Problem 69 - Chemistry: Principles and Reactions

Question

A crude oil burned in electrical generating plants contains about \(1.2 \%\) sulfur by mass. When the oil burns, the sulfur forms sulfur dioxide gas: $$ \mathrm{S}(s)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{SO}_{2}(g) $$ How many liters of \(\mathrm{SO}_{2}(d=2.60 \mathrm{~g} / \mathrm{L})\) are produced when \(1.00 \times 10^{4} \mathrm{~kg}\) of oil burns at the same temperature and pressure?

Step-by-Step Solution

Answer

Answer: The volume of sulfur dioxide gas produced is approximately 9.23 x 10^4 L.

Step 1: Calculate the mass of sulfur in the crude oil

We are given that the percentage of sulfur in crude oil is \(1.2\%\) and the mass of crude oil burned is \(1.00\times10^4\,\text{kg}\). Multiply the mass of crude oil by the percentage of sulfur to find the mass of sulfur in the crude oil: $$\text{mass of sulfur} = (1.2\%) (1.00\times10^4\,\text{kg})$$.

Step 2: Calculate the mass of sulfur dioxide gas produced

From the balanced chemical equation, we know that 1 mole of sulfur reacts with 1 mole of oxygen to produce 1 mole of sulfur dioxide gas. Using the molar masses of sulfur (\(32.07\,\text{g/mol}\)) and sulfur dioxide (\(64.07\,\text{g/mol}\)), we can convert the mass of sulfur in the crude oil to the mass of sulfur dioxide produced: $$\frac{\text{mass of sulfur}}{32.07\,\text{g/mol}} = \frac{\text{mass of sulfur dioxide}}{64.07\,\text{g/mol}}$$.

Step 3: Calculate the volume of sulfur dioxide gas produced

We are given the density of sulfur dioxide gas (\(2.60\,\text{g/L}\)) and the mass of sulfur dioxide gas produced. We can calculate the volume of sulfur dioxide gas using its mass and density: $$\text{volume of }\mathrm{SO}_{2} = \frac{\text{mass of sulfur dioxide}}{2.60\,\text{g/L}}$$. Now, we can combine all the steps to find the volume of sulfur dioxide gas produced when \(1.00\times10^4\,\text{kg}\) of crude oil is burned. #Solution#

Step 1: Calculate the mass of sulfur in the crude oil

We need to calculate the mass of sulfur in the crude oil: $$\text{mass of sulfur} = (1.2\%) (1.00\times10^4\,\text{kg}) = 120\,\text{kg} = 1.20\times10^5\,\text{g}$$.

Step 2: Calculate the mass of sulfur dioxide gas produced

Now, we use the stoichiometry of the given chemical equation in terms of molar masses to convert the mass of sulfur to the mass of sulfur dioxide produced: $$\frac{\text{mass of sulfur}}{32.07\,\text{g/mol}} = \frac{\text{mass of sulfur dioxide}}{64.07\,\text{g/mol}}$$ $$\text{mass of sulfur dioxide} = \frac{1.20\times10^5\,\text{g} \times 64.07\,\text{g/mol}}{32.07\,\text{g/mol}} = 2.40\times10^5\,\text{g}$$.

Step 3: Calculate the volume of sulfur dioxide gas produced

Finally, we can calculate the volume of sulfur dioxide gas using its density: $$\text{volume of }\mathrm{SO}_{2} = \frac{\text{mass of sulfur dioxide}}{2.60\,\text{g/L}} = \frac{2.40\times10^5\,\text{g}}{2.60\,\text{g/L}} = 9.23\times10^4\,\text{L}$$. So, the volume of sulfur dioxide gas produced when \(1.00\times10^4\,\text{kg}\) of crude oil is burned at the same temperature and pressure is approximately \(9.23\times10^4\,\text{L}\).

Key Concepts

Chemical Reactions

Understanding chemical reactions is crucial in chemistry. A chemical reaction is a process where substances, known as reactants, are transformed into different substances, called products. In our example, when sulfur (\(\mathrm{S}(s)\)) reacts with oxygen (\(\mathrm{O}_2(g)\)), it forms sulfur dioxide (\(\mathrm{SO}_2(g)\)). This equation can be written as: \[\mathrm{S}(s) + \mathrm{O}_2(g) \longrightarrow \mathrm{SO}_2(g) \]This shows the transformation from reactants (sulfur and oxygen) to the product (sulfur dioxide). Notice how this reaction is balanced: one mole of sulfur reacts with one mole of oxygen gas to yield one mole of sulfur dioxide.

Balancing equations is essential to abide by the law of conservation of mass, which states that matter cannot be created or destroyed in a chemical reaction. The coefficients in the chemical equation provide a way to maintain equal numbers of each type of atom on both sides of the equation.

In stoichiometry, we use these balanced chemical equations to calculate the quantities of reactants and products involved. This ensures precise measurements for experiments and industrial processes.

Sulfur Dioxide

Sulfur dioxide, or \(\mathrm{SO}_2\)), is a significant molecule produced in various industrial processes, including the combustion of sulfur-rich fuels like crude oil. Sulfur dioxide is a colorless gas with a pungent odor, which can irritate the respiratory system when inhaled.

This compound plays a vital role in forming acid rain through atmospheric reactions with water vapor, leading to environmental issues. Hence, understanding and controlling \(\mathrm{SO}_2\) emissions is crucial for environmental protection.

Industrially, sulfur dioxide is used in the manufacture of sulfuric acid, which is one of the most critical chemicals in industrial applications. It's also used in the food industry as a preservative due to its antimicrobial properties. Thus, knowledge of its production and control is essential, especially given its dual roles in both benefit and harm.

Density of Gases

Density is a measure of how much mass is contained within a volume. When dealing with gases, this concept helps understand how much space a particular amount of gas will occupy under specified conditions.

The density of a gas is usually given in grams per liter (\(\text{g/L}\)). In our example, the density of sulfur dioxide is given as 2.60 \(\text{g/L}\). This means for every liter of sulfur dioxide gas, its mass is 2.60 grams.

To find the volume of a gas when its density and mass are known, use the formula:

\[\text{Volume} = \frac{\text{Mass}}{\text{Density}}\]This relationship helps predict and measure the behavior of gases under different conditions, which is particularly useful in applications like environmental engineering and the design of industrial systems. With accurate density and other related measurements, industries can optimize their processes, reduce waste, and lower emissions for better compliance with environmental regulations.