Problem 75 - 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 \(\mathrm{SO}_3\), about \(7.52 \times 10^{24}\) molecules, \(7.52 \times 10^{24}\) sulfur atoms, and \(2.26 \times 10^{25}\) oxygen atoms.

Step 1: Convert Mass to Moles

To find the moles of sulfur trioxide (\(\mathrm{SO}_3\)), we first need to use the mass formula: \(\text{moles} = \frac{\text{mass (g)}}{\text{molar mass}}\). The molar mass of sulfur trioxide is calculated as follows: \( \text{Molar mass of } \mathrm{SO}_3 = 32.07 \text{ g/mol (for S)} + 3 \times 16.00 \text{ g/mol (for O)} = 80.07 \text{ g/mol} \). Thus, \(1.00 \text{ kg} = 1000 \text{ g}\) of \(\mathrm{SO}_3\) is \(\frac{1000 \text{ g}}{80.07 \text{ g/mol}} \approx 12.49 \text{ moles}\).

Step 2: Calculate Number of Molecules

To find the number of molecules, use Avogadro's number (\(6.022 \times 10^{23}\)). Multiply the number of moles by Avogadro's number: \(12.49 \text{ moles} \times 6.022 \times 10^{23} \text{ molecules/mole} \approx 7.52 \times 10^{24} \text{ molecules}\).

Step 3: Find Number of Sulfur Atoms

Since each molecule of \(\mathrm{SO}_3\) contains one sulfur atom, the number of sulfur atoms is equal to the number of molecules: \(7.52 \times 10^{24} \text{ sulfur atoms}\).

Step 4: Find Number of Oxygen Atoms

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

Key Concepts

Moles to Molecules Conversion

When converting moles to molecules, we make use of a fundamental constant: Avogadro's number. This number tells us how many units — like atoms, ions, or molecules — are present in one mole of a substance.
In the case of sulfur trioxide ( SO_3 ), once you have calculated the moles, conversion to molecules is straightforward. Simply multiply the number of moles by Avogadro's number, which is approximately 6.022 imes 10^{23} molecules per mole.
For example, if you have 12.49 moles of SO_3 , it translates to approximately 7.52 imes 10^{24} molecules. This relationship is consistent across all molecular substances, making the mole-to-molecule conversion a cornerstone in chemistry.

Avogadro's Number

Avogadro's number is essential for chemists and students alike because it provides a link between the macroscopic world we can see and the microscopic world we cannot.
This number, 6.022 imes 10^{23} , represents the number of units in one mole of any substance and is named after the Italian scientist Amedeo Avogadro.
Whether you are dealing with SO_3 or any other compound, Avogadro's number allows us to determine the exact number of molecules, atoms, or ions we have when given a specific amount in moles.

• Crucial for connecting moles to particles.
• Widely used in calculations involving chemical reactions.
• Fundamental for understanding quantities in chemistry.

Molar Mass Calculation

The molar mass of a compound is critical for converting mass to moles. To find it, you add up the atomic masses of each element in the compound as listed on the periodic table.
For sulfur trioxide ( SO_3 ), the molar mass calculation involves adding the mass of one sulfur atom and three oxygen atoms:
\[ \text{Molar mass of } \mathrm{SO}_3 = 32.07 \text{ g/mol (for S)} + 3 \times 16.00 \text{ g/mol (for O)} = 80.07 \text{ g/mol}\].
This value allows us to convert grams to moles by dividing the mass of the sample by the molar mass. For instance, 1000 grams of SO_3 equates to 12.49 moles.
Understanding molar mass helps in accurately calculating amounts for reactions and solutions in chemistry.

Chemical Composition Analysis

Analyzing the chemical composition of a compound involves understanding the quantities of each type of atom present.
For sulfur trioxide ( SO_3 ), this means identifying how many sulfur and oxygen atoms are contained in a sample. Since each SO_3 molecule has one sulfur and three oxygen atoms, if you know the number of molecules, you can determine the number of each type of atom.
For example, with 7.52 imes 10^{24} SO_3 molecules, there are 7.52 imes 10^{24} sulfur atoms and 2.26 imes 10^{25} oxygen atoms. This analysis helps chemists understand the nature and behavior of compounds and provides insights into molecular interactions and reactions.