Introduction
In chemistry, the mole is the bridge between the microscopic world of atoms and molecules and the macroscopic world of grams that we can measure in a lab. Understanding how to relate mass to the number of particles is fundamental to solving problems in stoichiometry.
Understanding the Problem
We are asked to compare the number of molecules in 32 grams of Oxygen gas ($O_2$) versus 32 grams of Sulfur ($S$). To solve this, we must determine the number of moles present in each sample.
The Concept: Molar Mass
- Oxygen ($O_2$): The atomic mass of one Oxygen atom is approximately 16 g/mol. Since oxygen exists as a diatomic molecule ($O_2$), its molar mass is $16 \times 2 = 32 \text{ g/mol}$.
- Sulfur ($S$): The atomic mass of a Sulfur atom is approximately 32 g/mol. For standard calculations, unless specified as $S_8$, we treat it as monatomic $S$.
Step-by-Step Calculation
1. Oxygen ($O_2$)
- Given mass = 32 g
- Molar mass of $O_2$ = 32 g/mol
- Number of moles ($n$) = $\frac{\text{mass}}{\text{molar mass}} = \frac{32 \text{ g}}{32 \text{ g/mol}} = 1 \text{ mole}$.
- Since 1 mole contains $6.022 \times 10^{23}$ particles (Avogadro's constant), 32 g of $O_2$ contains $6.022 \times 10^{23}$ molecules.
2. Sulfur ($S$)
- Given mass = 32 g
- Atomic mass of $S$ = 32 g/mol
- Number of moles ($n$) = $\frac{32 \text{ g}}{32 \text{ g/mol}} = 1 \text{ mole}$.
- Since 1 mole of atoms contains $6.022 \times 10^{23}$ atoms, 32 g of Sulfur contains $6.022 \times 10^{23}$ atoms.
Conclusion
While both substances have the same mass (32 g) and the same number of moles (1 mole), it is important to note the nature of the substance. Oxygen exists as diatomic molecules ($O_2$), so 1 mole equals $6.022 \times 10^{23}$ molecules. Sulfur is typically treated as monatomic in this context, so 1 mole equals $6.022 \times 10^{23}$ atoms.
Therefore, 32 g of Sulfur contains $6.022 \times 10^{23}$ atoms.