepts

Understanding Chemical Reactions in Sulfur Dioxide Production

In the exercise, we deal with a type of chemical reaction that transforms sulfur from coal into sulfur dioxide, a gas. This reaction occurs when coal is burned in the presence of oxygen from the air. Chemical reactions are processes where substances interact to form new products. Here, the chemical formula is quite simple:- Sulfur (S) reacts with Oxygen (\( O_2 \)) to form Sulfur Dioxide (\( SO_2 \))The balanced chemical equation for this process is:\[ S + O_2 \rightarrow SO_2 \]This equation tells us that 1 mole of sulfur combines with 1 mole of oxygen to produce 1 mole of sulfur dioxide. Understanding the concept of balancing equations is crucial in chemistry as it ensures that the same amount of each element is present before and after a reaction, maintaining the law of conservation of mass. It is through this balance that we can predict how much product will form from a given amount of reactant.

Applying Stoichiometry to Find Product Quantities

Stoichiometry helps us relate the quantities of reactants and products in a chemical reaction based on the balanced chemical equation. In this exercise, we use stoichiometry to determine how much sulfur dioxide can be produced from the sulfur present in coal.Once we know the mass of sulfur, we can convert this into moles (\( \text{moles} \)), since stoichiometry calculations work with moles. The first step is finding the amount of sulfur, which is 3% of 25,000 kg coal (\( 25 \text{ metric tons} = 25,000 \text{ kg} \)). If you follow the equation:- Mass of sulfur (\( \text{kg} \)) = 25,000 kg × 0.03 = 750 kgThen, converting it into moles involves dividing by the molar mass:- \( \text{moles of sulfur} = \frac{750}{32.06} \text{ moles} \)With this calculation, stoichiometry tells us that 750 kg of sulfur reacts to form the exact same number of moles of sulfur dioxide (\( SO_2 \)).

How to Use Molar Mass for Conversion

Molar mass is a key concept which helps in converting between mass and moles. It is defined as the mass of one mole of a substance, with units typically in grams per mole (\( \text{g/mol} \)). In our exercise, understanding molar mass enables us to convert between the mass of sulfur or sulfur dioxide and their corresponding moles.- The molar mass of sulfur is 32.06 g/mol. This means one mole of sulfur weighs 32.06 grams. - For sulfur dioxide (\( SO_2 \)), its molar mass is the combined weight of its atoms: 32.06 g/mol for sulfur and 2 * 16.00 g/mol for oxygen, totaling 64.06 g/mol.When converting the calculated moles of sulfur to the mass of sulfur dioxide:\[ \text{mass of sulfur dioxide} = \text{moles} \times 64.06 \text{ g/mol} \]This calculation provides the weight of sulfur dioxide initially in grams, so further conversions are needed for ton units.

Mastering Unit Conversion for Real World Applications

Conversion of units is vital to solve problems efficiently in chemistry. In this example, the end goal is to express the produced sulfur dioxide in metric tons, rather than the more commonly used grams or kilograms. Initially, sulfur's quantity is provided in metric tons, which we are more familiar on a day-to-day basis. We know: - 1 metric ton = 1000 kilograms (kg). After finding the mass of sulfur dioxide in grams using the molar mass: - Convert grams to kilograms: Since 1 kg = 1000 grams, divide the amount in grams by 1000. - Then, kilograms to metric tons: Again, divide by 1000 because 1 metric ton = 1000 kg. These unit conversions ensure that chemical calculations align with practical, real-world quantities, allowing you to communicate results in units that make sense for large scale industrial processes like power production.