Problem 39 - Chemistry and Chemical Reactivity

Question

Sulfur trioxide, \(\mathrm{SO}_{3},\) is made industrially in enormous quantities by combining oxygen and sulfur dioxide, \(\mathrm{SO}_{2}\) What amount (moles) of \(\mathrm{SO}_{3}\) is represented by \(1.00 \mathrm{kg}\) of sulfur trioxide? How many molecules? How many sulfur atoms? How many oxygen atoms?

Step-by-Step Solution

Answer

12.49 moles of \(\text{SO}_3\), 7.52 x 10^24 molecules, 7.52 x 10^24 sulfur atoms, 2.26 x 10^25 oxygen atoms.

Step 1: Determine Molar Mass of SO3

First, calculate the molar mass of sulfur trioxide, \(\text{SO}_3\). The molar mass of sulfur (\(\text{S}\)) is approximately 32.07 g/mol, and the molar mass of oxygen (\(\text{O}\)) is approximately 16.00 g/mol. Since there are three oxygen atoms in \(\text{SO}_3\), the molar mass is calculated as: \[ \text{Molar mass of } \text{SO}_3 = \text{(1) } (32.07\,\text{g/mol}) + \text{(3) } (16.00\,\text{g/mol}) = 80.07\,\text{g/mol}. \]

Step 2: Convert Mass to Moles

Convert the given mass of \(\text{SO}_3\) to moles using the molar mass found in Step 1. We have 1.00 kg of \(\text{SO}_3\), which is equivalent to 1000 grams. Use the formula: \[ \text{moles of } \text{SO}_3 = \frac{1000\,\text{g}}{80.07\,\text{g/mol}}. \] This equals \(12.49\,\text{moles of } \text{SO}_3\).

Step 3: Calculate Number of Molecules Using Avogadro's Number

To find the number of molecules, multiply the moles of \(\text{SO}_3\) by Avogadro's number \(6.022 \times 10^{23}\,\text{molecules/mol}\): \[ \text{Number of molecules} = 12.49\,\text{moles} \times 6.022 \times 10^{23}\,\text{molecules/mol} = 7.52 \times 10^{24}\,\text{molecules}. \]

Step 4: Find Number of Sulfur Atoms

Each molecule of \(\text{SO}_3\) contains one sulfur atom. Therefore, the number of sulfur atoms is equal to the number of \(\text{SO}_3\) molecules, which is \(7.52 \times 10^{24}\,\text{atoms of S}\).

Step 5: Find Number of Oxygen Atoms

Each molecule of \(\text{SO}_3\) contains three oxygen atoms. Therefore, multiply the number of molecules by three: \[ \text{Number of oxygen atoms} = 3 \times 7.52 \times 10^{24} = 2.26 \times 10^{25}\,\text{atoms of O}. \]

Key Concepts

Molar Mass

Molar mass is a fundamental concept in stoichiometry, as it allows us to convert between mass and moles of a substance. Simply put, molar mass is the weight of one mole of a chemical compound. For sulfur trioxide, \(\text{SO}_3\), it is calculated by adding the atomic masses of all the atoms in the molecule. Sulfur has an atomic mass of approximately 32.07 g/mol, and oxygen has an atomic mass of about 16.00 g/mol. Since \(\text{SO}_3\) contains one sulfur and three oxygen atoms, its molar mass is computed as follows:

• 32.07 g/mol (for sulfur) + 3 × 16.00 g/mol (for oxygen)
• This adds up to a total molar mass of 80.07 g/mol for \(\text{SO}_3\)

Understanding molar mass is crucial in chemical calculations as it connects the mass of the substance with the number of moles, a bridge necessary for many calculations in chemistry.

Avogadro's Number

Avogadro's number is a key element in the world of chemical calculations. It is the number of units (atoms, molecules, etc.) in one mole of a substance. This number is an incredibly large value: \(6.022 \times 10^{23}\). This means that if you have one mole of any substance, you have \(6.022 \times 10^{23}\) units of it.

• It helps bridge the macroscopic scale that we can measure with scales and balances to the microscopic scale of atoms and molecules
• In this problem, it allows us to calculate the number of \(\text{SO}_3\) molecules by multiplying the number of moles by Avogadro's number

For instance, using the 12.49 moles of \(\text{SO}_3\) from the exercise, we find the number of molecules: \(12.49 \times 6.022 \times 10^{23} = 7.52 \times 10^{24}\) molecule units of \(\text{SO}_3\).

Chemical Calculation

Chemical calculations often involve converting between different units and understanding the relationships between substances in a reaction. This exercise demonstrated several fundamental calculations:

• Converting mass to moles using molar mass
• Using Avogadro's number to find the number of molecules
• Determining the number of atoms within molecules

Each type of chemical calculation builds on the others and requires both fundamental concepts, like molar mass and Avogadro's number, to perform accurately. It is essential to follow a logical step-by-step process to avoid errors. For example, to determine the number of oxygen atoms, you must first determine the number of \(\text{SO}_3\) molecules, which relies on accurately calculating the moles and using Avogadro's number.

Sulfur Trioxide

Sulfur trioxide, or \(\text{SO}_3\), is a significant industrial compound, used primarily for producing sulfuric acid. In terms of its molecular composition, \(\text{SO}_3\) contains one sulfur atom and three oxygen atoms:

• It can react with water to form sulfuric acid, \(\text{H}_2\text{SO}_4\), a vital industrial chemical
• The calculations in the exercise focus on quantifying the number of molecules and their constituent atoms in a given mass

Understanding the composition and reactions of \(\text{SO}_3\) is critical in industrial chemistry, environmental science, and the broader field of chemistry itself. By calculating moles, molecules, and atoms, chemists can predict and control reactions in industrial processes and laboratory settings.