Question

When coal is burned, the sulfur present in coal is converted to sulfur dioxide \(\left(\mathrm{SO}_{2}\right),\) which is responsible for the acid rain phenomenon: $$ \mathrm{S}(s)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{SO}_{2}(g) $$ If \(3.15 \mathrm{~kg}\) of S reacts with oxygen, calculate the volume of \(\mathrm{SO}_{2}\) gas (in mL) formed at \(30.5^{\circ} \mathrm{C}\) and \(1.04 \mathrm{~atm} .\)

Short answer

The volume of \(\text{SO}_2\) gas formed is approximately 2,378,450 mL.

Step-by-step solution

Convert Mass to Moles

First, convert the mass of sulfur to moles using its molar mass. The molar mass of sulfur (S) is approximately 32.07 g/mol. So, you need to convert 3.15 kg of sulfur to grams first. Then use the formula: \[ \text{moles of } S = \frac{\text{mass of } S}{\text{molar mass of } S} \] which results in: \[ \text{moles of } S = \frac{3150}{32.07} \approx 98.21 \text{ moles} \]

Use Stoichiometry to Find Moles of SO2

The balanced chemical equation shows that 1 mole of sulfur reacts with 1 mole of oxygen to produce 1 mole of sulfur dioxide. Therefore, \(\text{moles of SO}_2\) produced is equal to the moles of sulfur: \[ \text{moles of SO}_2 = 98.21 \text{ moles} \]

Apply Ideal Gas Law

Now, use the ideal gas law \( PV = nRT \) to find the volume of \(\text{SO}_2\). First, convert the temperature from Celsius to Kelvin: \[ T = 30.5 + 273.15 = 303.65 \text{ K} \]. Next, use \(R = 0.0821 \text{ L atm mol}^{-1}\text{ K}^{-1}\). Solve for volume \(V\): \[ V = \frac{nRT}{P} = \frac{(98.21)(0.0821)(303.65)}{1.04} \approx 2378.45 \text{ L} \]

Convert Volume to Milliliters

Finally, convert the volume in liters to milliliters by multiplying by 1000: \[ 2378.45 \text{ L} = 2378450 \text{ mL} \]

Key concepts

Stoichiometry

Stoichiometry is a fundamental concept in chemistry that helps us understand the quantitative relationships between reactants and products in a chemical reaction. It is based on the balanced chemical equation and the law of conservation of mass, which states that mass is neither created nor destroyed in a chemical reaction. This is crucial for predicting the amount of each substance involved.

In the context of our problem, stoichiometry allows us to use the balanced equation:

• Sulfur (S) + Oxygen ( O_2 ) → Sulfur Dioxide (SO_2)

With this equation, we know that 1 mole of sulfur reacts with 1 mole of oxygen to produce 1 mole of sulfur dioxide. This relationship is used to calculate how many moles of SO_2 are produced from a given amount of sulfur.

By understanding stoichiometry, you can determine the proportion of reactants required and ensure efficient use of resources in industrial processes.

Molar Mass

Molar mass is a concept that helps us convert between mass and moles, which are critical for solving chemical equations. It is defined as the mass of one mole of a substance, and its units are grams per mole (g/mol).

For example, sulfur (S) has a molar mass of approximately 32.07 g/mol. This tells you that one mole of sulfur weighs 32.07 grams. In a stoichiometric calculation, this information helps convert the mass of a substance into moles, which is a step demonstrated in our problem.

Given 3.15 kg of sulfur, we converted it into grams first (3150 grams) and then used the molar mass to find the number of moles involved:

• Moles of S = \( \frac{\text{mass of } S}{\text{molar mass of } S} = \frac{3150}{32.07} \approx 98.21 \text{ moles} \)

This conversion is essential for subsequent stoichiometric calculations.

Chemical Reactions

Chemical reactions are transformations where substances, known as reactants, convert into different substances, known as products. The process is represented by a chemical equation that is emblematic of the rearrangement of atoms.

In our exercise, the transformation of sulfur to sulfur dioxide is an example of a chemical reaction. The balanced equation:

• \( \text{S} + \text{O}_2 \rightarrow \text{SO}_2 \)

shows that sulfur reacts with oxygen to produce sulfur dioxide. This reaction is especially significant because SO_2 is a gas that contributes to air pollution and acidic precipitation, commonly known as acid rain.

Understanding chemical reactions and their equations allows chemists to predict the outcomes of reactant combinations and manage chemical processes effectively.

Sulfur Dioxide

Sulfur dioxide ( SO_2 ) is a colorless gas with a sharp odor. It is a significant air pollutant with adverse environmental and health impacts. This gas is primarily released by burning fossil fuels, like coal, containing sulfur, as demonstrated in our problem.

When sulfur dioxide is emitted into the atmosphere, it can lead to the formation of acid rain. Acid rain occurs when SO_2 interacts with water vapor to form sulfuric acid. This can damage ecosystems by lowering the pH of soil and water bodies, harming aquatic life, and degrading plant health.

From an industrial perspective, knowing the amount of SO_2 produced in a reaction is vital for controlling emissions and meeting environmental regulations. The Ideal Gas Law, used in our exercise, helps estimate the volume of SO_2 , which is critical for understanding its environmental footprint.