Understanding the Concept of Molecules and Molar Mass

The number of molecules in a given sample of a substance is directly related to the number of moles of that substance. One mole of any substance contains Avogadro's number (approximately $\text{6.022} \times \text{10}^{23}$) of molecules.

To find the number of moles from a given mass, we use the formula:

$\text{Moles} = \frac{\text{Mass (in grams)}}{\text{Molar Mass (in grams per mole)}}$

Therefore, to find which sets contain the same number of molecules, we need to calculate the number of moles for each substance in each set and compare them. If the number of moles is the same, the number of molecules will also be the same.

Calculating Molar Mass of Substances

Let's determine the molar mass for each substance mentioned in the question:

• Oxygen gas ($\text{O}_2$): Atomic mass of Oxygen ($\text{O}$) is approximately 16 g/mol. Molar mass of $\text{O}_2$ is $2 \times 16 = 32$ g/mol.
• Sulfur dioxide ($\text{SO}_2$): Atomic mass of Sulfur ($\text{S}$) is approximately 32 g/mol. Molar mass of $\text{SO}_2$ is $32 + 2 \times 16 = 32 + 32 = 64$ g/mol.
• Carbon dioxide ($\text{CO}_2$): Atomic mass of Carbon ($\text{C}$) is approximately 12 g/mol. Molar mass of $\text{CO}_2$ is $12 + 2 \times 16 = 12 + 32 = 44$ g/mol.
• Nitrous oxide ($\text{N}_2\text{O}$): Atomic mass of Nitrogen ($\text{N}$) is approximately 14 g/mol. Molar mass of $\text{N}_2\text{O}$ is $2 \times 14 + 16 = 28 + 16 = 44$ g/mol.
• Ozone ($\text{O}_3$): Atomic mass of Oxygen ($\text{O}$) is approximately 16 g/mol. Molar mass of $\text{O}_3$ is $3 \times 16 = 48$ g/mol.

Analyzing Each Set

Now, let's calculate the number of moles (and thus compare the number of molecules) for each set:

Let's look at the results:

• Set A: 1 gram of $\text{O}_2$ and 2 grams of $\text{SO}_2$ both contain $\frac{1}{32}$ moles. This means they contain the same number of molecules.
• Set B: 1 gram of $\text{CO}_2$ and 1 gram of $\text{N}_2\text{O}$ both contain $\frac{1}{44}$ moles. This means they contain the same number of molecules.
• Set C: 1 gram of $\text{O}_2$ contains $\frac{1}{32}$ moles, while 1 gram of $\text{O}_3$ contains $\frac{1}{48}$ moles. These are different values, so they contain a different number of molecules.

Conclusion

Based on the calculations, sets A and B contain the same number of molecules, while set C does not. Therefore, the set containing the same number of molecules are A and B.